# WORKSHEET NEW COUNTDOWN SECOND EDITION OXFORD CLASS 4

NOTES/ SOLVED EXERCISES /WORKSHEET NEW COUNTDOWN SECOND EDITION OXFORD CLASS / GRADE / LEVEL 4
PART ONE:
NUMBERS
5-Digit Numbers: Notation
5-Digit Numbers: Place Value
Introducing One Lakh
One Lakh Equals One Hundred Thousand
International Place Value: 6-Digit Numbers 1-10

THE FOUR OPERATIONS
5-Digit second 6-Digit Numbers
Subtraction: 5-Digit second 6-Digit Numbers
Welcome to Multiplication Hall!
Multiplication
Multiplication by IO second Its Multiples
Multiplying by 2-Digit Numbers
Multiplication: Some New Words
Multiplicands of 4 Digits second Multipliers of 3 Digits
Review
Multiplication second Division with
Bigger Numbers
Division with Bigger Numbers
Divisors with 2 Digits
Dividends with 4 Digits
Multiply to Check!
Using Division in Word Problems
Dividing by I0 second Its Multiples
Review 11-33
THE UNITARY METHOD
Thinking second Solving
Remembering the Calendar
34-35
TIME
Time
Using Timetables
Playing with Time: Conversion
Conversion: Minutes second Seconds
Playing with Time: Word Problems
Review 36-45
PART TWO
LCM SECOND HCF
Common Multiples: The Venn Diagram 47
Lowest Common Multiple (LCM) 48
Introducing Factors 49
More about Factors: Common Factors second HCF 50
Co-Prime Numbers 51
Prime Numbers second Composite Numbers 53
Prime Factorization 55
Tests of Divisibility 56
The LCM second HCF of Larger Numbers:
The Division Method 57
Review 59 46-60
FRACTIONS
Remembering Fractions 61
Reducing Equivalent Fractions 63
Remembering Like second Unlike Fractions 65
Proper second Improper Fractions 66
Mixed Numbers second Improper Fractions 67
Fractions second Division 70
Comparing Fractions:
The Common Denominator 71
Subtraction of Fractions 75
Subtraction of Mixed Numbers 76
Review 78 61-79
AREA SECOND PERIMETER
More about Shapes: Surface second Area 80
Comparison of Areas 81
Area: Square Centimeters 84
Area second Perimeter 85
Review 88 80-88
PART THREE
DECIMALS
Number Line, Decimal Point, second the Four Operations 92
Tenths second Hundredths Q6
Decimals second Fractions 99
Decimals second Money I00
Decimals second Money: The Four Operations 101
Decimals second Money: More about Bills
Decimals: Metres second Centimetres
Decimals second Metres: The Four Operations
Decimal Fun Page!
Decimals: Tenths, Hundredths, second Thousandths
Tenths, Hundredths, second Thousandths
Review
89-111
MEASUREMENT
Decimals second Measurement
Sid’s History of the Metric System
Decimals second Measurement: The Metric System
The Metric System
Metric Word Problems
Review 112-120
GEOMETRY
Looking at Lines
Making Angles
Finding the Right Angle!
Angles, Degrees, second the Protractor
Using the Protractor
Triangles second Their Angles
Angles in Triangle
Perpendicular Line 121-137
GRAPHS
Column Graphs
The Pie Chart
Review of the Year
Meet Mick, Mandy, Meg, Mani, second Mona
Worksheets
Maths Lab Activities 138-155

PAGE:1
1.MAGIC SQUARES
NOW COMPLETE THESE MAGIC SQUARES.
A 7 8 B 6 14
2 6 10 8
4 5 2

c 15 22 D 14 13 18
18 15
21 12
A 7 8 3 B 6 4 14
2 6 10 16 8 0
9 4 5 2 12 10

c 15 22 17 D 14 13 18
20 18 16 19 15 11
19 14 21 12 17 16

a. 100 less than 40188
b. 28 +——————– = 45
c. Roman number tor 6 s
d. 3 hundreds minus 7 tens
e. 81- ——————-=22
f. Write in numerals: seven thousand second nine
g. 2 hour = minutes
h. 3 years = ——————- months
i. Roman number for 24
j. Write the next number: 130, 1 10, 90, ——————
k- 7/8 – 4/8
l. Write the missing numbers: I636, 1639, ——————, 1645 —1648—————-
m. The total cost of three ice creams at Rs 12 each.

n. What is the cost of each pencil if 6 pencils cost Rs 36.60?
a.3918 b.17 c.vi d.300-70=230 e.59 f.7009 g.45 h.36 i. XXVI j.70 k.3/8 l.1642,648

PAGE:2
3. WRITE IN WORDS.

a. 4957
ANSWERS:: four thousands nine hundred and fifty seven.
b. 5012
C. 7408
ANSWERS:: Seven thousands four hundred and eight.
d. 3001

4. WRITE IN NUMBERS.
a. nine thousands and nine
b. five thousands second twenty-four
c. seven thousands nine hundred second thirty-seven

5. WRITE THE MISSING NUMBERS.
a. ——————- -8=I2-5
b. 450+——————-=910
c. 580 ÷ 10=——————-
d. 325cm=,m——————-cm
e. 12 x ——————-=6 x 8
f. 3660 ml =————L—————–ML
g. 9kg 7g=———-g
h. 9m3cm=——–cm
i. 1h 45 min =————min
j. 600÷ 10 =10 x—————–
ANSWERS:S: (a-15)(b-460)(c-58)(d-3m 25cm)(e-4)(f-3 L 660 ML)(g-9007)(h-903)(i-105)(j-6)
6. GUESS WHICH LINE IS LONGER. THEN MEASURE EACH LINE SECOND WRITE THE LENGTHS IN CM.
a. ————————–

b. >—————————-<

7. DRAW THESE LINE SEGMENTS.
a. AB=4 cm b. PQ=14cm

a. If I0 books cost Rs I5-40, how much does I book cost?

b. If Rehan saves Rs. 275 every month, how much does he save in a year?

c. If 4 boxes of equal weight weigh I kg 792 g altogether, how much does one box weigh?

d. What is the largest number these numerals: 3, Q, 0, 8?

a. cost of 10 books = Rs.1540 so cost of 1 book = 1540 ÷ 10 = Rs.154
b. amount which Rehan save 5 every month = Rs.775 so in a year , amount saved = 12 × 775 = Rs.9300
c. numbers of boxes 4 total weight of 4 boxes 1 kg 792g

0kg 448g
4 1 7 9 2

0
1 7
1 6
1 9
1 6
3 2
3 2
0

9- COPY AND MULTIPLY.
a. 197
X 24 b. 248
X 33

1 9 7
× 2 4
7 8 8
+ 3 9 4
= 4 , 7 2 8
248
× 33
744
744
8,184

10- COPY AND DIVIDE.
a. 6/476

0 7 9
6 4 7 6
0
4 7
4 2
5 6
5 4
2
b. 8/592

0 7 4
8 5 9 2
0
5 9
5 6
3 2
3 2
0
C. 5/405

0 8 1
5 4 0 5
0
4 0
4 0
0 5
5
0
a. 2/3+ 1/3
SOLUTION:
2/3+ 1/3 = 3/3 =1
b. 9/10+ 1/10
SOLUTION:
. 9/10+ 1/10 =10/10 =1

c. 4/7 + 2/7
SOLUTION:
4/7 + 2/7 =6/7

d. 5/11 + 2/11
SOLUTION:
5/11 + 2/11=2/11
12- WRITE FRACTIONS IN THE BLANKS.
a. 2/(3 ) ,4/6 ,6/9 ,———-,————,12/18
b. 1/5 ,2/10 , 3/15 , ———,———–6/30

a. 2/(3 ) ,4/6 ,6/9 ,8/12,10/15,12/18
b. 1/5 ,2/10 , 3/15 ,4/20,5/25,6/30

PAGE: 3
13- WRITE NUMBERS IN THE BLANKS.
a. 3779, 3789, ————–,————-3819

b. 5702, 5802 , ————-,————–6102

c. 1101 , 2101 ,—————, ———————, ——————–

a. 3779, 3789, 3799,3809,3819

b. 5702, 5802 , 5902, 6002, 6102

c. 1101 , 2101 , 3101, 4101, 5101
14- COUNT BACKWARDS SECOND WRITE NUMBERS IN THE BLANKS.
984I, 9831, ———, ————-, 9801
4394, 4294, ————, 4094,
6530, 6525,—————,—————–, 6510
7619, 7519, ——————,—————–,—————
984I, 9831, 9821, 9811, 9801
4394, 4294, 4194, 4094, 3994
6530, 6525, 6520, 6515, 6510
7619, 7519, 7419, 7319, 7219

15- WRITE THE PLACE VALUE OF 7 IN EACH OF THESE NUMBERS.
a. 675
b. 5687
c. 7002
a. PLACE VALUE OF 7 IN 675 = hundredth
b. PLACE VALUE OF 7 IN 5687= unit
c. PLACE VALUE OF 7 IN 7002= ten

16- WRITE IN EXPANDED FORM.
a. 5692
b. 8601
c. 4029
d. 1001
e. 3728
f. 6907
a. 5692 =5000+600+90+2
b. 8601=8000+600+0+1
c. 4029=4000+0+20+9
d. 1001=1000+0+0+1
e. 3728 =3000+700+20+8
f. 6907=6000+900+0+7

17- WRITE:
a. The largest 2-digit number

b. The smallest 3-digit number

c. The largest 3-digit number

d. The smallest 4-digit number

18- Using the digits 2, 5, 6, and 9, write as many 4-digit numbers as you can. Which is the largest number you can write? Which is the smallest?
2569,2596,2559,2695,2956,2965,5269,5296,5629,5692,9652,9625, and so on————
largest number=2569
smallest number=9652

19- WRITE IN EXPANDED FORM.
7094………7000+0+90+4
a.8695
b. 3292
c. 9351
d. 5064
e. 3195
f. 7676
a.8695=8000+600+90+5
b. 3292=3000+200+90+2
c. 9351= 9000+300+50+1
d. 5064 = 5000+0+60+4
e. 3195 = 3000+100+90+5
f. 7676=7000+600+70+6

20- Using the digits I, 7, 3, second 8, write as many 4-digit numbers as you can, making sure that each ’ number is placed in periods.
Then add the Largest number to the smallest number.
1378, 1387, 3178, 3187, 1873, 1837, 1738, 1783,3817,3871 ,8731,8713 ——- largest number=8731
smallest number=1378
sum of largest number and smallest number= 8731+1378= 10109

PAGE: 4 5-DIGIT NUMBERS: NOTATION
1- WRITE THE NUMBER NAMES ( TWELVE THOUSAND 12,000)
a. 20,000

b. 80,000

c. 14,000

d. 57,000

TWENTY THOUSAND
EIGHTY THOUSAND
FOURTEEN THOUSAND
FIFTY- SEVEN THOUSAND

2-WRITE THE NUMBER, PLACING THE VCOMMA CORRECTLY.
eleven thousands . …………. . 11,000
eighteen thousands……………………….
twenty-three thousands ……………….
forty-two thousands …………………….
seventy thousands. ……………………
fifty thousands ……………………………….
forty-four thousands …………………….
ANSWERS: a. 18,000 b. 23,000 c. 42,000 d. 70,000 e. 50,000 f. 44,000

3. PLACE THESE NUMBERS IN PERIODS SECOND WRITE THEIR NAMES.
84,067 . . . eighty-four thousand and sixty-seven
a. 23 124
b. 53400
c.49,639
d. 80964
e. 15 503
f. 12550

a. 23 124= twenty – three thousand, one hundred and twenty-four
b. 53400= fifty- three thousand and four hundred
c.49,639= forty-nine thousand , six hundred and thirty-nine
d. 80964= eighty thousand , nine hundred and sixty-four
e. 15 503= fifteen thousand , five hundred and three
f. 12550= twelve thousand , five hundred and fifty

4. WRITE THE NUMBER, PLACING THE COMMA CORRECTLY.
* forty-three thousands, two hundred and ten 43,210

eighty-one thousands, six hundred second forty-seven
nineteen thousands second twenty-five.
Seventy thousands one hundred second sixteen
ANSWERS: a. 81,647 b. 19,025 c. 70,116

PAGE: 5
5-DIGIT NUMBERS: PLACE VALUE

1- WRITE THE VALUE OF THE CIRCLED DIGIT.
48397 —-9 tens or 90
a. 30,029
b. 27,090
c.17,00 5
d. 31,561
e.94617
f. 84,069

ANSWERS: a. 0 hundred b. 20000 c. 0 ten d. 1 unit e. 6 hundred f. 4000s

2- WRITE THE NUMBERS THAT MATCH THESE EXPANDED FORMS.
30,000 + 5000 + 800 + 20 + 6 …….35,826
90,000 + 2000 + 400 + 30 + 0
80,000 + 40 + 600 + 40+2
50,000+ 0+700+ 0+3
40,000 + 3000 + I00 + 0 + 0
70,000 + 0 + 0 +020 + 7
20,000 + 4000 + 300- + 0 + 9
60,000 + 8000 + 0 + 80 + 8

ANSWERS: a. 92,430 b. 80,642 c. 50,703 d. 43,100 e. 70,027 f. 24,309 g. 68,088

3- WRITE THESE NUMBERS IN EXPANDED FORM.
69,504—– 60,000 + 9000 +500 + 0 + 4
a.71,623
b. 82,590
c. 60,902
d. 14,075
e. 51,029
f. 10,503
g.40,505
h. 34,650
i.99,099
j. 12,470
a. 70000 + 1000 + 600 + 20 + 3
b. 80,000 + 2000 + 500 + 90 + 0
c. 60000 + 0 + 900 + 0 + 2
d.10000 + 4000 + 0 + 70 + 5
e. 50000 + 1000 + 0 + 20 + 9
f. 10000 + 0 + 500 + 00 +3
g. 40000 + 0 + 500 + 0 + 5
h. 30000 + 4000 + 600 + 50 + 0
i. 90000 + 9000 + 0 + 90 + 9
j. 10000 + 2000 + 400 + 70 + 0

4- WRITE THE PREDECESSOR OF EACH NUMBER.
56,800 ——56,700
a.85,487
b. 64,600
c. 16,0101
d. 32,4803
e.51,300
f. 99,000
g. 48290
h. 80,000
a.85,486
b. 64,599
c. 16,009
d. 32,479
e.51,299
f. 98,999
g. 48289
h. 79,999

5- WRITE THE SUCCESSOR OF NUMBER.
30 999—— 31000
a. 42,489
b. 90,999
c. 70,609
d. 19,009
e.18,099
f. 10,000
g. 23,999
h.37,999

a. 42,490
b. 91000
c. 70,610
d. 19,010
e.18,100
f. 10,001
g. 24,000
h.38,000

6- FILL IN <,>, OR =
47,204
80, 100
23,020
19,758
94,065
82, 1 93
34,201
10, 010 42,704
80, 11 0
23,002
1 9,758
94,605
81,193
43,203
10,110

ANSWERS: a. > b.< c. > d.= e.< f. > g.< h. <

PAGE: 6
INTRODUCING 0NE LAKH
1- WRITE THE NUMBER NAMES. (2,00,000 two lakh)
a.4,00,000
b. 7,00,000
c. 5,00,000
d. H,00,000
a. four lakhs b. seven lakhs c. five lakhs d. eleven lakhs

2- WRITE THE NUMBER, PLACING YOUR COMMAS CORRECTLY. (five Lakh 5,00,000)
a. three Lakh
b. nine lakh
c. one Lakh
d. twelve Lakh
a. 3,00,000 b. 9,00,000 c. 1,00,000 d. 12,00,000

3- ADD THE MISSING COMMAS (405962 —- 4,05,962)
a. 340816
b. 290062
c. 900700
d. 3010 10
a. 3,40,816 b. 2,90,062 c. 9,00,700 d. 3,01,010
4- PLACE THESE 6-DIGIT NUMBERS IN PERIODS SECOND WRITE THEIR NAMES.
4,60,293 four lakh, sixty thousand , two hundred second ninety-three
a. 5 1 0937
b. 906403
c.19602 1
d. 240682
a. 5 1 0937 = Five lakhs, Vten thousand, nine hundred and thirty seven.
b. 906403= Nine lakh, six thousand, four hundred and three
c.19602 1= One lakh ninety six thousand and twenty-one.
d. 240682= Two Iakh forty thousand six hundred and eighty two.

5- WRITE THE NUMBER, PLACING YOUR COMMAS CORRECTLY.
three Lakh, eighty-two thousand second twenty-seven 3,82,027
a. five Lakh, nineteen V thousand, three hundred second two
b. nine lakh, two thousand, five hundred second sixteen
c. four Lakh, nine hundred second fifty-one
a. 5,19,302 b. 9,02,516 c. 4,00,951

PAGE: 7

ONE LAKH EQUALS ONE HUNDRED THOUSAND
1- PLACE THESE 6-DIGIT NUMBERS IN PENODS, FHSTH1THE PAKISTANI WAG SECOND THEN IN THE INTERNATIONAL WAG. 639243 (I) 6,39,243 (2) 639,243
a. 854020
b. 405300
c. 703164
d. 162802
e. 300698
f. 820036
a. 8,54,020 – 854,020 b. 4,05,300 – 405,300c. 7,03,164 – 703,164 d.1,62,802 – 162,802 e.3,00,698 – 300,698 f. 8,20,036

2- WRITE THESE NUMBERS ACCORDING TO INTERNATIONAL PERIODS. 6,01,584 601,584
a. 7,53,028
b. 2,70,042
c. 4,00,028
d. 9,09,510
a. 753,028
b. 270,042
c. 400,028
d. 909,510

3- CHANGE THESE NUMBERS ACCORDING TO PAKISTANI PERIODS. 758,06 I 7,58,06 I
a. 104,695
b. 450,104
c. 500,629
d. 642,003
a. 1,04,695
b. 4,50,104
c. 5,00,629
d. 6,42,003

4- WRITE THE NUMBER NAMES 638,342 SIX HUNDRED SECOND THIRTY-EIGHT THOUSAND, NINE HUNDRED SECOND FORTY-TWO
a. 422,3 1 8

b. 909,999

c. 351,602

d. 500,384

a- Four hundred and twenty-two thousand, three hundred and eighteen.
b- Nine hundred and nine thousand, nine hundred and ninety.-nine.
c- Three hundred and fifty-one thousand, six hundred and two.
d- Five hundred thousand, three’ hundred and eighty-four.

5- WRITE THE NUMBERS, PLACING YOUR COMMAS CORRECTLG. FIVE HUNDRED SECOND TWENTG THOUSAND, SIX HUNDRED SECOND THIRTY-ONE 520,631
a. four hundred second thirty-eight thousand, one hundred second eighteen

b. six hundred second ninety-nine thousand, five hundred second seventy

a. 4,38,118 b. 6,99,570
PAGE: 8
INTERNATIONAL PLACE VALUE: 6-DIGIT NUMBERS
1- WRITE THE VALUE OF THE CIRCLED DIGIT.
54,629 —– five hundred thousand or 500,000
a. 629,30 I
b. 205,4 83
c. 730, 598
d. 800,269
a. 629,30 I = nine thousand
b. 205,4 83= four thousand
c. 730, 598 = seven thousand
d. 800,269= eight thousand

2- WRITE THE NUMBERS THAT MATCH THESE EXPANDED FORMS
600,000 + 20,000 + 8000 + 400 + 60 + 0 —– 628,460
700,000 + 50,000 +1000+ 300 + 0 + 8
100,000 + 90,000 +0+ 200 + 90 + 3
500,000 + 70,000 +800+ 0 + 50 + 2
400,000 + 0 +9000+ 600 + 80 + 5
200,000 + 60,000 + 700 + 40 + 0
300,000 + 10,000 +5000+ I00 + 0 + 6
300,000 + 10,000 +5000+ 900 + 90 + 9
800,000 + 70,000 + I00 + 70,000 +2000+100+70+ 9
(a-751308)(b-190293)(c-578052)(d-409685)(e-260740)(f-315106)(g-999999)(h-872172)

3- WRITE THESE NUMBERS IN EXPANDED FORM.
691,053——— 600,000 + 90,000 + 1000+0+50+3
a. 752,119
b. 120,640
c. 804,623
d. 358,037
e.950,85 1
f. 606,666
a. 752,119=700,000+50,000+2,000+100+10+9
b. 120,640=100,000+20,000+0+600+40+0
c. 804,623 =800,000+0+4,000+600+20+3
d. 358,037=300,000+50,000+8,000+0+30+7
e.950,85 1=900,000+50,000+0+800+50+1
f. 606,666=600,000+0+6,000+600+60+6

4-WRITE THE SUCCESSOR OF EACH NUMBER. 151,999 152,000
a. 484,303
b. 399,998
c. 502,999
d. 246, 1 89
a. 484,304
b. 399,999
c. 503,000
d. 246, 1 90

5- WRITE THE PREDECESSOR OF EACH NUMBER. 380,000 —— 379,999
a. 963,380
b. 102, 100
c. 593,000
d. 899,090
a. 963,379
b. 102, 099
c. 592,999
d. 899,089

6-WRITE IN NUMBERS.
seven hundred second fifty thousand second sixty ——–750,060 ,
a. one hundred second forty-eight thousand, four hundred second twelve
b. two hundred second thirty thousand second six
c. six hundred second two thousand, five hundred second seventy
a. 148,412
b. 230,006
c. 602,570

PAGE: 9

INTERNATIONAL PLACE VALUE: 6-DIGIT NUMBERS
7- FIND THE VALUE OF THESE EXPANDED FORMS.
600,000 + 30,000 + 7000 + 50 + 7 —— 637,057
a. 100,000 + 20,000 + 5000 + 400 + 20 + 6
b. 200,000 + 40,000 + 7000 + 300 + 7
(a-125,426)(b-247,307)

8- WRITE NUMBERS IN THE BLANKS.
444,4q6 = 400,000 + —————-+4000+400+—-+6
40,000 and 90
a. 326,41 1 = ————+ 20,000 + 6000 + ————+ 10 + 1
b. 560,312 = ————– + 60,000 + 3000 +————– + ————–
c. 843,029 = 800,000 +——————— +3000 +—————– + 9
d. 305,699 = 300,000 + ——————– + _ + 90 + 9
e. 999,999=————– + ————— + —————- +900 + ————– + ———
f. 480,003 = ————- + 80,000 + —————-
(a-300,000 – 400)
(b-500,000 – 10 – 2)
(c- 40,000 – 20 )
(d- 5000 – 600 )
(e-900,000 – 90,000 – 9000 – 90 – 9)
(f- 400,000 – 3)
9- FILL IN < , > OR = ( 240,000 > 24,000 )
870, 500 ———–807,500
12 1,500 ———–121,500
199,584———–189,589
158,603 ———– 158,603
305,001———– 305,001
(a- >)(b- =)(c – >)(d- >)(e- =)

10- ARRANGE IN ASCENDING ORDER
140,040 ; 104,440 ; 114,004 ; 4 1 0,440
…I04,440 ; 114,004 ; 140,040 ; 4 I 0,440
a. 502,398; 205,938; 520,480 ; 501,695
b. 462,591; 642,589; 458,431;824,951 ; 824,941
c. 10,000; 100,899; 101,010 ; I00,901; 101,100
d. 384,029; 348,290; 388,420 ; 346,999
e. I25,456; I24,546; 142,456 ; 124,654 ; 125,556

a. 205, 938; 501,695; 502,398; 520,480
b. 458,431; 62,591; 642,589; 824,941; 824,951
c. 100,899; 100,901; 101,000; 101,010; 101,100
d. 346,999; 348,290; 384, 029; 388, 429
e. 124,546;124,654; 125,456;125,556;142,456.

PAGE: 10
5-DIGIT & 6-DIGIT NUMBERS

1- COUNTING IN HUNDREDS, WRITE NUMBERS IN THE BLANKS.
97,000;————— ; ———; ——-
97,100; 97,200; Q7,300
102,700; 102,800; ————–; —————–
385,800; _________ ; _______ ; 386,100
422,900; _________ ; _________ ; _______ ;
909,800; ————— ; —————; 910,100; —————-
a. 102,900; 103,000
b. 385,900; 386,000
c. 423,000; 423,100; 423,200 ‘
d. 909,900; 910,000; 910,200

2- COUNTING IN THOUSANDS, WRITE NUMBERS IN THE BLANKS.
98,000;———— ;—————; 101,000 —————-99, 000; 100,000
79,800; 80,800; ————–; 82,800
1144,250; ———–; 116,250; 0
506,499; ———–;—————-; , 50Q,LIQQ;

81,800
b.115,250,117,250
c. 507,499, 500,499; 510,499

3- CIRCLE THE LARGEST NUMBER. 602,189; 620,198; 620,199
405,613; 406,513; 401,563
739,468; 739,648; 739,486
249,406; 249,946; 249,046
101,321; 110,123; 111,032
850,050; 805,550; 850,005
ANSWERS: (a-406,513 ) (b-739,648 ) (c-249,946 ) (d-111,032 ) (e-850,050 )

4- ARRANGE IN” DESCENDING ORDER.
584,622; 5Q4,266; 604,626; 464,226 —— 604,626; 504,266; 584,622 ; 464,226
48,504; 48,450; 47,950; 48,5 54

103,952; 130,995; 113,005 ; 133,050

465,0 1 5; 456, 1 50; 486,952 ; 406,250

998,889; 989,980; 989,990 ; 999,808; 909,898

26,103; 26,301; 26,113; 26,331; 26,003

a. 48,554; 48,504; 48,450; 47,950
c. 133,050; 130,995; 113,005; 103,952
d. 486,952; 465,015; 456,150; 406,250
e.999,808; 998,889; 989,990;1989,980; 909,898

5- LOOK AT THE NUMBERS, THEN REARRANGE THE DIGITS TO FORM (A) THE SMALLEST AND (B) THE LARGEST POSSIBLE NUMBER.
142,657——(A) 124,567
(B) 765,421

a. 1 35,027
b. 989,884
c. 1 78,964
d. 625,589
e. 24 1 ,698
f. 78,463
g. 234,580
h. 848,332

Smallest Biggest
1012357 531,720
488,899 998,884
146,789 987,641
125,689 986,552
124,689 986,421
34,678 87,643
023,458 854,320
233,488 884,332

PAGE: 11

a. 6382 + 465 + I496 b. 2477 + 3Iq3 + I568
6382
+ 465
+ I 496

2477
+ 3I93
+ I568
8343 7238

2- ADD THESE TO FIND THE ODD ANSWERS: OUT’ IN EACH GROUP OF SUMS.
a- (i) 375 + 405 + 163

(ii) 5 I 6 + 185 + 252

(iii) I04 +142 +697

b- (i) 173 +254 +385

(ii) 478 +136 +188

(iii) 116 +549 +137

A
375
405
+I63
516
185
+252
1 04
142
+297
943 odd 953 odd 643 odd
B
173
254
+385
516
185
+252
116
549
+137
812 even 802 even 802 even

3- FIND THE NUMERALS TO REPLACE THE * IN EACH SUM.
5 * 6
1 3 *
* 4 2
1099
a.
5 1 *
* 4 2
4 * 2 b.
* 3 2
2 * 3
6 1 *
1257 1186
c. 8 *5
32 *
*43 d.
4 * 2
* 6 3
6 1 *
1298 1797

SOLUTION:
a.
5 1 3
34 2
+4 0 2 b.
3 3 2
2 4 3
+ 6 1 1
1257 1186
c.
8 3 5
3 2 0
+1 4 3 d.
4 2 2
5 6 3
+ 6 1 2
1298 1797

4. COPY AND COMPLETE.

a. 43,846
+ 35,017
b. 753,865
+ 169,530
C. 465,357
+ 32,986
d. 329,436
+ 281,274

(a- 78863) (b-923395 ) (c-498343 ) (d-610710 )

5- WRITE VERTICALLY SECOND ADD (BE CAREFUL WITH THE COLUMNSL).
a. 24,639 + 10,251

24,639
+ 10,251 b. 50,466 + 18,974
50,466
+ 18,974
34890 69440
c. 2,16,154 + 1,58,309

2,16,154
+ 1,58,309

d. 14,838 +249,501 + 108,633
14,838
+ 249,501
+ 108,633
374463 372972
e. 3,16,010 + 1,87,684 + 3472

3,16,010
+ 1,87,684
+ 3472 f. 204,469 + 20,496 + 2460

204,469
+ 20,496
+ 2460
507166 227425

6- WRITE THE NUMBER WHICH IS:
500 more than 16,100 ———–16,600
200 more than 1,25,000
I000 more than 200,000
900 more than 4,60,100
400 more than 509,600
ANSWERS: (a- 125500) (b-201000 ) (c-461000 ) (d-510000 )

PAGE: 12
SUBTRACTION: 5-DIGIT SECOND 6=DIGIT NUMBERS
1- WRITE VERTICALLY SECOND SUBTRACT.
a. 1401 – 758

1401
– 758 b. 6008 – 4739

6008
– 4739
643 1269
c. 8003 – 5626

8003
– 5626 d. 3600 – 1498

3600
– 1498
2377 2102

2- WRITE THE NUMBER WHICH IS: 200 Less than 1100 —– 900
a. 500 Less than 3160
b. l000 less than 9686

3- WRITE THE NUMBERS TO REPLACE THE * IN EACH SUM
a.
* 8 7 *
– 3 * * 2 8985
6362 b.
4**9
– *25*
4969
-3259
2623 2623 1710
c.
*9*8
– 5*2*
8928
-5520 d.
6 * 9 *
* 5 * 0 6897
-6520
3408 3408 377
4- COPY AND SUBTRACT, THEN CHECK.
8,45,289 2,24,28 I – 6,2 I ,008 +6,2 I ,008
2,24,28 I 8,45,Z89

a. 7,46,389 b. I,05,003
– 94,247 -87,675
6,52,142 17,328

c. 5,02,395 d. 7,62,043
– I,49, I46 – 5,09,567
353249 2,52,476

5- WRITE THESE VERTICALLY AND SUBTRACT. THEN CHECK BY ADDITION!
a. 36,738 – 1 2,849

36,738
– 1 2,849 b. 256,704 – 103,028

256,704
– 103,028 c. 2,00,03 1 – 1,89,764

2,00,03 1
– 1,89,764
23889 153676 10267
d. 500,000 – 360,824

500,000
– 360,824 e. 750,000 – 1 25,255

750,000
– 1 25,255
139176 624745

6- SUBTRACT I00 FROM EACH NUMBER.
a. 1,46,952
100 b. 500,000
100 c. 305, 103
100 d. 810,000
100
1,46,952 499900 305, 103 809900

7- SUBTRACT 500 FROM EACH NUMBER.
a. 385,620
500 b. 284,320
500 c. 505,400
500 d. 69,0 I 0
500
386120 283820 504900 68510

PAGE: 13

1- WORD PROBLEMS
Decide whether you should add or subtract to solve them. Then work them out, making complete statements.

a. A factory made 64,750 jute bags on Mseconday second 51,060 more on Tuesday.
How many bags were made altogether?

b. In second election, M; Kamal got l,56,720 votes’ second Mrs Abid got 1,58,986 votes. Who got more votes? How many more?
c. A library has 46,918 books in English second l,O8,625 books in Urdu. What is the total
number of books?

d. A shopkeeper earns Rs 170,920 in one year. If his expenses for the year are Rs 129,486, how much money does he save in a year?

e. Find the difference between the largest 4-digit number second the smallest 6-digit number.
f. A man bought a house for Rs 9,56,780. He sold it for Rs 1,20,000 less than the cost price. How much did he sell the house for?

a. 12,500 – ? = 5600

b. I00 more than 99,990 equals – .

c. 10,000 + 6000 + Q00 + 5 =

d. In 129,564, the 2 stseconds for ——————————-

e. 49,396 – ? = 10,086

f. What must be added to 100,050 to make lO2,550?

g. 564+210-50 =—————-

h. A school needs Rs 4,00,000 for a new building. The children collect Rs l,50,000. How much more money must be collected?

i. The largest 5-digit number plus the smallest 4-digit number equals ———-.

j. 1280 – 400+35 = ———————

PAGE: 14
WELCOME TO MULTIPLICATON!
PAGE: 15
MULTIPLICATON

I. COPY SECOND MULTIPLY.
a. 115
X 6 b. 2 6 4
× 1 8
2 1 1 2
+ 2 6 4
= 4 , 7 5 2
c. 569
X 5
690
2845
d. 708
X 9 e.
5 7 3
× 1 6
3 4 3 8
+ 5 7 3
= 9 , 1 6 8
f.
4 5 1
× 2 2
9 0 2
+ 9 0 2
= 9 , 9 2 2

6372

2. SOLVE THE WORD PROBLEMS, MAKING COMPLETE STATEMENTS

a. If one book of stickers contains 78 stickers, how many stickers will there be in 5 books?
SOLUTION:

7 8
× 5
3 9 0
= 3 9 0
b. If a bar of soap costs Rs 49, how much will 6 such bars cost?
SOLUTION:

4 9
× 6
2 9 4
= 2 9 4
c. There are I45 mangoes in one basket. How many mangoes are there in 32 baskets?
SOLUTION:

1 4 5
× 3 2
2 9 0
+ 4 3 5
= 4 , 6 4 0
d. 48 chalk sticks are packed in one box. How many sticks in 26 such boxes?
SOLUTION:

4 8
× 2 6
2 8 8
+ 9 6
= 1 , 2 4 8
e. How many minutes are there in I7 hours?
SOLUTION:
6 0
× 1 7
4 2 0
+ 6 0
= 1 , 0 2 0
f. 25 boxes are loaded on 0 truck. If each box weighs 22 kg, what is the total weight of the Load?
SOLUTION:

2 5
× 2 2
5 0
+ 5 0
= 5 5 0
g. A can of oil costs Rs 60.50 If the Zaid family bugs 4 can, how much will their bill be?
SOLUTION:

6 0 . 5 0
× 4
2 4 2 0 0
= 2 4 , 2 . 0 0
3- WRITE VERTICALLY AND MULTIPLY.
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R I078
1964
360
18
65
39
2382
452
325
252
57
83
I05
261
300
372
169
416 X
X
X
X
x
X
X
X
X
X
X
X
X
X
X
X
X
X 7
3
10
70
80
100
4
20
15
6
14
22
35
18
26
15
24
42 =
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=

a.
1 0 7 8
× 7
7 5 4 6
= 7 , 5 4 6
c.
3 6 0
× 1 0
0
+ 3 6 0
= 3 , 6 0 0
e.
6 5
× 8 0
0
+ 5 2 0
= 5 , 2 0 0
g.
2 3 8 2
× 4
9 5 2 8
= 9 , 5 2 8
i.

3 2 5
× 1 5
1 6 2 5
+ 3 2 5
= 4 , 8 7 5
b.
1 9 6 4
× 3
5 8 9 2
= 5 , 8 9 2
d.
1 8
× 7 0
0
+ 1 2 6
= 1 , 2 6 0
f.
3 9
× 1 0 0
0
+ 0
+ 3 9
= 3 , 9 0 0
h.

4 5 2
× 2 0
0
+ 9 0 4
= 9 , 0 4 0
j.
2 5 2
× 6
1 5 1 2
= 1 , 5 1 2

k.

5 7
× 1 4
2 2 8
+ 5 7
= 7 9 8
l.

8 3
× 2 2
1 6 6
+ 1 6 6
= 1 , 8 2 6
m.

1 0 5
× 3 5
5 2 5
+ 3 1 5
= 3 , 6 7 5
n.

2 6 1
× 1 8
2 0 8 8
+ 2 6 1
= 4 , 6 9 8
O.

3 0 0
× 2 6
1 8 0 0
+ 6 0 0
= 7 , 8 0 0
p.

3 7 2
× 1 5
1 8 6 0
+ 3 7 2
= 5 , 5 8 0
q.

1 6 9
× 2 4
6 7 6
+ 3 3 8
= 4 , 0 5 6
r.

4 1 6
× 4 2
8 3 2
+ 1 6 6 4
= 1 7 , 4 7 2
PAGE: 16
MULTIPLICATION BY I0 SECOND ITS MULTIPLES
1- MULTIPLY BY I0. (340 x 10 —–3400)

a. 581 x 10 = 5810
b. 9123 x 10 =91230
c. 629 x 10 =6290
d. 7082 x 10 =70820

2- MULTIPLY BY I00. (I63 X I00 —– l6,300)
a. 475 x 100 = 47500
b. 5692 x 100 =569200

3- MULTIPLY BY I000. (400 x I000 490.006)
a. 582 x 1000 = 582000
b. 205 x 1000 =205000

4- MULTIPLY BY I0,000. (78 x I0,000 —–780,00)
a. 19 x 1000 0=190000
b. 95 x 10000 =950000

5- FILL IN THE BLANKS.
A 16 X = 16,000
B 290 X = 2,900
C X 1000 = 480,000
D 56 X 10,000 =
E 78 X = 780,000
F X 10,000 = 670,000
(a-1000 ) (b- 10) (c- 480) (d- 560000) (e- 10000) (f- 67)

6- CHANGE M INTO CM.
(I m= I00 cm)
a. 7000 m =700000 cm
b. 4960 m=496000 cm

PAGE: 17
MULTIPLICATION BY I0 SECOND ITS MULTIPLES
7. NOW MULTIPLY THESE NUMBERS.
a. 27 X 200
b. 24 x 6000
C. 22 X 9000
d. 51 X 70
e. 38 X 7000
f. 87 X 2000

a.
2 7
× 2 0 0
0
+ 0
+ 5 4
= 5 , 4 0 0
b.
2 4
× 6 0 0 0
0
+ 0
+ 0
+ 1 4 4
= 1 4 4 , 0 0 0
c.
2 2
× 9 0 0 0
0
+ 0
+ 0
+ 1 9 8
= 1 9 8 , 0 0 0
d.
5 1
× 7 0
0
+ 3 5 7
= 3 , 5 7 0
e.
3 8
× 7 0 0 0
0
+ 0
+ 0
+ 2 6 6
= 2 6 6 , 0 0 0

8 7
× 2 0 0 0
0
+ 0
+ 0
+ 1 7 4
= 1 7 4 , 0 0 0

PAGE: 18
MULTIPLICATION BY I0 SECOND ITS MULTIPLES
8. SOLVE THESE.
a. 54×300

5 4
× 3 0 0
0
+ 0
+ 1 6 2
= 1 6 , 2 0 0
b. 48x 3000

4 8
× 3 0 0 0
0
+ 0
+ 0
+ 1 4 4
= 1 4 4 , 0 0 0
c. 4I5x600

4 1 5
× 6 0 0
0
+ 0
+ 2 4 9 0
= 2 4 9 , 0 0 0
d. 25×20,000

2 5
× 2 0 0 0 0
0
+ 0
+ 0
+ 0
+ 5 0
= 5 0 0 , 0 0 0

9. I HOUR = 60 MIN. FIND OUT HOW MANY MINUTES IN:
a. 5hours (h) b. 32h
c. 21 h d. 36h

ANSWERS: (a- 300 minutes ) (b- 1920 minutes) (c- 1260 minutes ) (d- 2160 minutes )

I0. THERE ARE 50 PEOPLE IN THIS BUS (INCLUDING THE DRIVER). FIND OUT HOW MANY PEOPLE IN:
FIND OUT HOW MANY PEOPLE IN:
a. I6 buses b. I02 buses

c. 98 buses d. I000 buses
ANSWERS: (a- 800 peoples) (b-5100 peoples ) (c- 4900 peoples ) (d- 50000 peoples )

11. MULTIPLY EACH NUMBER BY 40, THEN BY 400, THEN BY 4000.
a. 28
b. I20
c. 83
d. I33
a. 28 x4=112
28 x40=1120
28 x400=11200
28 x4000=112000

b. I20x40=4800
I20x400=48000
I20x4000=480000
c. 83 x 40=3320
83 x 400=33200
83 x 4000=332000

d. I33x40=5320
I33x400=53200
I33x4000=532000

I2. I m =, I00 cm. Convert m into cm in the following: (580 m = 58,000 cm)
a. 630 m
b. I200 m
c. 84 m
d. 382I m
ANSWERS: (a- 63000 cm) (b-120000 cm) (c-8400 cm) (d-3821 cm )

13. I km = I000 m. Convert km into m in the following: ( 6 km = I6,000 m)
a. 47 km
b. 309 km
c. 100 km
d. 4 km
ANSWERS: (a- 47000m) (b-309000 m) (c-100000m ) (d-4000 m )

I4. 1 kg = I000 g. Convert kg into g in the following: (129 kg = 129,000 g)
a. 560 kg
b. 999 kg
c. 111 kg
d. 4q3 kg

I5. 1 L = I000 ml. Convert l into ml in the following: ( 295 l = 295,000 ml)
a. 141 L
b. 902 L
C. 39 L
d. 800L
ANSWERS: (a- 141000 ml) (b-902000 ml) (c- 39000 ml) (d-800000 ml )

PAGE: 19
MULTIPLYING BY 2-DIGIT NUMBERS

I. COPY SECOND MULTIPLY. BE CAREFUL WITH YOUR COLUMNS!
a. 643
x72 b. 305
x64 c. 865
x 28

d. 996
x 37 e. 487
x53 f. 408
x 93

2. WRITE VERTICALLY SECOND MULTIPLY.
a. 749 x62 b. 643 x59 c. 816 x 94
d. 838 x 67 e. 567 x 81 f. 950 x 48

3- SOLVE THE WORD PROBLEMS, MAKING COMPLETE STATEMENTS.
a. A train in Germany travels 528 km in one hour. How far will it travel in 24 hours?

b. A machine in a factory makes 615 togs every day. How many togs will it make in 6 weeks?
If 48 mangoes are packed in 1 box, how many mangoes are there in 650 such boxes?

d. A room in Hotel Palm Magic costs Rs Q52 per night. If all 58 rooms are occupied, how much money will the hotel manager collect in one night?

e. If Sohail runs 650 m every morning, how many metres will he gun in 5 weeks of ‘
daily training?

PAGE: 20
MULTIPLICATION: SOME NEW WORDS

I. COPY SECOND MULTIPLY THE FOLLOWING. THEN LABEL THEM
462 — Multiplicand
X 75 -——- multiplier
2310
32340 ———–product

a. 619
x 77 b. 964
x 79

C. 385
X 47 d. 474
X 36

a.
6 1 9
× 7 7
4 3 3 3
+ 4 3 3 3
= 4 7 , 6 6 3
b.
9 6 4
× 7 9
8 6 7 6
+ 6 7 4 8
= 7 6 , 1 5 6
c.
3 8 5
× 4 7
2 6 9 5
+ 1 5 4 0
= 1 8 , 0 9 5
d.
4 7 4
× 3 6
2 8 4 4
+ 1 4 2 2
= 1 7 , 0 6 4

2- WRITE SUMS TO MATCH THESE WORDS. THEN SOLVE THEM.
Multiplier 62, multiplicand
416 6
4l6
x 62
25792

a. Multiplicand 82,
multiplier I6

8 2
× 1 6
4 9 2
+ 8 2
= 1 , 3 1 2
b. Multiplicand I76,
multiplier 10

1 7 6
× 1 0
0
+ 1 7 6
= 1 , 7 6 0
c. Multiplicand 395,
multiplier 72

3 9 5
× 7 2
7 9 0
+ 2 7 6 5
= 2 8 , 4 4 0

3- WRITE THESE VERTICALLY SECOND MU-TIP-G THEM. THEN LABEL THEIR PARTS.
a. 648 X 52 b. 783 X 89
6 4 8
× 5 2
1 2 9 6
+ 3 2 4 0
= 3 3 , 6 9 6

7 8 3
× 8 9
7 0 4 7
+ 6 2 6 4
= 6 9 , 6 8 7
c. 7351 X 69 d. 650 X Q5
7 3 9
× 6 9
6 6 5 1
+ 4 4 3 4
= 5 0 , 9 9 1

6 5 0
× 9 5
3 2 5 0
+ 5 8 5 0
= 6 1 , 7 5 0

4- SOLVE THESE SUMS IN YOUR HEAD. THEN JOIN THEM TO THE CORRECT PRODUCT.
Products
120 x 40
36 x 500
115 x 200
81 x 60
500 x 500
42 x 30
15 x 70
430 x 50 1260
4800
18000
4860
23000
250000
21500
1050
ANSWERS: (a- 2) (b- 3 ) (c- 5) (d-4 ) (e- 6 ) (f- 1 ) (g- 8 )(h-7 )

PAGE: 21
MULTIPLICANDS OF 4 DIGITS SECOND MULTIPLIERS OF 3 DIGITS

NOW COPY SECOND MULTIPLY THESE. BE CAREFUL WITH YOUR COLUMNS.
a. 1 634
X24 b. 3472
X48

3- COPY SECOND MULTIPLY. BE SURE TO WRITE YOUR COLUMNS L CAREFULLY.
a. 356
X142 b. 2l8
X208

2- SOLVE THESE WORD PROBLEMS, MAKING COMPLETE STATEMENTS
a. A leaking tap wastes 3750 ml of water in I hour. How
much water will be wasted
in a day?

b. Rehan found out that he
can save 4726 ml of water
every day by not Leaving
the tap open continuously,
duringhis bath. How much
water can be saved in 25¢
days in this manner?
c. There are I440 minutes in a
day. How many minutes
are there in 8 weeks?
4- WRITE SUMS TO MATCH THE WORDS, THEN SOLVE THEM.

Multiplicand 226,
multiplier 483
226
X 483
l09l58

Multiplicand 381
multiplier 422

Multiplier 604,
Multiplicand 304
a. 84 X 200 b. 763 X 400 c. 483 X I00

d. 258 X 900 e. 834 X 300 f. 582 X 700

PAGE: 22

REVIEW
1. COPY THE SUMS, THEN FILL IN THE MISSING SIGNS, X OR +.
A 9 7 = 63
B 84 12 = 7
C 60 10 = 6
D 40 14 = 560
ANSWERS: (a. x) (b. ÷ )(c. ÷ )(d. x)

2. COPY AND COMPLETE.
140 ÷ 2 =
A 300 ÷ 6 =
B 750 ÷ 5 =
C 160 ÷ 8 =
D 630 ÷ 9 =
SOLUTION:
a.
0 5 0
6 3 0 0
0
3 0
3 0
0 0
0
0
b.
1 5 0
5 7 5 0
5
2 5
2 5
0 0
0
0
c.
0 2 0
8 1 6 0
0
1 6
1 6
0 0
0
0
d.
0 7 0
9 6 3 0
0
6 3
6 3
0 0
0
0

3. WRITE THE NUMBER THAT IS:
A 1/2 of 24 =
B 1/6 of 36 =
C 1/3 of 27 =
D 1/4 of 124 =
SOLUTION:
A 1/2 of 24 = 2/2 = x 24/2 =12
B 1/6 of 36 = 6/6 = x 36/6 = 6
C 1/3 of 27 = 3/3 = x 27/3 = 9
D 1/4 of 124 = 4/4 = x (124 )/4 = 31

4. SOLVE THESE WORD PROBLEMS
a. How many nines are there in eighty-one?
SOLUTION:
81÷ 9=9

b. If six pencils cost Rs 36 how much does one pencil cost?
SOLUTION:
Number of pencils= 6
Cost of pencils = 36
So cost of 1 pencil= 36÷ 6=6
5. SOLVE THE FOLLOWING
a. 1000 ÷ 5

0 2 0 0
5 1 0 0 0
0
1 0
1 0
0 0
0
0 0
0
0
b. 7000 ÷5

1 4 0 0
5 7 0 0 0
5
2 0
2 0
0 0
0
0 0
0
0
c. 7200 ÷8

0 9 0 0
8 7 2 0 0
0
7 2
7 2
0 0
0
0 0
0
0
d. 9900 ÷9

1 1 0 0
9 9 9 0 0
9
0 9
9
0 0
0
0 0
0
0
6. DIVIDE THESE NUMBERS BY I0

a. 50÷10 = 5 r 0 b. 574÷10=57 r 4 c. 210 ÷10=21 r 0 d.1000÷10=100 r 0

7. WRITE THE MISSING QUOTIENTS
A 360 ÷ 9 =
B 6400 ÷ 8 =
C 480 ÷ 6 =
ANSWERS: (a- 40) (b- 800 ) (c- 80 )

8. FIND THE MISSING DIVIDENDS
A ÷ 5 = 2
B ÷ 8 = 8
C ÷ 5 = 9
ANSWERS: (a-2 ) (b- 8 ) (c- 9 )

9. FIND THE MISSING DIVISORS
a. I0 ÷ ———- =5
b. 45 ÷ ———-=9
c. 56 ÷ ———-=7
ANSWERS: (a- 5 ) (b- 9 ) (c- 7)

10- WRITE THESE SUMS IN LONG DIVISION FORM, THEN COMPLETE
a. Dividend 437, divisor 7

0 6 2
7 4 3 7
0
4 3
4 2
1 7
1 4
3
b. Divisor 8, dividend I44

0 1 8
8 1 4 4
0
1 4
8
6 4
6 4
0
c. Dividend 32, divisor 8

0 0 3
8 6 3 2 9
0
3 2
0
3 2 9
2 5 8
7 1
PAGE: 23
MULTIPLICATION SECOND DIVISION WITH BIGGER NUMBERS

1. LOOK AT THIS CHART CAREFULLY SECOND COMPLETE IT. WHEN YOU HAVE FINISHED, YOU WILL HAVE WRITTEN TABLES FROM 11-19
11 12 13 14 15 16 17 18 19
1 11 14
2 22 32
3 33 39 57
4 48 68
5
6 108
7 105
8 104
9 144
10 180
11 12 13 14 15 16 17 18 19
1 11 12 13 14 15 16 17 18 19
2 22 24 26 28 30 32 34 36 38
3 33 36 39 42 45 48 51 54 57
4 44 48 52 56 60 64 68 72 76
5 55 60 65 70 75 80 85 90 95
6 66 72 78 84 90 96 102 108 114
7 77 84 91 98 105 112 119 126 133
8 88 96 104 112 120 128 136 144 152
9 99 108 117 126 135 144 153 162 171
10 110 120 130 140 150 160 170 180 190
2. NOW COMPLETE THESE SUMS, WITH THE HELP OF THE CHART
108 ÷ 18 = 6
a. 91 ÷ 13=
b. 112 ÷ 14 =
c. 96 ÷ 12 =
d. 119÷ 17 =
e. 152 ÷ 19 =
F. 144 ÷ 18 =
ANSWERS: (a- 7) (b- 8) (c- 8) (d- 7) (e- 8) (f- 8)

3. NOW COMPLETE THESE, WRITING REMAINDERS WHERE NECESSARY
145 ÷ 16 = 9 r 1
a. 128 ÷ 17 =
b. 185 ÷ 18=
c. 77 ÷15=
d. 113 ÷ 18=
e. 106 ÷ 11 =
ANSWERS: (a- 7 r 9) (b- 10 r 5 ) (c- 5 r 2 ) (d- 6 r 5 ) (e- 9 r 7)

PAGE:24

Q1 USING THE CHART ON PAGE 23 COPY AND COMPLETE THE FOLLOWING.
a. 14) 408

0 2 9
1 4 4 0 8
0
4 0
2 8
1 2 8
1 2 6
2
b. 16) 931

0 5 8
1 6 9 3 1
0
9 3
8 0
1 3 1
1 2 8
3
C. 12) 269

0 2 2
1 2 2 6 9
0
2 6
2 4
2 9
2 4
5
D. 17) 695

0 4 0
1 7 6 9 5
0
6 9
6 8
1 5
0
1 5
E. 15)530

0 3 5
1 5 5 3 0
0
5 3
4 5
8 0
7 5
5
F.18)586

0 3 2
1 8 5 8 6
0
5 8
5 4
4 6
3 6
1 0

Q2: WRITE THESE IN LONG DIVISION FORM AND SOLVE.

a. 744 ÷ 12

0 6 2
1 2 7 4 4
0
7 4
7 2
2 4
2 4
0
b. 384 ÷ 15

0 2 5
1 5 3 8 4
0
3 8
3 0
8 4
7 5
9
c. 407 ÷ 13

0 3 1
1 3 4 0 7
0
4 0
3 9
1 7
1 3
4
d. 492 ÷ 13

0 3 7
1 3 4 9 2
0
4 9
3 9
1 0 2
9 1
1 1

3. FIND THE MISSING DIVISORS
A 135 ÷ = 9
B 112 ÷ = 16
C 54 ÷ = 18
D 153 ÷ = 17
E 117 ÷ = 13
F 152 ÷ = 19
G 144 ÷ = 12
H 126 ÷ = 14
I 99 ÷ = 9
J 105 ÷ = 15
ANSWERS: (a- 15) (b- 7 ) (c- 3) (d- 9) (e- 9) (f- 8) (g- 12)(h- 9)(i- 11)(j- 7)

Q 4.SOLVE THE WORD PROBLEMS, MAKING COMPLETE STATEMENTS.
(a) In a relay race, I6 children
ran a total of 9600 m. How
many metres did each child
run? Solution:
Total children=16
Total race=9600m
Each child ran= 9600÷16
=600 meters
(b)A jug contains 1440 ml of
orange juice. If I2 children
share the juice equally, how
much does each child get? Solution:
Total children=12
Total juice=1440 ml
Each child got= 1440÷12
=120 ml
(c)If crayons are packed in
boxes of I6, how many
boxes are needed to pack
4000 crayons? Solution:
Total boxes=16
Total crayons=4000
Each child ran= 4000÷16
=250 crayons
(d)Rs 5530 is collected for 7
families whose homes have
been damaged by floods.
How much money will each
family get? Solution:
Total families=7
Total money=Rs 5530
Each family got= 5530÷7
= Rs 790
(e)Eleven children share the
first prize in a painting
contest. If the prize money is
Rs 5000, how much will each
child get, second how much
money will be left over? Solution:
Total children=11
Total money=Rs 5000
Each child got= 5000÷11
= Rs 454 left over =6

Q5: WRITE DIVIDENDS IN THE BLANKS.
A ——— ÷ 17 = 6
B ——— ÷ 4 = 12
C ——— ÷ 3 = 13
D ——— ÷ 15 = 7
E ——— ÷ 18 = 4
f ——— ÷ 6 = 11
ANSWERS: (a- 102) (b- 48) (c- 39) (d- 105) (e- 72) (f- 66)

P: 25
DIVISION WITH BIGGER NUMBERS
6. WHEN YOU HAVE COMPLETED THIS CHART, GOU WILL HAVE WRITTEN TABLES FOR THESE NUMBERS: I0, 20, 30, 40, 50, 60, 70, 80, SECOND 90.
10 20 30 40 50 60 70 80 90
1 10 20
2 80
3 60
4 240
5 150
6 480
7 630
8
9 450
10 700
10 20 30 40 50 60 70 80 90
1 10 20 30 40 50 60 70 80 90
2 20 40 60 80 100 120 140 160 180
3 30 60 90 120 150 180 210 240 270
4 40 80 120 160 200 240 280 320 360
5 50 100 150 200 250 300 350 400 450
6 60 120 180 240 300 360 420 480 540
7 70 140 210 280 350 420 490 560 630
8 80 160 240 320 400 480 560 640 720
9 90 180 270 360 450 540 630 720 810
10 100 200 300 400 500 600 700 800 900
7- WORK OUT THE FOLLOWMG
320 ÷ 40=
350 ÷70=
810 ÷ 90=
200 ÷ 40=
540 ÷ 60=
720 ÷ 90=
ANSWERS: (a- 5) (b- 9) (c- 5) (d- 9) (e- 8)

8. WORK OUT THE FOLLOWMG
424 ÷ 70 =
638 ÷ 90 =
69 ÷ 20 =
480 ÷ 60 =
513 ÷ 10 =
a-
0 0 6
7 0 4 2 4
0
4 2
0
4 2 4
4 2 0
4
b.
0 0 7
9 0 6 3 8
0
6 3
0
6 3 8
6 3 0
8
c.
0 3
2 0 6 9
0
6 9
6 0
9
d.
0 0 8
6 0 4 8 0
0
4 8
0
4 8 0
4 8 0
0
e.
Show Work:
0 5
1 0 5 1
0
5 1
5 0
1

P:26
DIVISORS WITH 2 DIGITS

1. COPY AND DIVIDE, WORKING VERY CAREFULLY.
a. 420 ) 542
b. 62) 719
c. 23 ) 605
d. 35) 816
e. 34) 493
f. 51) 948
g. 56) 628
h. 47) 876
a.
0 1 1
4 8 5 4 2
0
5 4
4 8
6 2
4 8
1 4
b.
0 1 1
6 2 7 1 9
0
7 1
6 2
9 9
6 2
3 7
c.
0 2 6
2 3 6 0 5
0
6 0
4 6
1 4 5
1 3 8
7
d.
0 2 3
3 5 8 1 6
0
8 1
7 0
1 1 6
1 0 5
1 1

e.
0 1 4
3 4 4 9 3
0
4 9
3 4
1 5 3
1 3 6
1 7
f.
0 1 8
5 1 9 4 8
0
9 4
5 1
4 3 8
4 0 8
3 0
g.
0 1 1
5 6 6 2 8
0
6 2
5 6
6 8
5 6
1 2
h.
0 1 8
4 7 8 7 6
0
8 7
4 7
4 0 6
3 7 6
3 0
2. WRITE THESE DIVISIONS IN LONG FORM SECOND WORK OUT.
a. 62I ÷ 36
b. 800 ÷ 76
c. 7I8 ÷ 42
d. 956 ÷ 83
e. 699 ÷ 33
f. 792 ÷ 23
g. 888 ÷ 11
h. 791 ÷ 57

0 1
3 6 6 2
0
6 2
3 6
2 6
b.
0 1 0
7 6 8 0 0
0
8 0
7 6
4 0
0
4 0
c.
0 1 7
4 2 7 1 8
0
7 1
4 2
2 9 8
2 9 4
4
d.
0 1 1
8 3 9 5 6
0
9 5
8 3
1 2 6
8 3
4 3
e.
0 2 1
3 3 6 9 9
0
6 9
6 6
3 9
3 3
6
f.
0 3 4
2 3 7 9 2
0
7 9
6 9
1 0 2
9 2
1 0

g.
0 8 0
1 1 8 8 8
0
8 8
8 8
0 8
0
8
h.
0 1 3
5 7 7 9 1
0
7 9
5 7
2 2 1
1 7 1
5 0

3. WRITE THESE DIVISIONS IN LONG FORM SECOND DIVIDE.

Dividend 385, divisor 24
Divisor 57, dividend 640
Divisor 62, dividend 719
Dividend 700, divisor 37
Divisor 91, dividend 938
Dividend 999, divisor 53
a.
0 1 6
2 4 3 8 5
0
3 8
2 4
1 4 5
1 4 4
1
b.
0 1 1
5 7 6 4 0
0
6 4
5 7
7 0
5 7
1 3
c.
0 1 1
6 2 7 1 9
0
7 1
6 2
9 9
6 2
3 7
d.
0 1 8
3 7 7 0 0
0
7 0
3 7
3 3 0
2 9 6
3 4
e.
0 1 0
9 1 9 3 8
0
9 3
9 1
2 8
0
2 8

0 1 8
5 3 9 9 9
0
9 9
5 3
4 6 9
4 2 4
4 5

P:27
DIVISORS WITH 2 DIGITS

4. COPY AND DIVIDE.

a. 23)117
b. 47)377
c. 45)269
d. 61)795
5. WORK OUT THESE DIVISIONS IN LONG FORM.

a. 118 ÷ 25
b. 371 ÷ 45
c. 209 ÷ 24
d. 469 ÷ 57
e. 320 ÷ 36
f. 544 ÷ 63

6. COPY AND DIVIDE:
a. 37) I57
b. 235723
c. 58472
d. 565332
e. 74§823
f. 35;q00
7. SOLVE THE WORD PROBLEMS, MAKING COMPLETE STATEMENTS
a. At a school camp, 800 children are divided into groups of 25 children each. How many groups are there altogether?
b. For the best campaign on ‘Saving the Tiger’, all 36 children in class 4B shared a reward of Rs 936. How much did each child get, second how much money was left over?

c. Kashif has only 943 L of petrol left in his petrol pump. If 52 cars are in the queue for petrol, how much does each receive if the petrol is shared equally? How much is left over?

P:28
DIVIDENDS WITH 4 DIGITS

1. COPY AND DIVIDE, WORKING VERY CAREFULLY.

A 28) 4042
B 26) 1064
C 31) 6485
D 18) 1002
E 43)5629
F 39)2084
G 62)9858
H 24)8914
I 51)4092
J 65)5000

a.
0 1 4 4
2 8 4 0 4 2
0
4 0
2 8
1 2 4
1 1 2
1 2 2
1 1 2
1 0
b.
0 0 4 0
2 6 1 0 6 4
0
1 0
0
1 0 6
1 0 4
2 4
0
2 4
c.
0 2 0 9
3 1 6 4 8 5
0
6 4
6 2
2 8
0
2 8 5
2 7 9
6
d.
0 0 5 5
1 8 1 0 0 2
0
1 0
0
1 0 0
9 0
1 0 2
9 0
1 2
e.
0 1 3 0
4 3 5 6 2 9
0
5 6
4 3
1 3 2
1 2 9
3 9
0
3 9
f.
0 0 5 3
3 9 2 0 8 4
0
2 0
0
2 0 8
1 9 5
1 3 4
1 1 7
1 7
g.
0 1 5 9
6 2 9 8 5 8
0
9 8
6 2
3 6 5
3 1 0
5 5 8
5 5 8
0

0 3 7 1
2 4 8 9 1 4
0
8 9
7 2
1 7 1
1 6 8
3 4
2 4
1 0
i.
0 8 1 8
5 4 0 9 2
0
4 0
4 0
0 9
5
4 2
4 0
2
j.
0 0 7 6
6 5 5 0 0 0
0
5 0
0
5 0 0
4 5 5
4 5 0
3 9 0
6 0

2. WRITE IN LONG DIVISION FORM AND DIVIDE.

a. 4618 ÷ 29
b. 9310 ÷ 86
c. 3047 ÷ 53
d. 6593÷ 72
e. 327l ÷ 49
f. 6999÷33
g. 8l20÷ 91
h. 3024 ÷45
i. 4002÷ 58
j. 5430 ÷66

a.
0 1 5 9
2 9 4 6 1 8
0
4 6
2 9
1 7 1
1 4 5
2 6 8
2 6 1
7
b.
0 1 0 8
8 6 9 3 1 0
0
9 3
8 6
7 1
0
7 1 0
6 8 8
2 2
c.
0 0 5 7
5 3 3 0 4 7
0
3 0
0
3 0 4
2 6 5
3 9 7
3 7 1
2 6
d.
0 0 9 1
7 2 6 5 9 3
0
6 5
0
6 5 9
6 4 8
1 1 3
7 2
4 1
e.
0 0 6
4 9 3 2 7
0
3 2
0
3 2 7
2 9 4
3 3
f.
0 2 1 2
3 3 6 9 9 9
0
6 9
6 6
3 9
3 3
6 9
6 6
3
g.
0 0 8 9
9 1 8 1 2 0
0
8 1
0
8 1 2
7 2 8
8 4 0
8 1 9
2 1
h.
0 0 6 7
4 5 3 0 2 4
0
3 0
0
3 0 2
2 7 0
3 2 4
3 1 5
9
i.
0 0 6 9
5 8 4 0 0 2
0
4 0
0
4 0 0
3 4 8
5 2 2
5 2 2
0
j.
0 0 8 2
6 6 5 4 3 0
0
5 4
0
5 4 3
5 2 8
1 5 0
1 3 2
1 8

P:29
MULTIPLY TO CHECK!

A 24) 604
0 2 5
2 4 6 0 4
0
6 0
4 8
1 2 4
1 2 0
4
B 19) 1624

0 0 8 5
1 9 1 6 2 4
0
1 6
0
1 6 2
1 5 2
1 0 4
9 5
9
C 32) 859

0 2 6
3 2 8 5 9
0
8 5
6 4
2 1 9
1 9 2
2 7

D 43) 6205

0 1 4 4
4 3 6 2 0 5
0
6 2
4 3
1 9 0
1 7 2
1 8 5
1 7 2
1 3
E 61) 962

0 1 5
6 1 9 6 2
0
9 6
6 1
3 5 2
3 0 5
4 7
F 28) 3100

0 1 1 0
2 8 3 1 0 0
0
3 1
2 8
3 0
2 8
2 0
0
2 0

2. Write the sums, complete them, then multiply to check.

Dividend 399, divisor 17
Dividend 4082, divisor 62
Divisor 49, dividend 6351
Dividend 5641, divisor 13
Divisor 81, dividend 3001
Dividend 1069, divisor 72
Divisor 27, dividend 1111
Divisor 55, dividend 3030

a. b. c. d.

0 2 3
1 7 3 9 9
0
3 9
3 4
5 9
5 1
8
0 0 6 5
6 2 4 0 8 2
0
4 0
0
4 0 8
3 7 2
3 6 2
3 1 0
5 2
0 1 2 9
4 9 6 3 5 1
0
6 3
4 9
1 4 5
9 8
4 7 1
4 4 1
3 0
0 4 3 3
1 3 5 6 4 1
0
5 6
5 2
4 4
3 9
5 1
3 9
1 2
e.
0 0 3 7
8 1 3 0 0 1
0
3 0
0
3 0 0
2 4 3
5 7 1
5 6 7
4
f.
0 0 1 4
7 2 1 0 6 9
0
1 0
0
1 0 6
7 2
3 4 9
2 8 8
6 1
g.
0 0 4 1
2 7 1 1 1 1
0
1 1
0
1 1 1
1 0 8
3 1
2 7
4
h.
0 0 5 5
5 5 3 0 3 0
0
3 0
0
3 0 3
2 7 5
2 8 0
2 7 5
5

3. WRITE QUOTIENTS IN THE BLANKS.

4900 ÷ 49 =
6500 ÷ I0 =
8000 ÷ 20 =
5100 ÷ 17 =
4800 ÷ 40 =
ANSWERS: (a- 100) (b- 650) (c- 400) (d- 300 ) (e- 120)

P:30
USING DIVISION IN WORD PROBLEMS

1- SOLVE THESE WORD PROBLEMS, MAKING COMPLETE STATEMENTS. THEN MULTIPLY TO CHECK THE ANSWERS:S.

a. Thirty children made 5280 paper bags. How many did each child make?

b. How many pieces of cloth can be cut from a 5-metre length of cloth, if each piece is 50 cm long?

c. From several orchards, delicious apples are packed in boxes of 72 each. How many boxes will be required for 900 apples?
(This is tricky!)

d. Five doctors travel from Karachi to Lahore to attend a conference. The total bill for their train tickets is Rs 9675. How much does each doctor pay?

e. How many hours are there in 2700 minutes?

f. Four friends share a flat. Their total expenses for January are Rs9256. How much money must each friend contribute?

2. NOW SOLVE THESE PROBLEMS. THINK CAREFULLY WHETHER YOU SHOULD MULTIPLY OR DIVIDE TO GET THE ANSWERS:.

a. From one roll of film, I can get 24 photographs. How many rolls do I need to take 360 photographs?

b. How many days are there in 39 weeks?

c. A jungle path is 645 km long. If an explorer can I travel I5 km in a dag, how many days will she take to cover the whole distance?

Mrs Bilal withdraws Rs 6160 from her account. She wants the money in Rs 20 notes. How many notes will the bank clerk give her?

P:31
DIVIDING BY 10 AND ITS MULTIPLES

P:32
DIVIDING BY 10 AND ITS MULTIPLES

1. WRITE QUOTIENTS IN THE BLANKS. l3,000 + I00 I30
2000 ÷ 10 =
3000 ÷ 100 =
767,200 ÷ 100 =
77,000 ÷ 1000 =
124,000 ÷ 10 =
500,100 ÷ 1000 =
ANSWERS: (a- 200 ) (b-30 ) (c-672 ) (d-77 ) (e-12,400 ) (f-5001 )

2. DO YOU REMEMBER? NOW WORK THESE OUT.

a. 422 ÷10
b. 6103÷10
c. 8952÷10
d. 96,302÷10
e. 70,111÷10
f. 84,605÷10
ANSWERS: (a-42 r 2 ) (b- 610 r 3) (c- 895 r 2) (d- 9630 r 2) (e-7011 r ) (f-8460 r 5 )
3. LOOK CAREFULLY AT THESE SUMS. NOW COMPLETE THESE.

a. 6420 ÷ 100 =
b. I2,472 ÷ 100 =
c. 45,505 ÷ 100 =
d. 80,720 ÷ 100 =
e. 1,16,304 ÷100=
ANSWERS: (a- 64 r 20) (b- 124 r 72) (c- 455 r 5) (d- 807 r 29) (e- 1163 r 4)

4. NOW LOOK AT THESE EXAMPLES. DIVIDE EACH OF THESE BY 1000

a. 4,300
b. 3,10,400 ÷ 1000
c. 11,100÷ 1000
d. 8,96,000÷ 1000
ANSWERS: (a- 4 r 300) (b- 310 r 400) (c- 11 r 100) (d- 896 r 0)
P:33
REVIEW

18 x 20=
64+82 =
91 – 59=
511 ÷10=
831 x 500 =
6200+ I000 =
146+23+40 =
524+48 – 62=
ANSWERS: (a-360 ) (b- 146) (c- 32) (d- 51 r 1) (e- 4,15,500) (f- 6 r 200)
(g- 169 + 40 = 209) (h- 510)

2. COPY AND COMPLETE, USING VERTICAL FORM FOR +, -, AND X SUMS, AND LONG DIVISION FOR ÷ SUMS.

a. 32,069 – 18,478
b. 8243 ÷ 49
c. 384 x 72
d. 48,162 + 530,694
e. 62,432 + 30, 149 + 6828
f. 645 x 49
g. 5031 + 64
h. 1,40,300 – 89,699
ANSWERS: (a- 13,591) (b- 168 r 11) (c- 27,648) (d- 5,78,856) (e-99,409)
(f- 31,605) (g- 78 r 39) (h- 50,601)

3. SOLVE THE WORD PROBLEMS AFTER DECIDING WHICH OF THE FOUR OPERATIONS YOU NEED TO USE.

a. The Shahid family keeps
aside Rs I550 every month
for charity. How much does
the family donate to charity annually? SOLUTION:
Shahid donates every month= Rs I550
As 1 year =12 months
So house rent for a year = 1550×12
=
1 5 5 0
× 1 2
3 1 0 0
+ 1 5 5 0
Rs = 1 8 , 6 0 0

b. There are 382! children in
junior school, 27q8 children
in middle school, second 2462
in senior school. What ‘is the total strength of the school? Children in junior school = 3821
Children in middle school = 2796
Children in senior school = 2462
Total strength of school= 3821+2796+2462
=9081

c. 36 children went on a field
trip. The total expenses
were Rs 4860. How much
did the trip cost each child? Total number of children = 36
Total expenses = Rs 4860
Trip cost per child= 4860 ÷ 36
=135

0 1 3 5
3 6 4 8 6 0
0
4 8
3 6
1 2 6
1 0 8
1 8 0
1 8 0
0
d. Out of 2069 people working in a shoe factory, I387 were women. How many
men worked in the factory? Total people in a factory = 2090
Women working = 1387
Remaining =2069 – 1387
Working men = 682

e. An orphanage needs
Rs 89,000 to buy a second-
hand car. It has collected
only Rs J57,6q7 so far. How
much money still needed? Cost of car = Rs 89000
Money collected = Rs 57697
More needed = 89000 – 57697
= Rs31303

P:34
UNITARY METHOD: THINKING SECOND SOLVING
P:35
UNITARY METHOD:

1. WHAT IS THE COST OF:
a. 3 bananas at Rs 36 per
dozen? SOLUTION:
12 bananas = Rs36
1 bananas = 36 ÷12=3Rs.
3 bananas cost = 3×3=Rs.9
b T-shirts at Rs 220 for 2? SOLUTION:
2 T-shirt Rs 28
1T-shirt =220 ÷2=110
9 T-shirts =9×100=RS.990

c. 23 notebooks at Rs 60 for 3? SOLUTION:
3 note books = Rs.60
1 note book = 60÷3=20
23 note books = RS 209 x 23
= Rs. 4600
2. NOW SOLVE THESE, GIVING COMPLETE STATEMENTS.
a. A year’s rent for a house is
Rs 18,000. If the Shal’1\./<-4,’
family wants to rent the ‘
house for only 7months1’
how much rent will theﬁgy
have to pay?
A year’s rent for a house = Rs. 18,0000
1 month rent =18000 ÷12 = Rs.1500
7 month rent = 1500 x7 = 10500
7 month rent is Rs.10,500.

b. With I5 l of petrol in its
tank, a car can cover
270 km. What distance can
the car cover with only I2 l
of petrol? petrol in car’s tank = 15 L
car can cover in 15 L = 270 km
car can cover in 1 L = 270 ÷ 115 = 18 km
Car cover with 12 L petrol = 18 x 12 = 216

3. CAN THE UNITARY METHOD BE USED TO SOLVE THESE PROBLEMS? THINK CAREFULLY, SECOND THEN EXPLAIN YOUR ANSWERS:.
a. If a Rs I00 note is I5 cm
long, how long will a Rs 20
note be?
1 Size of Rs. 100 note = 15cm
size of Rs.1 note = 15 ÷ 100cm
. size of Rs.20 note = 15/100 x 20cm
= 30 cm
b. If Anila is I32 cm tall at the age of I2, hpw tall was she
when she was 2 years old? b. Anila’s height in the age of 12 = 132 cm

Height of Anila’s in the age of 1 = 132/12cm 1

Height of Zehra in the age of 2 = 132/12 x 2
=11×2=22cm
c. If a cat catches I8 mice
during one night’s hunting,
how many cats will be
needed to catch 20 mice? c. Number of cat that catch 18 mice =1
Number of cats that catch 1 mice= 1/18

Number of cats that catch 20 mice = 1/18 x 20
= 20/18 = 10/9
P:36
TIME: REMEMBERING THE CALENDAR

1. IN THE YEAR 3000 WHAT DATE IS: The first Tuesday, in October? 7 October
a. The first Wednesday in May?
b. The first Monday in January?
c. The fourth Saturday of the year?
d. Two weeks after I4 June?
e. Two weeks after 21 November?
f. One week before I0 June?
g. Two weeks before 6 August?
h. 10 days before I8 April?
i. The first day of the new millennium?
ANSWERS: a. 7th may b. 6th January c. 25th January d. 28th June e. 5th December f. 3rd June g. 23rd July h. 8th April i. 1st January s

2. WRITE THESE DATES IN SHORT FORM. 6 February 6.2.197l
a. I6 July I940
b. 23 May l98l
d. Tomorrow’s date
ANSWERS: a. 16.7.49 b. 23.5.81 c. 3.11.2004 d. 27.10.2016

3. LOOK AT THE CALENDAR FOR THE YEAR 3000 SECOND WRITE THE DAY WHICH MATCHES. 4. 1l.3000 Tuesday
a. 18.9.3000
b. 27.4.3000
c. 5.l.3000
d. l.1l.3000
e. 2.8.3000
f. 31.10.3000
ANSWERS: a. Thursday b. Sunday c. Monday d. Saturday e. Saturday f. Friday

P:37
TIME

1. WHAT TIME DOES TRIE CLOCK SHOW?

ANSWERS: (a- 15 past 12 or 12:15) (b- 20 past 11 or 11:20 ) (c- half past 4 or 4:30 )

ANSWERS: (a- 25 min to 2 or 1:35) (b- quarter to 4 or 3:45 ) (c- 10 to 7 or 6:50)

3. WRITE THE TIME IN FIGURES Quarter to seven =6:45

a. 20 past three
b. quarter post ten
c. 25 to eleven
d. quarter to two
e. 10 to ten
f. 6:45
ANSWERS: a. 3.20 b. 10.15 c. 10.35 d. 1.45 e. 9.50
4. LOOK CAREFULLY AT THESE CLOCK FACES. THEN WRITE THE TIME IN WORDS AND IN FIGURES.

ANSWERS: (a- 9 min to 5 or 4:51) (b- 22 min past one or 1:22) (c- 27 min past 2 or 2:27 )
P:38
TIME
5. USING A FIVE-RUPEE COIN, DRAW 6 CLOCK-FACES.

Then mark minutes: remember, 5 in each segment.

6. NOW, DRAW THE TIME ON YOUR CLOCK-FACES.

a. quarter to four
b. 3:43
c. 5:17
d. I8 min to 9
e. quarter past 7
f. 11:08

6. WRITE THE TIME IN FIGURES.
12 minutes to 3 2:48
a. 33 minutes past I2
b. I4 minutes to 7
c. I7 minutes past 2
d. 13 minutes to q
e. 29 minutes past I
ANSWERS: (a-12:33 ) (b- 6:46) (c- 2:17) (d- 8:47) (e- 1:29)

7. WHAT TIME DO THESE DIGITAL WATCHES SHOW? WRITE YOUR ANSWERS IN WORDS.
SOLUTION:
17 min past 1
40 min past 4
12 min past 10
8. COPY THIS TABLE IN YOUR NOTEBOOK SECOND COMPLETE IT
SOLUTION:
a. 23 min to 5 = 4:37
b. 21 min past 6 = 6:21
c.18 min to 3 = 2:42
d. quarter to 11 = 10;45
e.
9. WRITE THE TIME THAT IS:

I0 minutes earlier than 4:15
4:05

a. 6 minutes earlier than 9:30
b. 1/2 hour later than 10:55
c. 1/4 hour earlier than 7:30
d. 25 minutes earlier than 6:20
e. 30 minutes earlier than 3:12
f. 1/2 hour earlier than 5:15
g. 11 minutes later than I2:59
ANSWERS: (a- 9:24) (b- 11:25) (c- 7:15) (d- 5:55) (e- 2:42) (f- 4:45)
(g- 1:10)

10. FIND THE NUMBER OF MINUTES

3 hours 45 minutes
180 + 45 = 225 min

2h 10min b.I0h
5h35min d. 4h23min

P:39
Time: a.m second p.m
11. WRITE THESE CLEARLY AS MORNING TIME.
quarter post 3 3:l5 a.m

25 to six
5 o’clock
28 post two
quarter to four
ANSWERS: (a- 5:35 am) (b- 5:00 am) (c- 2:28 am) (d- 3:45 am)

12. WRITE THESE CLEARLY AS AFTERNOON-SECOND-EVENING TIME.
3 o’clock 3:00 p.m.

half post five
quarter to 10
12 minutes to 6
23 minutes to 2
eleven thirty
quarter post 4
ANSWERS: (a- 05:30 pm) (b- 09:45 pm) (c- 05:48 pm) (d- 01:37 pm)
(e- 11:30 pm) (f- 04:15 pm)

13. WHAT TIME WILL IT BE 3 HOURS AFTER:
11:00 p.m. 2:00 a.m.

6: 15 a.m.
8:40 a.m
10:10 a.m.
I2 midnight
ANSWERS: (a- 9:15 am) (b- 11:40 am) (c- 1:10 pm) (d- 3:00 am)

14. WHAT TIME WAS IT 4
HOURS EARLIER THON:
2:I5 p.m. I0:I5 a.m.

a. 7:30 a.m.
b. 2:05 a.m.
c. 10:20 p.m.
d. 12 noon
ANSWERS: a. 3:30 am b. 10:05 pm c. 6:20 pm d. 8:00 am
P:40
Time: The 24-Hour Clock

15. WRITE THE TIME AS IT WOULD BE ON THE 24-HOUR CLOCK.
4:10 p.m. + 12 =16:10 hours
4:05 a.m. = 04:05 hours
a. 9:00 p.m.
b. 12:02 a.m.
c. 2:00 p.m.
d. 8:23 p.m.
e. 3:15 p.m.
f. 11:05 p.m.
ANSWERS: a. 09:00 hours b. 12:02 hours c. 14:00 hours d. 20:23 hours e. 15:15 hours f. 23:05 hours

16. Write as I2-hour clock time, using a.m. second p.m.
06:15 hours = 6:15 a.m.

18:03 hours
0520 hours
1716 hours
0000 hours
0045 hours
I200 hours
ANS;
05:20 am
17:16 am
00:00 am
00:45 am
I2:00 pm
17. ANSWERS: THE QUESTIONS GIVING 24-HOUR CLOCK TIME.

a. An airbus Left Karachi at 18:40 hours second “arrived at
Peshawar 2% hours Later. At what time did it arrive at Peshawar?
b. A train left Cantt Station in Karachi at 09:10 hours second reached Multan 15 hours later. What time was that?

P:41

TIME: USING TIMETABLES

1. USE SID’S TIMETABLE TO ANSWERS: THESE QUESTIONS.

How long does it take Bus to travel from Planet City to Rocket Bay? …13 hours 35 minutes

a. How long does Bus 2 take to travel from Startown to Planet City?

b. If Sid needs to be in Planet City at 14:30 hours, which bus should he catch from Startown?

c. At Moonrock, Sid just misses Bus I. How long must he wait for Bus 2 to arrive?

d. What is the total journey time of Bus 2 from Startown to Rocket Bay?

2. Study the train timetable, then ANSWERS: these questions

How long does Train I take to travel from Colombo
Fort to Nanu Oga? 6 hours 8 minutes

a. If I catch Train I, what will my total journey time be from Colombo Fort to Badulla?

b. At Nanu Oga, a passenger who wants to travel to Badulla just misses Train?

c. How long must he wait for the next train? If a doctor needs to be in Ksecondy to see a patient at 14:00 hours, which train should she catch from Colombo Fort? How long will she have for herself at Ksecondy before her appointment?

P:42
PLAYING WITH TIME: CONVERSION

1. How many minutes in:
6 h 47 min 407 min

a. 8h 15min
b. 24h
c. 10 h 20 min
d. I8 h 25 min

2. HOW MANY HOURS SECOND MINUTES IN:
l02 min I h 42 min

a. 275 min
b. 575 min
c. 400 min
d. 8l0 min

3. WRITE VERTICALLY SECOND SOLVE

a. 58min+42min
b. 1 h 23 min+ 50 min
c. 4 h l6min+1 h 2min

4. WRITE VERTICALLY SECOND SUBTRACT
a. I h 34 min – 48 min
b. 6 h 7min- l h l2min
P:43
CONVERSION: MINUTES SECOND SECSECONDS

1. IF 60 SECSECONDS MAKE 1 MINUTE, HOW MANY SECSECONDS (SEC) IN:
4 min (4 X 60) = 240 sec

a. 5 min
b. 25 min
ANSWERS: (a- 300 sec) (b- 1500 sec)
2. HOW MANY SECSECONDS IN:
2 min 41 sec (2 X 60) + 41 = 161 sec

3 min 15 sec
21 min 30 sec
90 min 18 sec
ANSWERS: (a- 195 sec) (b- 1290 sec) (c- 5418 sec)

3. HOW MANY MIN SECOND SEC IN:

69 sec (69 + 60) = I min 9 sec

a. 85 sec
b. 200 sec
c. 103 sec
d. 3I6 sec

HOW MANY SEC IN:
3h…3x60x60sec = I0,800 sec

a. 2h
b. 9h
c.4h
d. 24h(I day)
ANSWERS: (a- 7200 sec) (b- 32400 sec) (c- 14,400 sec) (d- 86400 sec)

5. WE KNOW THAT I H = 3600 SEC. QUICKLY CONVERT THESE INTO SEC.
I h 20 min 3600 +
(20 X 60) = 3600 + I200 = 4800 sec

I h I5 min
2h 5min
I h44min
2h20min

6. WRITE VERTICALLY SECOND COMPLETE.

44+ sec + 28 sec
59 sec – 28sec
I min I5 sec + 45 sec
7 min 32 sec + 3 min 28 sec
8 min I0 sec – 2 min 25 sec

P:44
PLAYING WITH TIME: WORD PROBLEMS

1. Tahir is training to swim for the national championships. For 7days, he kept a record of when he began each swimming practice second when he finished. COPY AND COMPLETE the table to find out how long he practiced each day.

2. THINK CAREFULLY, THEN ANSWERS: THESE QUESTIONS.

a. An express bus left Town A at 18:15hours 1nd reached Town B at 21:05 hours. How long did the journey take?

b. A tennis match between Ayesha second Tonia started
at 3:20 p.m. second ended at 7:05 p.m. How Long did the
match Lost?

c. Mrs Majid wants her coke to be ready at 4:00 p.m. If the cake takes 45 min to bake, at what time must it be put in the oven?

Write 2 min 28 sec in secseconds.
Write this date in words: 2I.4.I5
Write in 24 h clock time: 8:32 p.m.
Write in min second sec: 84 sec
Write in short form: 3 September I972.
Write in I2 h clock time: I9:40 h.
Write the time that is I5 min later than 9:46 a.m.
Write in sec: I h 5 min.
Write the date that is 2 weeks before 21 May.

NOW SOLVE THESE.

a. Shaista went to bed at
2I:40 hours second got up at
06:30 hours. How long did
she sleep?

b. Sahir took I h 22 min to do his English homework, 45 min to do his maths
homework, second IO min to
do his Urdu. How long did
he take to complete all his
homework?

P:45
REVIEW

1. WRITE THE NUMBER, PLACING YOUR COMMA(S) CORRECTLY.

a. eighteen thousand second forty-seven

b. three lakh, two thousand, eight hundred second sixtg-four
2. WRITE IN EXPANDED FORM.
a. 27,02
b. 5,09,624
SOLUTION:
a. 27,02 = 20,000 + 7,000 + 0 + 20 + 9
b. 5,09,624 = 500,000 + 0 + 9,000 + 600 + 20 + 4

3. FILL IN THE BLANKS.

a. 62,824;————-; ————-,63, I 24; 63,224
b. I78,699; I 79,699; ————–;————–
ANSWERS: (a- 62,924 ; 63,024 ) (b- 180,699 ; 181,699)
4. UNDERLINE THE SMALLEST NUMBER.

a. 864,509; 864,905; 864,950
b. 719,024; 718, 240; 781,004

5. WRITE VERTICALLY SECOND COMPLETE.
a. 48,I68 + I5,777 + I37,692

b. 4,60,421 – 2,79,‘53

6. Multiply by I00 second place in periods.
a. 279
b. I507
c. 73I
ANSWERS: (a- 27,900) (b- 15,0,700) (c- 73,100)
7. DIVIDE BY I00.
a. 5 16

b. 63 18

c. 1,47,038

d. ‘972

e. 23,049

f. 9,62,704

ANSWERS: (a- 5 r 16) (b- 63 r 18) (c- 1470 r 38) (d- 9 r 72) (e- 9627 r 4) (f- )
8. CONVERT KG INTO G.

a. 49 kg
b. I4 kg
c. 68 kg
d. 50I kg
e I64 kg
f. 9 kg
ANSWERS: (a- 49,000g) (b- 14,000g) (c- 68,000g) (d- 501000g) (e- 164,)
(f- )
9. CONVERT ML INTO L SECOND ML.
a. 7000ml
b. 31,112ml
c. 62110 ml
d. 3,95,041 ml
e 2,600 ml
f. 29,500 ml

10. WRITE VERTICALLY SECOND MULTIPLY.

a. 1 862 x 58
b. I473 x 60
c 495 x 63
d. 957 x 700
SOLUTION:
A. 49996 B.88,380 C. 31,185 D. 669900

11. DIVIDE IN LONG DIVISION FORM.
a. I38 ÷ I8
b. 290 ÷ 40
c. 7329 ÷ 84
d. 506I ÷ 38
SOLUTION:
A. 7 R 12 B. 7 R 10 C. 87 R 21 D. 133 R 7

12. SOLVE THESE PROBLEMS, MAKING COMPLETE STATEMENTS.
A crossword book contains 540 puzzles. If Sue solves I2 puzzles every day, how many dogs will it take her
to complete the book?
b. If Adil con cycle I5 km
l(I5,000 / h) in one hour, how for con he cycle in I2
minutes?
c. Rido went to school at
7:20 a.m. second returned 61/2 h later. At what time did she reach home?

P:46
PART T W 0

1. LOOK CAREFULLY AT THE LIST OF NUMBERS, THEN TICK ALL THE MULTIPLES=OF 4.
6, 8, 10, 12, I7, 23, 28, 34, 40
ANSWERS:s: 6, 8, 10, 12, I7, 23, 28, 34, 40

2. TICK ALL THE MULTIPLES OF 9.

I5, 27, 48, 55, 81, 99, I26, I35, I44
ANSWERS:s: I5, 27, 48, 55, 81, 99, I26, I35, I44

3. LOOP THE COMMON MULTIPLES
a. MULTIPLES OF 4 4, 8, I2, I6, 20, 24, 28, 32

MULTIPLES of 6 6, 2, 8, 24, 30

b. MULTIPLES of 3 3, 6, 9, I2, 15, I8, 21, 24, 27

MULTIPLES of 5 5, 0, 5, 20, 25
ANSWERS:s: (a-12,12, 24,24 )(b- 15,15 )

4. WRITE THE SETS OF MULTIPLES, THEN LOOP THE COMMON MULTIPLES.

a. Multiples of 3 (up to 30) and multiples Of 4 (up to 32)

Multiples of 3 = 3,6,9,12,15,18,21,24,27,30

multiples Of 4 = 4,8,12,16,20,24,28,32
common multiples = 12,24

b. Multiples of 2 (up to 20) and multiples of 5 (up to 20)

Multiples of 2 = 2,4,6,8,10,12,14,16,18,20
multiples of 5 = 5,10,15,20
common multiples = 10 , 20
P:47
COMMON MULTIPLES: THE VENN DIAGRAM
I. STUDY THE DIAGRAM, THEN ANSWERS: THE QUESTIONS.

a. Write down the multiples of 4 as shown in the diagram.

b. Write down the multiples of 3 as shown in the diagram.

c. What are the common multiples of 3 second 4 shown here?

d. Which numbers are not multiples of 4 but only of 3?
e. Which numbers are multiples of neither 3 nor 4?

2. NOW MAKE A VENN DIAGRAM TO SHOW THE COMMON MULTIPLES OF 4 SECOND 6. IN YOUR RECTANGLE, INCLUDE ALL WHOLE NUMBERS UP TO 30. BELOW YOUR DIAGRAM, WRITE:

a. All the multiples of 4 shown.

b. All the multiples of 6 shown.

c. All the numbers which are not multiples of 4 but only of 6.
d. All the numbers which are multiples of neither 4 nor 6.

e. The common multiple(s) of 4 second 6 shown in your diagram.

P:48
LOWEST COMMON MULTIPLE (LCM)

Study the diagrams on page 47 second the Venn. diagrams you hove drown 22in your notebook. -Now
write down.

a. LCM of numbers 2 second 3

b. LCM of numbers 3 second 4
c. LCM of numbers 4 second 6

2. LIST THE FIRST 5 MULTIPLES OF THE FOLLOWING PAIRS OF NUMBERS. THEN FIND THE LCM
a. 8 second 12

b. 3second8

3. NOW FIND THE LCM OF THESE SETS OF THREE NUMBERS BY LISTING THE FIRST SIX (OR MORE) MULTIPLES OF EACH NUMBER.

2, 3, second 4
multiples of 2: 2, 4, 6,8, I0, I2
multiples of 3: 3, 6,9,l2,I5,l8
multiples of 4: 4, 8, I 2, I 6,20,24
LCM = I2

a. 2, 4, second 5
b. 6, 7, second I4

c. 3,4,second6
d. 3, 8, second I2
4. THINK CAREFULLY SECOND COMPLETE.
a.If we add an even number to on other even number, we get on ———— number.
b. If we odd on odd number to another odd number, we get on ———- number.
c. If we add an even number to an odd number, we get
on ———- number.
SOLUTION:
A. EVEN B. EVEN C. ODD
P:49
INTRODUCING FACTORS

1. Just as Sid did with his pebbles, orange 20
counters in as many types of equal groups as you con. Then, COPY AND COMPLETE this table, second write ll the factors of 20.

2. By arranging counters using other small objects, find the Factors of these numbers.
a. I5
b. ll
c. I8
d. 21

e. 24
f. 9
P:50

MORE ABOUT FACTORS: COMMON FACTORS SECOND HCF

Is I I a factor of 24?»… No
(24 -1- I I = 2 r 2)

Is I2 a factor of 36?
Is 7 a factor of 45?
Is 6 a factor of 66?
Is 20 a factor of I00?
Is I6 a factor of 64?

2. WRITE DOWN THE FACTORS OF THESE NUMBERS. HOW MANY FACTORS DOES EACH NUMBER HAVE?

a. 25
b. 36

c. 54

d.32

e. 45
f. 50

Write the factors of these pairs of numbers, second ;I
underline the common factors.

a. I2, I5

b. I6, 20

c. 25, I5
d. I0, 32

4. FIND THE HCF OF THE FOLLOWING.

a. 32, 24

b. 50, 25
c. 48, 30
d. A2, 70

P:51

1. FIND THE COMMON FACTORS SECOND HCF OF EACH OF THE FOLLOWING SETS.
A: 9, 12 second 15
9= 1, 3, 9
12=1, 2, 3, 4, 12
15=1, 3, 5, 15
HCF= 3
COMMON FACTOR=1, 3
B: 5, 25 second 35

5=1, 5
25=1, 5, 25
35=1, 5, 7, 35
HCF=5
COMMON FACTOR=1, 5
C: 18, 20 second 24

18=1, 2, 3, 6, 9, 18
20=1, 2, 4, 5, 10, 20
24=1, 2, 3, 4, 6, 8, 12, 24
HCF=2
COMMON FACTOR=1, 2
D: 18, 27 second 39

18=1, 2, 3, 6, 9, 18
27=1, 3, 9, 27
39=1, 3, 13, 39
HCF=3
Common factor=1, 3
E: 12, 16 second 20

12=1, 2, 3, 4, 6, 12
16=1, 2, 4, 8, 16
20=1, 2, 4, 5, 10, 20
HCF=4
Common factor=1, 2, 4
F: 14, 49 second 28

14=1, 2, 7, 14
49=1, 7, 49
28=1, 2, 4, 7, 14, 28
HCF=7
Common factor=1, 7

2. ARE THESE STATEMENTS TRUE (T) OR FALSE (F)

A: 5 is a factor of 30
30=1, 2, 3, 5, 6, 10, 15, 30
So statement is TRUE
B: 1, 3 second 4 are only common factors of 12 second 24

12=1, 2, 3, 4, 6, 12
24=1, 2, 3, 4, 6, 8, 12, 24
Common factors=1, 2, 3, 4, 6, 12
So the statement is FALSE
C: 3 is HCF of 12 second 18

12= 1, 2, 3, 4, 6, 12
18= 1, 2, 3, 6, 9, 18
So the statement is FALSE, HCF is 6
D: the HCF of 10 second 20 is 10.

10=1, 2, 5, 10
20=1, 2, 4, 5, 10, 20
HCF=10
So the statement is TRUE.
E: 6 is a factor of 9.

9=1, 3, 9
So the statement is FALSE.

3. LOOK AT THESE PAIRS OF NUMBERS. CIRCLE THE PAIRS THAT ARE CO-PRIME NUMBERS:
A: 4 second 8
4= 1, 2, 4
8= 1, 2, 4, 8
NOT co-prime
B: 2 second 10

2= 1, 2
10= 1, 2, 5, 10
NOT co-prime
C: 5 second 9

5=1, 5
9=1, 3, 9
CO-PRIME NUMBERS

D: 2 second 17
2= 1, 2
17= 1, 17
CO- PRIME NUMBERS

E: 5 second 10

5= 1, 5
10=1, 2, 5, 10
NOT co-prime

F: 14 second 4
14= 1, 2, 7, 14
4=1, 2, 4
NOT co-prime
4. FACTORS GAME.

P:52

1. SID SPACEWALKER IS TRYING TO REMEMBER ALL THE FACTORS OF NUMBERS FROM 1- 18. HELP HIM FILL IN THE TABLE.

NUMBER FACTORS
1 1
2 1,2
3 1,3
4 1,2,4
5 1,5
6 1,2,3,6
7 1,7
8
9
10
11
12
13
14
15
16
17
18

SOLUTION:
NUMBER FACTORS
1 1
2 1,2
3 1,3
4 1,2,4
5 1,5
6 1,2,3,6
7 1,7
8 1,2,4,8
9 1,3,9
10 1,2,5,10
11 1,11
12 1,2,3,4,6,12
13 1,13
14 1,2,7,14
15 1,3,5,15
16 1,2,4,8,16
17 1,17
18 1,2,3,6,9,18

2- NEXT SID WANTS TO SHOW HIS RESULTS ON A COLUMN GRAPH. CAN YOU DRAW THE GRAPH FOR HIM?

3. LOOK AT THE GRAPH CAREFULLY, THEN WRITE DOWN THE NUMBERS WHICH HAVE ONLY TWO DIFFERENT FACTORS.
SOLUTION:
Sid has written his answer upside down 2,3,5,7,11,13,17
DID YOU FIND SEVEN SUCH NUMBERS ALTOGETHER? SID HOS WRITTEN HIS ANSWERS: UPSIDE DOWN.

4. Think carefully, then tick ( ) the numbers which are
prime numbers.
a.I5
b. 31
c. 24
d. 21
e. 32
f. 25
g. 29
h. 3
I. 37
j. I7
k. 45
l. I I
m. I8
n. 33
0. 25

P:53
PRIME NUMBER
P:54
PRIME NUMBERS AND COMPOSITE NUMBERS

3. Look at the numbers. Are they prime (P) or composite (C) numbers? Write your ANSWERS:s in your notebook. 49…. C (factors: I, 7, 49)

a. 35
b. 33
c. 57
d.41
e. 54
f. 83

a. Are there any even prime numbers? Can you explain?
b. How many composite numbers and how many
prime numbers are there between I and 50?
c. What is the greatest prime number which is less than 40?
d. What is the smallest prime number between I and I00?
e. What is the greatest composite number below
I00?

5. COPY THESE SENTENCES IN YOUR NOTEBOOK AND FILL IN THE BLANKS.

a. Every prime number except is odd.
b. Each prime number has exactly ——— factors.
c. Number ——— is neither prime nor composite.
d. All composite numbers have at Least ——— factors.
SOLUTION:
a. 2 b. 2 c. 1 d. 3

6. USING PATTERNS OF YOUR OWN CHECK WHETHER. SID’S DISCOVERY IS CORRECT. CAN THESE NUMBERS BE ARRANGED IN EXACT RECTANGLES?

a. 25
b. I2
c. I7
d I5
e. 8
f. 22

P:55
PRIME FACTORIZATION

1. Here is another prime factorization.
Prime factors of I8 = 2, 3, and 3
93 OR
66 3x 2×3= I8
Now draw trees of your own to show the prime factors of these.
a. 5
b. 20
c. 14
d. s
e. 21
f. 22
g. I6
h. 27
i. 42

2. DRAW AS MANY DIFFERENT TREES AS YOU CON TO SHOW THE PRIME FACTORS OF THESE NUMBERS.
a.40
b. 48
c. so
d. 24
e. 50
f. 72
A. Write down the list of prime numbers from i00 to 200.

b. Find the difference between every pair of two consecutive prime numbers.

P:56 TESTS OF DIVISIBILITY

I. CIRCLE THE EVEN NUMBERS.

a. 200
b. 126
c. 427
d. 187
e. 134
f. 2032
SOLUTION:
200,126,134,2032
2. WHICH OF THE FOLLOWING ORE DIVISIBLE BY 3?

a. 624
b. 2358
c. I30
d. 3612

3. WHICH OF THESE ARE DIVISIBLE BY 9 ?
a. 188
b. 2439
c. 693
d. I800

4. WHICH OF THESE ARE DIVISIBLE BY 5?
a. 2900
b. 6054
c. 4085
d. 840,050

P:57 THE LCM AND HCF 0 LARGER NUMBERS:
THE DIVISION METHOD

1. FIND THE PRIME FACTORS AND THEN THE LCM OF THESE PAIRS OF NUMBERS, USING THE DIVISION METHOD.
a. 18 & 24
b. I2 and l6
c. 20 & 25

d. 24 and 32
2. USE THE DIVISION METHOD TO FIND THE PRIME FACTORS OF THESE NUMBERS.
a. 84
b. 1I7
c. 333
d. I26
e. 520
f. 99

P:58 MORE ABOUT THE DIVISION METHOD

1. Using the division method, find the HCF of these pairs of numbers.

a. I2 and 20
b. 36 and 24

c. I4 and 35

d. 48 and 30

e. I5 and 21

f. I2I and I32

4. NOW, FIND THE HCF AND LCM OF THESE PAIRS.

a. 30 and I2

b. I8 and 56

c. I6 and 48
d. 36 and 60

e. 24 and 39

f. 22 and I32
5. IN YOUR NOTEBOOK, DRAW THE TABLE SHOWN ABOVE. WORK OUT THE RESULTS FOR THESE PAIRS OF NUMBERS.
a. I0 and I5
b. 32 and 48
c. I8 and 30
d. 28 and 70
6. Use the division method to find the prime factors of these numbers (do not forget your tests of divisibility):

a. 230
b. 3200
c. 459
d. 4545

P:59
REVIEW

1. WRITE DOWN THE FACTORS OF EACH NUMBER, THEN FIND THE HCF OF EACH PAIR.
a. 9 and I5

b. I2 and 30
c. 7 and 21
d. 25 and 20

2. DRAW A VENN DIAGRAM TO SHOW THE COMMON MULTIPLES OF 5 AND 4 LESS THEN 40. WHAT IS THE LCM?
3. FIND THE LCM BY LISTING THE FIRST I0 MULTIPLES OF EACH NUMBER.

a. 2, 4, and 5
b. 8, 6, and I2
c. 2, 3, and 4
d. 5, 4, and I0
4. WRITE THE FACTORS OF THESE NUMBERS.
a. 22
b. 48
c. 63
d. 32
e. 39
f. 56

5. WRITE THE COMMON FACTORS AND HCF OF THESE PAIRS OF NUMBERS.
a. 20, 32
b. 56, 28
c. I2, 72
d. 84, 24

6. FIND THE COMMON FACTORS AND HCF OF THESE.
a. 8, 20, and 32
b. 28, 21, and 35
c. I5, I8, and 24
d. I6, 20, and 40

e. I0, I2, and 22
f. 27, 36, and 45
7. CIRCLE THE PAIRS OF NUMBERS THAT ARE CO-PRIME.
a. 2and7
b. 2and I2
c. I7and4

d. 7and 11
8. TICK THE PRIME NUMBERS ONLY.
a. 51
b. 630
c. 37
d. l9
e I62
f. 5005
g. 101
h. 41
i. 217

Composite numbers have only two factors.
The HCF of I2 and 20 is 2.
5 is a factor of 1,00,000.
I5 is not a factor of 3000.
The LCM of 4 and I2 is 48
The LCM of 6 and I0 is 30
51 is not a prime number.
9 is not a factor of I620.

USE THE DIVISION METHOD TO SHOW THE PRIME FACTORS OF THESE.
a. 240
b. 603

c. 715
11. FIND THE LCM AND HCF USING THE DIVISION METHOD.
a. 36 and 42
b. I5 and40
P:60
P:61 REMEMBERING FRACTIONS

I. WRITE THE FRACTION FOR THE COLOURED PORT OF EACH SHAPE

2. WRITE FRACTIONS RD MATCH THE WORDS. Denominator 6, Numerator 4 = 4/6

Numerator 5, Denominator 7 =

Denominator 10 Numerator 3 =

3. WRITE > ,< OR =
2/5 — 3/5 5/8 — 3/6 5/8 — 5/8 6/8 — 6/7
4. WRITE FIRST IN ASCENDING ORDER AND THEN IN ASCENDMG ORDER.

5. WRITE WORDS IN THE BLANKS.
a. Fractions with different denominators are called———–
b. In like fractions, the————-the numerator, the greater the fractional number.
c. In the pair of fractions 2/7 and 3/7, 3/7is————-than 2/7
d. In the pair of fractions 3/9 and 3/8, 3/9 is————-than 3/9
ANSWERS: a. unlike fraction b. greater c. greater d. greater
6. WRITE FRACTIONS IN THE BLANKS

4/10 +3/10
7/9 – 3/9 2/9 + 3/9 + 3/9

7. HOW MANY / MUCH IS:

1/3 of 36 pens? —- 12 pens
(1 )/6 of 2460 km
1/10 of 120 kg?
1/8 of 48 tickets?
1/9 of Rs 36,345?

I. WRITE THE EQUIVALENT FRACTIONS THAT MATCH THE DIAGRAMS.

2. FOR EACH FRACTION, WRITE 3 EQUIVALENT FRACTIONS.
1/5

2/5

2/7

1/2

3/4

3/10

3. COMPLETE THESE EQUIVALENT FRACTIONS, WRITING THE NUMERATOR OR DENOMINATOR
IN PLACE OF *.
1/2 = /4 10/100 = 50/ 2/3 =/6 5/50 = 10/ 7/10 = /30
20/40 =40/ 3/5= 9/ 11/70= /140 3/10 =6/ 21/30 = /60

4. FOR EACH FRACTION, WRITE 4 EQUIVALENT FRACTIONS.

1/30 2/40 7/12 4/20 3/16 8/14

P:63

REDUCING EQUIVALENT FRACTIONS

I. WRITE THE EQUIVALENT FRACTIONS THAT MATCH THE DIAGRAMS.
2. COMPLETE THESE EQUIVALENT FRACTIONS.
16/20 = 4/ 9/ = 3/8 27/30 = 9/ 15/50 = /10
/10 = 3/5 36/ = 12/18 10/ = 1/3 32/40 = 4/

3. FOR EACH FRACTION GIVEN BELOW, HOW MANG
EQUIVALENT FRACTIONS CAN YOU MAKE BY DIVIDING BOTH THE NUMERATOR AND THE
DENOMINATOR BY THE SAME FACTOR?
a 16/20 b 24/32 C 30/50 d 24/30 i
e 36/48 f 45/90 G 20/60 h 49/63 32/40

P:64
REDUCING EQUIVALENT FRACTIONS: LOWEST TERMS

4. IN EACH SET OF EQUIVALENT FRACTIONS, CIRCLE THE FRACTION THAT IS IN ITS LOWEST TERMS.

A 2/5 4/10 6/20 8/15
B 6/14 12/28 3/7 9/21
C 9/30 3/10 12/40 21/70
SOLUTION:
5. REDUCE
THESE FRACTIONS TO THEIR LOWEST TERMS.
A b C D e f
18/24 15/25 10/12 36/48 12/18 14/42
6. WRITE THE HCF OF THESE PAIRS OF NUMBERS.
12 and 18…HCF =6
a. 2o and 16
b. 17 and 7
c. 35 and 45
d. 35 and 14

7. REDUCE THESE FRACTIONS TO THEIR LOWEST TERMS.

a 12/20 b 10/100 C
30/31
d 44/99 E

25/35 f 33/110
8. WRITE THE FRCICTION THAT IS:

a. Equivalent to 2/3 and has a Denominator of 24.

b. Equivalent to 16/32 but is in its Lowest terms.

P:65

REMEMBERING LIKE AND UNLIKE FRACTIONS

I. CIRCLE THE SETS OF LIKE FRACTIONS.

A 3/12 2/11 5/12
B 9/20 8/10 16/20
C 4/14 1/15 6/15
D 91/100 96/101 89/100
2. ARRANGE THESE LIKE FRACTIONS IN ASCENDING ORDER.
a 18/20 11/20 19/20 3/20 5/20
b 21/25 15/25 17/25 11/25 22/25

3. WRITE WHETHER THE FOLLOWING PAIRS OF FRACTIONS ARE LIKE OR UNLIKE.

a 3/12 , 5/12 b 10/15 , 12/15 c 18/20 , 19/21
d 11/20 , 19/20 e 6/15 , 8/14 f 4/9 , 4/11
4. ARRANGE THESE UNLIKE FRACTIONS INASCENDING ORDER
A 5/12 5/15 5/9 5/16
B 6/13 6/7 6/12 6/11
C 8/14 8/17 8/12 8/16
d 10/18 10/22 10/19 10/11

P:66 PROPER AND IMPROPER FRACTIONS

1. LOOK OT THE SHOPES AND ANSWERS: THE QUESTIONS IN YOUR NOTEBOOK.

How many sixths ore coloured? 4

a. How many fifths are Coloured?

b. How many thirds ore Coloured?

c. How many sixths are Coloured?

2. LOOK CAREFULLY AT THESE OF FRACTIONS AND CIRCLE THE IMPROPER FRACTIONS.

3. IN YOUR NOTEBOOK, DRAW A TABLE LIKE THIS (BUT MOKE IT LONGER).

NOW PLACE ALL THESE FRACTIONS IN THE CORRECT COLUMN.

P:67 MIXED NUMBERS AND IMPROPER FRACTIONS

1. LOOK OT THESE SHAPES CAREFULLY. NOTE DOWN THE COLOURED FROCTIONS AS (I) IMPROPER FRACTIONS AND (II) MIXED NUMBERS.
2. EXPRESS THESE WHOLE NUMBERS AS IMPROPER FRACTIONS.

3. EXPRESS THESE MIXED NUMBERS AS IMPROPER FRACTIONS.

P:68 MIXED NUMBERS AND IMPROPER FRACTIONS

4.CHANGE THE WHOLE NUMBERS INTO THE IMPROPER FRACTION INDICATED.

5 into thirds——

3 into sixths
2 into tenths
4 into quarters
7 into fifths
6 into thirds
5 into eighths

5. CHANGE THESE IMPROPER FRACTIONS INTO WHOLE NUMBERS.
a 12/4 b 20/10 c 18/6
d 15/5 e 24/6 f 14/7
g 12/3 h 30/5 i 32/4
ANSWERS: a.3 b.2 c.3 d.3 e. 4 f.2 g.4 h. 6 i.8

6.USING THE SHORT METHOD CHANGE THESE MIXED NUMBERS INTO IMPROPER FRACTIONS.
A 31/4 = /4 b 23/10 = /10 c 3 7/8 = /8
D 15/12 = /12 e 51/4 = /4 f 26/8= /8
G 35/7 = /7 h 64/11 = /11
SOLUTION:
A 3 1/4 =(3X4+1)/4 = 13/4
B 2 3/10 = (2X10+3)/10 = 23/10
C 3 7/8 = (3 X 8 +7)/8 = 31/8
D 1 5/12 = (12 X 1+5)/12 = 17/12
E 51/4 = (5 X 4+1)/4 = 21/4
F 26/8 = (2 X 8 +6)/8 = 22/8
G 35/7 = (3 X 7+5)/7 = 26/7
H 64/11 = (6 X 11+4)/11 = 70/11

P:69 MIXED NUMBERS AND IMPROPER FRACTIONS

7. USE THE SHORT METHOD TO CHANGE THESE INTO MIXED NUMBERS.
A 9/2 b 15/4 c 45/8
D 7/3 e 50/7 f 36/11
G 8/5 h 22/10 i 62/8
J 12/7 k 30/8 l 35/6

8. REDUCE THESE IMPROPER FRACTIONS TO THEIR LOWEST TERMS. THEN, CHANGE THEM INTO MIXED NUMBERS.
A 6/4 b 15/6 c 150/100
D 14/8 e 18/12 f 120/70
G 9/6 h 15/10 i 54/36
J 12/9 k 20/6 l 28/21
P:70 FRACTIONS AND DIVISION

a 26÷5=
b 31÷8=
c 43÷4=
d 52÷7=
e 53÷10=
f 45÷8=
g 20÷6=
h 135÷10=
i 150÷20=
j 58÷6=
a 26 ÷ 5 = 26/5 = 5 1/5
b 31 ÷ 8 = 37/8 =3 7/8
c 43 ÷ 4 =43/4 = 10 3/4
d 52 ÷ 7 = 73/7 =7 3/7
e 53 ÷ 10 = 10
f 45 ÷ 8 = 53/10
g 20 ÷ 6 = 32/6 = 31/3
h 135 ÷ 10 = 138/10 = 13 1/2
I 150 ÷ 20 = 150/20 = 15/2 = 7 1/2
j 58 ÷ 6 = 58/6 = 9 4/6 = 9 2/3

2. REWRITE THESE DIVISIONS AS FRACTIONS.
a 13 ÷8=
b 21 ÷11=
c 15 ÷4=
d 100 ÷15=
e 4 ÷6=
f 84 ÷20=
a 13/8
b 21/11
c 15/4
d 100/15
e 4/6
f 84/20

3. REWRITE THESE DIVISIONS AS FRACTIONS. WHERE POSSIBLE, REDUCE THEM TO THEIR LOWEST TERMS.
a 18÷10=
b 100÷50=
c 25÷15=
d 84÷40=
e 30÷18=
f 56÷49=
g 15÷12=
H 60 ÷35=
A 18÷10= 18/10 ÷ 2 = 9/5
B 100÷50= 100/50 ÷ 10 = 10/5 ÷ 5 = 2/1
C 25÷15=25/15 ÷ 5 = 5/3
D 84÷40= 84/40 ÷ 4 = 21/10
E 30÷18= 30/18 ÷ 6 = 5/3
F 56÷49= 56/49 ÷ 7 = 8/7
G 15÷12= 15/12 ÷ 3 = 5/4
H 60 ÷35= 60/35 ÷5 = 12/7

P:71 COMPARING FRACTIONS: THE COMMON DENOMINATOR

I. COPY IN YOUR NOTEBOOK AND FILL IN THE MISSING SYMBOL > OR <.
A 8/9 ——– 4/9 b 23/32 ——– 21/32
C 5/12 ——– 3/12 d 38/100 ——– 77/100
2. COPY AND FILL THE MISSING SYMBOL < OR >.
A 8/17 ——– 8/20 b 10/100 ——– 100/150
C 6/21 ——– 6/15 d 50/100 ——– 50/70

3. REWRITE THESE FRACTIONS SO THAT THEY HAVE A COMMON DENOMINATOR.
A 1/2 and 1/4 B 3/5 and 7/15
C 2/3 and 5/6 D 11/16 and 1/6
A 1/2 X 2/2 = 2/4
2/2 and 2/4 is answer B 3/5 X 7/15 =/
3/5 X 3/3 = 9/15
So 9/15 and 7/15
C 2/3 X 5/6 =
2/3 X 2/2 = 4/6
SO 4/6 and5/6 D 11/16 X 1/6 =
11/18 and 3/18

4. REWRITE THESE FNOCTIONS SO” THAT THEY HAVE COMMON DENOMINATOR.
A 1/2 and 2/3 b 1/6 and 2/9 c 4/5 and 1/3
D 3/8 and 5/12 e 3/10 and 3/4 f 2/7 and 5/14
G 1/4 and 2/5 h 3/4 and 5/6
1/2 x 3/3 = 3/6 and 2/3 x 2/2 = 4/6 so 3/6 and 4/6

1/6 x 3/3 = 3/18 2/9 x 2/2 = 4/18 so 3/18 and 4/18

4/5 x 3/3 = 12/15 and 1/3 x 5/5 = 5/15 so = 12/15 and 5/15

3/8 x 3/3 = 9/24 and 5/12 x 2/2 = 10/24 so 9/24 and 10/24
3/10 x 2/2 = 6/20 and 3/4 x 5/5 = 15/20 so = 6/20 and 15/20

2/7 x 2/2 = 4/14 so 4/14 and 5/14

1/4 x 5/5 = 9/12 and 2/5 x 4/4 = 8/20 so = 5/20 and 8/20

4/3 x 3/3 = 9/12 and 5/6 x 2/2 = 10/12 so = 9/12 and

a 1/2 and 3/3 = 3/6 X 2/3 x 2/2 = 4/6 so 3/6 and 4/6
b 1/6 and 2/9 =3/18X 2/9 x 2/2 = 4/18 so 3/18 and 4/18
c 4/5 and 1/3 =12/15X 1/3 x 5/5 = 5/15 so 12/15 and 5/15
d 3/8 and 5/12 =9/24X 5/12 x 2/2 = 10/24 so 9/24 and 10/24
e 3/10 and 3/4 =6/20X 3/4 x 5/5 = 15/20 so 6/20 and 15/20
f 2/7 and 2/2 = 4/14 so 4/14 and 5/14
g 1/4 and 5/5 = 5/20 and 2/5 x 4/4 = 8/20 so 5/20 and 8/20
h 4/3 and 3/3 = 9/12 and 5/6 x (2 )/2 = 10/12 so 9/12 and 10/12

5. REWRITE THESE PAIRS OF FRACTIONS SO THAT THEY HAVE A COMMON DENOMINATOR. THEN FILL IN THE CORRECT SYMBOL > OR <.
a 2/7 —– 3/10 b 4/11 —– 3/8 c 3/8 —– 4/5
d 9/14 —– 19/28 e 7/10 —– 8/15 f 11/12 —– 9/10
g 2/9 —– 3/7 h 5/9 —– 20/27
ANSWERS: (a- <)(b- <)(c- <)(d- <)(e- >)(f- >)(g- <)(h- <)

6. LOOK CAREFULLY AT THE SETS OF FRACTIONS. REWRITE THEM SO THAT THEY HAVE A COMMON DENOMINATOR. THEN, WRITE THEM IN ASCENDING ORDER.
a 4/5 , 7/10 , 9/20 b 5/6 , 4/9, 13/18 c 3/9 , 2/3, 5/6
d 5/8 , 11/16, 3/4 e 3/4 , 5/6 , 3/8 f 3/10, 1/4, 7/2
g 2/3 , 8/21, 4/7 h 3/8 , 5/12, 11/24
a- 4/5 x 4/4 = 16/20 7/10 x 2/2 = 14/20 and 9/20 ascending order is 9/20 < 7/10 < 4/5

b- 5/6 x 3/3 = 15/18 4/9 x 2/2 = 8/18 and 13/18 8/18 < 13/18 < 15/18 ascending order is 4/9 ,13/18 , 5/6

c- 3/9 x 2/2 = 6/18 2/3 x 6/6 = 12/18 5/6 x 3/3 = 15/18 6/18 < 12/18 < 15/18 ascending orders 3/9 , 2/3 , 5/6

d- 5/8 x 2/2 x 10/16 and 3/4 x 4/4 = 12/16 10/16 < 11/16 < 12/16 so ascending order is 5/8 , 11/16 , 3/4

e- 3/4 x 6/6 = 18/24 5/6 x 4/4 = 20/24 3/8 x 3/3 = 9/24 9/24 < 18/24 < 20/24 so ascending order is 3/8 , 3/4 , 5/6

f- 3/10 x 2/2 = 6/20 1/4 x 5/5 = 5/20 and 7/20 5/20 < 6/20 < 7/20 so ascending order is 1/4 , 3/10 , 7/20

1. COPY AND COMPLETE
a 5/12 + 2/11 b 5/21 + 6/21 c 4/18 + 3/18
d 3/14 + 8/18

2. ADD THESE, WRITING YOUR ANSWERS:S FIRST OS IMPROPER FROCTIONS OND THEN OS MIXED NUMBERS, WHEREVER POSSIBLE.
a 3/4 + 3/4 b 8/15 + 9/15

3. ADD THESE FRACTIONS, GIVING YOUR ANSWERS:S AS MIXED NUMBERS AND REDUCING THEM TO THE LOWEST TERMS.
a 4/12 + 10/12 b 3/10 + 7/10 +5/10
c 11/15 + 9/15 d 5/8 + 6/8 +1/8

a 11/3 +44/10 b 10 2/7 + 13/7 c 65/9 + 6 2/9
d 155/8 + 6 1/8

a 53/5 + 2 1/10 b 23/8 +31/4 c 45/9 + 3 1/18
d 97/10 + 2 1/5

2. SOLVE THE PROBLEM IN..YOUR NOTEBOOK.
PARVEZ CYCLES 1 1/4 KM IN THE MORNING AND 2 2/5 KM IN THE EVENING. HOW FOR DOES HE CYCLE ALTOGETHER?
a. TANIA AND RIDA WERE MAKING SOME PAPER FLOWERS. TANIA USED 17/10 M OF PAPER AND
RIDA 1 1/10 M. HOW MUCH PAPER DID THEY USE
ALTOGETHER?

a 22/5 + 3 7/10 b 82/3 + 2 5/6
c 13/8 +2 3/4 d 67/10 +33/5
a 31/2 +1 3/4 + 1/8 b 41/3 + 6 1/4 + 1/2
c 53/10 + 11/5 +1 1/2 d 62/9 + 1/3 +10 2/3
P:75 SUBTRACTION OF FRACTIONS

1. COPY AND COMPLETE

a 11/12 – 6/12 b 17/18 – 10/18
c 13/15 – 4/15 d 19/24 – 4/24

a / b / c /
d / e / f /
g / h / i /
j / k / l /

a / = / b / = / c / = /
d / = / e / = / f /= /
g / = / h / = / i / = /
2. COMPLETE THESE

a 25/8 – 12/8 b 1011/12 – 86/12
c 49/10 – 26/10 d 97/10 – 86/10
3. SUBTRACT THESE BY FIRST REWRITING THE FRACTIONS WITH A COMMON DENOMINATOR.
a 5/8 – 1/2 b 7/8 – 3/4 c 3/8 – 1/4
d 1/5 – 1/20 e 3/4 – 1/8 f 2/3- 1/6
a 11/12 – 2/3 b 1/2 – 6/16
c 4/5 – 9/15 d 2/3 – 2/8

P:76 SUBTRACTION OF MIXED NUMBERS

1. COMPLETE THESE
a 61/2 – 41/8 b 95/6 – 4 1/2 c 53/4 – 12/3
d 78/9 – 55/18 e 79/10 – 2 2/5 f 82/3- 3 1/12

2. NOW, SOLVE THESE PROBLEMS.

a. In one six that a batsman hit, the ball travelled 70 3/4 m. In the next, the ball travelled 90 1/2 m. How much further did the second ball travel than the first?
SOLUTION:
First ball traveled = 70 2/3 m
Second ball traveled = 90 1/5 m
Second ball traveled further than first bell = 90 1/5 – 70 2/3
For
90 1/5 – 70 2/3
= 1/5 x (4 )/4=4/24
3/4 x 5/5 = 15/20
= (4-15)/20 = – 11/20 (write sign of large number)
Because fraction has “”s -ve sign.
Add and subtract 1, such that
1/5 – 3/4 = 1 – 1- = 11/20 =
20/20 – 11/20 – 1
=
(20-11)/20-1= 9/20-1
And 90 -70 = 20
90 1/5 – 70 3/4 = (20-1) 9/20= 19 9/20
So
Second ball traveled 199/20 m more than the ﬁrst ball.
b. A bucket contains 12 3/5 L of water. If Wasif uses 1 3/4 L for his water pistol, how much water is left in the bucket?
SOLUTION:
bucket contains water = 12 3/4 L
Wasif took water A=13/4 L
Water left in bucket: 12 3/4 L – 1 3/4 L
Now for
12 3/4 L- 13/4 L
3/5 X 5/5 = 15/20

12/20 < 15/20=> 3/(5 ) < 3/4

12 3/(5 ) – 13/4 = 11+1+3/(5 ) – 3/4
= 11+20/20 + 12/20 – 1 15/20
= 10 (20+12±15)/20 = 10 17/20
So there is 10 17/20 water left in bucket
3. COMPLETE THESE CAREFULLY
a 21/4 – 12/3 b 41/10 – 2 1/5 c 52/5 – 17/10
d 75/8 – 4 7/8 e 33/8 – 13/4 f 61/2- 43/5
g 91/4 – 63/5 h 81/3 – 21/4 i 101/6 – 83/4
j 85/12 – 4 5/6
SOLUTION:
a 21/4 – 12/3
1/4X 3/3 = 3/12
2/3X 4/4 = 8/12
3/12<8/12=>1/4< 2/3
2 1/4 – 1 2/3 = 2 1/4+ 1 – 1 2/3- 1
2 3/12 + 12/12- 1 8/12 – 1
SO
3/12 + 12/12- 8/12= (3+12-8)/12= 7/12
2 -1-1=0 b 41/10 – 2 1/5
1/5 X 2/2 = 2/10
1/10 < 2/10 => 1/10 < 1/5
4 1/10 – 2 1/5 = 3 1/10 + 1 – 2 1/5= 3 1/10+ 10/10 – 2 2/10
WHERE
1/10 + 10/10 = 2/10-9/10
AND
3-1=2
=> 4 1/10 – 2 1/5 = 19/10 c 52/5 – 17/10
2/5 X 2/2 = 4/10
4/10 < 7/10 => 2/5 < 7/10
5 2/5-1 7/10=4 2/5+1-

17/10
= 4 4/10+ 10/10 – 1 7/10
= (4-1) + ((4+10-7)/10) = 3 + 7/10
=> 5 2/5 – 1 7/10 = 3 7/10
d 75/8 – 4 7/8
5/6 < 7/8
= 6 5/8 + 1 – 4 7/8
= 6 5/8 + 8/8 -4 7/8
= 6 – 4 +
7/8 + 8/8 – 7/8
= 2 + (5+8-7)/8 = 2 + 6/8
= 23/4 e 33/8 – 13/4
3/8< 6/8 => 3/8 < 6/8
= 2+1 + 3/8 – 1 3/4
=2-1+(8+3-6)/8
= 1+ 5/8
=1 5/8 f 61/2- 43/5
=61/2 +10/10 -4 6/10
=5-4 + 5/10+ 10/10- 6/10
= 1+ (5+10-6)/10
=1+ 9/10
=1 9/10

g 91/4 – 63/5
/ h 81/3 – 21/4 i 101/6 – 83/4
j 85/12 – 4 5/6

P:77 SUBTRACTION OF MIXED NUMBERS: REGROUPING

4. COMPLETE THESA BY CHANGING MIXED NUMBERS INTO IMPROPER FRACTIONS.

a 5 2/3 -2 3/10
SOLUTION:
5 2/3 -2 3/10= (5X3+2)/3 = (2X10+3)/10
=17/3 – 23/10
=17/3 X10/10 -23/10 X 2/2
=170/30- 69/30
= 101/30 = 3 11/30 b 75/6 – 211/12
SOLUTION:
75/6 – 211/12 =(7X6+5)/6 – (2X12+11)/12

= 47/6 – 35/12
= 47/6 X 2/2 – 35/12

= 59/12 = 4 11/12
C 61/8 – 4 3/4
SOLUTION:
61/8 – 4 3/4 = (6X8+1)/8 – (4X4+3)/4
= 49/8 – 19/4
= 49/8 – 19/4 X 2/2

=49/8 – 38/8
= 11/8 = 13/8 D
91/3 – 45/6
SOLUTION:

91/3 – 45/6 = (9X3+1)/3 – (4X6+5)/6
= 28/3 X 2/2 – 29/6
= 56/6 – 290/6
= 27/6 = 4 3/6 = 41/2
5. NOW COMPLETE THESE BY THE REGROUPING METHOD.
A
82/7 – 43/14
SOLUTION:
82/7 – 43/14
= (8X7+2)/7 – (4X14+3)/14
=58/7 – 59/14
=58/7 X 2/2 – 57/14 = 4 1/4 b 71/4 – 23/5
SOLUTION:
71/4 – 23/5 =29/4 – 13/5
=29/4 X 5/5 – 13/5 X 4/4
=145/20 – 52/20 = 93/20 = 413/20

C

95/8 – 33/4
SOLUTION:
95/8 – 33/4 =77/8 – 15/4
=( 77)/8 – 15/4 x 2/2
= 77/8 – 30/8
= 47/8 =57/8 d 101/2 – 64/5
SOLUTION:
101/2 – 64/5 =21/2 – 34/5
= 21/2 x 5/5 – 34/5 x 2/2
= 105/10 – 68/10
=37/10 = 37/10
E
111/9 – 82/3
SOLUTION:
111/9 – 82/3 =100/9 – 26/3
= 100/9 – 26/3 x 3/3
= 100/9 – 78/9
= (100-78)/9
= 22/9 = 2 4/9 f 92/5 – 3 3/4
SOLUTION:
92/5 – 3 3/4 =47/5 – 15/4
= 47/5 x 4/4 – 15/4 x 5/5
= 188/20 – 75/20
= 113/20 = 5 13/20

6. NOW SOLVE THESE.
On Monday morning, Sid spacewalker bugs 81/2 kg of potatoes. Friday morning, only 1 3/4 kg of them ore left how much of the potatoes has Sid used up?
SOLUTION:
Sid buys potatoes of Monday=8 1/2 kg
On Friday Potatoes left =1 3/4 kg
Sid used potatoes = 8 1/2 – 1 3/4
= 17/2 – 7/4
= 17/2 x 2/2 – 7/2
= 34/4 – 7/4 = 27/4 = 6 3/4 kg

So, Sid used 6 3/4 Kg potatoes

b. At the start of the journey, Mrs Khan has 15 2/5 L of petrol in her car. By the time, she reaches her destination, only 3 3/4 L of petrol is left. How much petrol hos the car used?
SOLUTION:

total petrol in car = 15 2/5 L
Petrol left in Car = 3 3/4 L
Petrol used in car = 15 2/5 L – 3 3/4 L
FOR 15 2/5 L – 3 3/4 L
= 77/5 – 15/4
= 77/5 X 4/4
= 308/20 – 75/20
= 233/20 = 11 13/20
car used 11 13/20 L petrol

P:78 REVIEW

1. COMPLETE THE EQUIVALENT FRACTIONS.
a 3/5 = /10 b 6/7 = /35
c 3/4 = /12
d 5/6 = /42
e 7/8 = /24 f 10/11 = /33
2. REDUCE THESE TO THEIR LOWEST TERMS.
a 24/36 b 24/30 c 26/39
d 120/150 e 18/56 f 36/96
SOLUTION:
A 24/36 (÷4) = 6/9(÷4) = 2/3
B 24/36(÷2) = 12/15 (÷3) = 4/5
C 26/39(÷13) = 2/3
D 120/150(÷10) = 12/15 (÷3) = 4/5
E 18/56 (÷2) = 9/28
F 36/96 (÷4) = 9/24 (÷3) = 3/8 /= /

3. WRITE THE FRACTION THAT IS:

equivalent to 5/6 and has a denominator of 30.
equivalent to 7/10 and has a numerator of 35.
equivalent to 48/72 but is written in its lowest terms.
SOLUTION:
A 5/6= /30
30÷ 6=5
So= 5/6= 25/30 b 7/10= 35/
= 7/10 = 35/50
c 48/72 (÷2)= 24/36 (÷4)
6/9 (÷3) = 2/3

4. CHANGE THESE WHOLE NUMBERS INTO IMPROPER FRACTIONS.

6 into sevenths =6X7/7 =42/7
7 into thirds =7X3/3 = 21/3
4 into tenths =4X10/10 = 40/10
10 into quarters =10X4/4 =40/4
5. WRITE THESE AS MIXED NUMBERS.
a 17/3 b 48/11 c 22/5
6. WRITE THESE AS IMPROPER FRACTIONS.
a 32/3 b 55/6 c 19/10
d 24/5 e 81/9 f 73/4
g 44/7 h 95/8 i 93/7
Answers : (a- 11/3)(b- 35/6)(c- 19/10)(d- 14/5)(e- 73/9)(f- 31/4)(g- 32/7)(h- 77/8)(i- 66/7)

7. REDUCE THESE TO THEIR LOWEST TERMS, THEN CHANGE INTO MIXED NUMBERS.
a 24/10 b 28/20 c 120/100
d 15/9 e 36/21 f 96/36
SOLUTION:
A 24/10 (÷2) = 12/6 = 2 2/5
B 28/20 (÷4) = 7/4 = 1 2/5
C 120/100 (÷10) = 12/10 = 6/5 =1 1/5
D 15/9 (÷3) = 5/3 = 1 2/3
E 36/21 (÷3) = 12/7 = 15/7
F 96/36 (÷3) = 32/12 = 8/3

8. SOLVE THESE, WRITING YOUR ANSWERS IN THE FORM OF MIXED NUMBERS.
A 55 ÷ 9 SOLUTION: 55 ÷ 9= 55/9 = 6 1/9
B 50 ÷ 12 SOLUTION: 50 ÷ 12 =50/12 25/6 = 4 1/6
C 62 ÷ 10 SOLUTION: 62 ÷ 10= 62/10 = 31/5 = 61/5
d 29 ÷ 7 SOLUTION: 29 ÷ 7= 29/7 = 4 1/7

9. REWRITE THESE SO THAT THEY HAVE A COMMON DENOMINATOR.
a 2/5 and 17/20 B 3/4 and 3/5
c 3/8 and 5/24 D 27/36 and 5/18
SOLUTION:
A 2/5 = 8/20
2/5 x 4/4 = 12/20 so 8/20 and 17/20
B 3/4 = 5/5 =15/20
3/5 x 4/4 = 12/20 so 15/20 and 12/20
C 3/8 = 9/24
3/8 x 3/3 = 9/24 so 9/24 and 5/24
d 5/18 x2/2= 10/32
so 27/36 and 10/36

a 31/4 + 124/5
SOLUTION:
31/4 + 124/5
= 13/4 + 64/5
= 13/4 x 5/5 + 64/5 x4/4
= 65/20 + 256/20= 321/20
=6 1/20 B 121/3 + 62/5
SOLUTION:
121/3 + 62/5
= 37/3 – 32/5
= 37/3 x 5/5 + 32/5 x3/3
= 185/15 – 95/15
= 89/15
=5 14/15
c 103/8 + 13/4
SOLUTION:
103/8 + 13/4
= 83/8 + 7/4
= 83/8 + 7/4 x2/2
= 83/8 + 14/8
= 97/8
=12 1/8 D 83/4 + 14/15
SOLUTION:
83/4 + 14/15
= 83/11 – 19/15
= 83/11 x 3/3 – 19/15 x2/2
= 249/30 – 38/30
= 211/30
= 71/30

P:79
SID KNOWS THAT WORKING OUT ANSWERS:S IN HIS HEAD IS GOOD FOR HIS BRAIN. JUST AS DOING EXERCISES IS GOOD FOR HIS BODY. HELP HIM WORK OUT THESE PROBLEMS MENTALLY.

How many months are there in 10 1/2 years?
How many days were there in 24 weeks?
I2 and————— are factors of 132.
1/5 of a metre = ———–cm.
The next prime number after 11 is ———
2/3of a day =————- h.
Which of these are prime numbers: 61, 49, 51, 97, 100?
4 1/2 – 1 3/4
3627÷ 9 = ———–
3/4 of a litre of milk= ———–ml.
The LCM of 4 and 5 = ————–
The HCF of 48 and 30 =————–
The prime factors of 12 are—————-
Which is divisible by 5: 4932 or 8255?
Write a 4-digit number that is divisible by 9
5 1/5 – 1 1/10 =————–
write 5 as an improper fraction.
how many seconds are there in 3% minutes?
Answers: (1-126 months)(2-168 days)(3-11)(4-20)(5-13)(6-16)(7-61,97)(8-23/4)(9-403)(10-750 ml)(11-20)(12-240)(13-2,3)(14-8255)(15-3564)(16-4 1/10)(17-47/8)(18-210 seconds)

P:80 MORE ABOUT SHAPES: SURFACE AND AREA

1. LOOK CAREFULLY AT THE GIVEN PAIRS OF SHAPES. TICK THE SHAPE IN EACH PAIR WHICH HAS A GREATER AREA.

2. TICK THE SHAPE WITH THE SMALLER AREA.

3. LOOK CAREFULLY AT THIS GRID AND OTHER RECTANGULAR SHAPES MARKED ON IT.
A B C D

E F G

I J
H

a. Which shapes have the same area as shape A?
b. Which shapes have the same area as shape H?
c. Which are the shapes with largest area and the smallest area?
a- Shapes C and J have same area as shapes A.
b- Shapes D and F have the same area as shape H.
c. Shape with largest area = shape I shapes with smallest area = shapes A,‘ C and J

P:81 COMPARISON OF AREAS

I. LOOK AT THIS GRID OF TRIANGLES AND THE SHAPES MARKED ON IT.

a. Which shape has the largest area? (Count the number of triangles in each shape.)
b. Which shape has the smallest area?
c. Which covers more area, shape B or shape D?
a. Shape E has the largest area because it has triangles.
b. L Shape C, has the smallest area because it has 2 triangles.
c. Both B and D cover same area.
2. WHICH TWO SHAPES IN EACH GROUP HAVE THE SOME AREA?

(Count the number of rectangles in each shape.)
a. = Shapes A and B have the same area = 4.
b. Shapes A and B have the same area = 8.
c. Shapes B and C‘ have same Area = 9 L

3. DRAW THESE SHAPES ON A GRAPH PAPER, AND WRITE THE AREA OF THESE SHAPES.

a. Area = 9 squares
c. Area =11 squares
e. Area = 7 squares b. Area = 11 squares
d. Area. = 12 squares
f. Area .= 8 squares
4. ON SQUARED PAPER, DRAW DIFFERENT’ SHAPES WITH ON AREA OF:

a.8 squares each
b. I0 squares each
c. 3 squares each
d. I6 squares each

P:82 COMPARISION OF AREAS
5. DRAW THESE SHAPES ON A GRAPH PAPER, AND WRITE THE AREA OF EACH SHAPE.
6. WHAT IS THE AREA OF:

a. the triangle ?
b. the parallelogram?
c. The hexagon ?
d. The square?
7. ON SQUARED PAPER DRAW A SHAPE THAT HAS AN AREA OF:
a. 2 1/2 square
b.101/2 square
c. 91/2 square
d. 141/2 square
P:83 COMPARISON OF AREAS
9. ESTIMATE THE APPROXIMATE AREAS OF THESE SHAPES (IN SQUARES)

I0. ASK YOUR TEACHER FOR A LARGE SHEET OF SQUARED PAPER (GRAPH PAPER). VERY CAREFULLY TRACE THE OUTLINE OF YOUR HAND ON IT.

a. Estimate the area covered by your hand. Then, count 7 the squares and find the actual area.
b. Now compare the outline of your hand with that of
neighbour.
c. Whose hand has a larger area?
P:84
AREA: SQUARE CENTIMETRES

1. WRITE DOWN THE UREA, IN CM, OF EACH SHAPE.

2. ASK YOUR TEACHER FOR SOME CENTIMETRE SQUARED PAPER. THEN, DRAW SHAPES WITH THESE AREAS.
a 8 1/2cm2
b 91/2 cm2
c 71/2 cm2
d 11/2 cm2

3. LOOK AT THESE SHAPES CAREFULLY

(i) Write the area of each shape in cm2.
(ii) Measure the perimeter of each shape in cm.
(m) Can you think of a quick way to find the perimeters of shapes b and d, without using your ruler?
P:85 AREA AND PERIMETER

I. EACH OF THESE SHAPES IS MODE UP OF TEN SQUARES AND HAS ON AREA OF I0 CM2.

(i) Calculate the perimeter of each shape.

(ii) Which has the greatest and which has the smallest
perimeter? On centimetre squared“ paper, draw as many shapes as you can using I6 squares (that is, each shape with an area of I6 cm2). Then measure the perimeter of each shape.
ANSWERS: i. a. 16 cm b. 14 cm c. 22 cm
ii. c has the greatest and b has the smallest perimeter
3. DRAW THESE RECTANGLES. THEN FIND THE UREA AND PERIMETER OF EACH.
a. l=4 cm, b. =3cm
area= 4×3=12 cm2
perimeter =2(4+3)= 7×2 =14 cm

b. l=7 cm, b. l=4cm
area = 7 cm x 4 cm =28 cm2
perimeter = 2(7+4) =11x 2 =22 cm

c. l=5cm, b. l=1cm
area = 5 cm x 1 =5 cm 2
perimeter = 2(5+1) =6 x2 =12 cm

d. l=8cm, b. l=2cm
area = 8 cm x 2 cm = 16 cm2
perimeter = 2 (8 +20) = 10 x 2 = 20 cm

P:86 AREA & PERIMETER

4. COPY THIS TABLE CAREFULLY IN YOUR NOTEBOOK. THEN COMPLETE IT.
RECTANGLE
4 cm 5 cm 20 cm2 18 cm
10 cm 2 cm 20 cm2 24 cm
9 cm 7 cm 63 cm2 32 cm
8 cm 7 cm 56 cm2 30 cm
11 cm 4 cm 44 cm2 30 cm

5. NOW COPY AND COMPLETE THIS TABLE.
RECTANGLE
l b Area
20 cm 5cm 100 cm2
9 cm 9cm 81 cm2
9cm 4 cm 36 cm2
9 cm 6cm 54 cm2
12 cm 10cm 120 cm2

6. NOW COPY AND COMPLETE
RECTANGLE
Perimeter l B
20 cm 6 cm 4 cm
28 cm 9 cm 5 cm
34 cm 12 cm 5 cm
70 cm 20 cm 15 cm
300 cm 100 cm 50 cm

7. NOW SOLVE THESE PROBLEMS IN YOUR NOTEBOOK.
a. A rectangle is I5 cm Long and 7 cm wide. What is its
area?
SOLUTION:
L= 15 cm
B= 7 cm
Area =15 cm x 7 cm =105 cm2
b. Sid Spacewalker’s space-bed is 2 m Long and 1 m wide. How much area of Sid’s spaceship does it occupy? And if Sid walks right round it once, what distance does he cover?
SOLUTION:
L= 2 m
B= 1 m
Area =2 m x 1 m =2 m2

Distance = perimeter =2 (2+1)
=2 x3 =6 cm

P:87 AREA AND PERIMETER

8. HERE IS SID SPACEWALKER’S COLLECTION OF MAGIC CARPETS WORK OUT THE AREA OF EACH ONE.

Which carpet has the largest area?
area = 6 m x 4 m =24m2
area =7 m x 3 m = 21 m2
area = 4 m x 3 m = 12 m2
9. SID HOPES TO BUILD A HOUSE ON THE MOON IN 2020 C.E. AND LIVE THERE FOR A PERIOD OF 6 MONTHS. THIS IS THE PLAN OF HIS HOUSE.
What is the total area of Sid’s house? Find this by adding together areas of all the six rooms.
Bed room= 2×4=8m2
Living room=3×5=15 m2
Play room=2×6=12 m2
Store=2×2=4 m2
Kitchen=3×2=6 m2
Bathroom=2×2=4 m2
Total area= 8+15+6+4+6+4=43 m2
10. SOLVE THESE PROBLEMS IN YOUR NOTEBOOK.

a. Mr Kamal has a beautiful lawn in his garden. Its area is 54 m2 and its breadth is 6 m. What is its length?
Solution :
Area = 54 m2
B= 6 m
L= 54/6 =9 m
b. A swimming pool is 10 m long and covers an area of 60 m2. What is its breadth?
Solution :
L= 10 m
A= 60 m
B= 60/10 = 6 m
c. The perimeter of a field is 300 m and its length is 100 m. What is its breadth?
Solution :
P= 300 m
L= 100 m
2(L+b) = p
L+b=P/2
100+ b= 300/2
100+ b= 150
B= 150 -100 =50m

d. The walls around a playground measure 410 m. If one wall along the length of the playground is 80 m long, what is the length of the wall along its breadth? What is the area of the playground?
Solution :
P=410 m
L= 80 m
2( L+B) = 410
L+b =410/2 = 205
80+5 =205
B=205 – 80
B=125 m
Area= l x b
=80 x125
=10000 m2
11. ASK YOUR TEACHER FOR A METRE RULE OR A MEASURING TAPE. THEN MEASURE AND WORK OUT:

a. The area of your desk.
b. The area of the board in your classroom.
c. The area of your classroom (to the nearest m2).

P:88 REVIEW

1. WRITE THE LCM OF EACH PAIR.
a. 7 and 8
b. 12 and 10
c. 4 and 6
d. 3 and 7
A. L.C.M = 7 X 8 = 56
B. L.C.M = 2 X 6 X 5 = 60
C. L.C.M = 2 X 2 X 3 = 12
D. L.C.M = 3 X 7 = 21

2. WRITE DOWN ALL THE FACTORS THESE NUMBERS.
a. 24
b. 19
c. 84
A. 24 = 2 X 2 X 2 X 3
B. 19 = 1 X 19
C. 84 = 2 X 2 X 3 X 7

3. WRITE THE COMMON FACTORS AND HCF OF THESE PAIRS OF NUMBERS.
a. 12,28
b. 27,45
A. 12 = 2 x 2 x 3
28 = 2 x 2 x 7
COMMON FACTORS = 2,2
HCF = 2 X 2 = 4

B. 27 = 3 X 3 X 2
45 = 3 X 3 X 5
COMMON FACTORS = 3,3
HCF = 3 X 3 = 9

4. TICK THE PAIRS THAT ARE CO-PRIME NUMBERS.
a. 5 and 9
b. 2 and 7
c. 3 and l8
d. 16 and 42
A. 5 & 9 TRUE
B. 2 & 7 TRUE
C. 3 & 18
D. 16 & 42

5. FILL IN THE BLANKS.
a. Numbers which have only two different factors are called ——————— numbers.
b. The factors of 5 are ——————– and——————–so5isa——————- number. X
c. The factors of I0 are ——————,—————–, —————- and ———————– so I0 is a —————- number.
d. Number I is not a ————————- number because it does not have two different factors.
A.PRIME
B. 1,5, PRIME
C.1,2,5, COMPOSITE
D. PRIME

6. DRAW TREES TO SHOW THE PRIME FACTORS OF THESE.
a. 28
b. 70
c. I08
7. USE THE DIVISION METHOD TO THE PRIME FACTORS OF THESE. SHOW
a. 963
b. I025
c. I42
963 = 3 x 3 x 107 b. 1025 = 5 x 5 x 41 c. 142 = 2 x 71

8. FIND THE PRIME FACTORS AND THEN THE LCM OF THESE NUMBER PAIRS, USING THE DIVISION METHOD.
a. 36 and 48
b. 56 and 21
A.36 = 2 X 2 X 3 48 = 2 X 2 X 2 X 2 X 3 L.C.M = 2 X 2 X 3 X 3 X 2 X 2 = 144
B.56 = 2 X 2 X 2 X 7 21 = 3 X 7 L.C.M = 2 X 2 X 2 X 3 X 7 = 168

9. FIND THE HCF AND LCM OF THESE PAIRS OF NUMBERS.
a. 60 and 48
b. I5 and 75
A. 60 = 2 X 2 X 3 X 5 48 = 2 X 2 X 3 X 2 X 2 H.C.F = 2 X 2 X 3 = 12 L.C.M 2 X 2 X 3 X 2 X 2 X 5 = 240

10. WRITE >,<, OR =.
3/5 ——5/8 7/8 ——17/18 16/24 ——2/3 100/6 ——16 2/3
A. <
B. >
C. =
D. =

11. REDUCE THESE TO THEIR LOWEST TERMS, THEN CHANGE INTO MIXED NUMBERS.
56/18 110/20 75/15

9 2/3 – 3 4/5 8 1/4 – 2 5/6 4 5/8 + 6 1/12 7 3/4 + 10 8/9

13. SOLVE THESE PROBLEMS.
a. Two big belts in a hall start
to ring together at 05:00
hours. One rings every I5
seconds and the other every
I2 seconds. How often will
they ring together? LCM = 3 X 4 X 5 = 60 they will ring together after every 60s
b. Maria bought 3 cakes of the
same size for her birthday.
Half of one cake was left
and one-third of the other.
How much cake was Ieft
over altogether? The cake left over = 1 + 1/2 + 1/3
(6+3+2)/6 = 11/6 = 15/6

PAGE:89
PART THREE
Q I. WORK WITH THE CALCULATOR SECOND FIND THE ANSWERS:S ‘FOR THE FOLLOWING.
a. 2/10 , 3/10 , 4/10 , 5/10 , 6/10 , 7/10 , 8/10 , 9/10 , 10/10
b. 1/2 , 2/2
c. 1/5 , 2/5 , 3/5 , 4/5 , 5/5 ,

P:90
2-WRITE THE COLOURED PORT OF THE SHAPE AS A FRACTION AN AS A DECIMAL
A. 2/10 ; .2
B. 3/10 ; .3

3- WRITE THESE FRACTIONS AS DECIMALS ?
A. 0.2
B. .8
C. 0.9

4-COPY THE SHAPES BELOW O squared paper then color as directed

P:91
5. LOOK CAREFULLY AT THESE RULERS. WRITE THE COLOURED PART AS A FRACTION SECOND AS A DECIMAL.
A. 5/10 CM = 0.5 CM
B. 7/10 CM = 0.7 CM
C. 3/10 CM = 0.3 CM
D. 9/10 CM = 0.9 CM

WRITE THESE LENGTHS IN DESCENDING ORDER.
6.NOW LOOK AT THESE LONGER PIECES OF RULERS. WRITE THE COLOURED PART AS A FRACTION SECOND AS A DECIMAL.

WRITE THESE LENGTHS IN ASCENDING ORDER.

P:92
DECIMALS: LINE SEGMENTS SECOND NUMBER LINE
1-MEASURE THESE LINES CAREFULLY WITH YOUR RULER, THEN WRITE THE LENGTH OF EACH LINE IN FOUR DIFFERENT WAYS, AS SHOWN.
4 cm 2 mm;
4 2/10 cm;
4.2 cm;
42 mm
A. 5CM 00MM, 5CM , 5.0CM , 50MM
B. 3CM 2MM , 3 2/10 CM , 3.2CM , 32MM
C. 4CM 7MM , 4 7/10 CM , 4.7 CM , 47MM
D. 5 CM 4MM , 5 4/10 CM , 5.4 CM , 54MM
E. 3CM 9MM , 3 9/10 CM , 3.9CM , 39MM

2- IN YOUR NOTEBOOK, DRAW LINE SEGMENTS OF THESE LENGTHS IN ASCENDING ORDER.
BE VERY ACCURATE!
a. PQ 1.2 cm
b. YZ 0.8 cm
c.ST 4.3 cm
d. EF 2.9 cm
e.CD 5.5 cm
f. MN 5.I cm
g. WX 3.7 cm
h. UV cm 1.9 m
g. ST = 3.7
f. MN = 5.1
e. = 5.5

3-WRITE THESE AS FRACTIONS.
2.7 9.4 11.4 4.9 0.6 9.5
2 7/10
9 4/10 11 4/10 4 9/10 6/10 9 5/10

4-WRITE THE POSITION OF THE POINT FROM 0 ON EACH OF THESE NUMBER LINES
A. 1 5/10 CM = 1.5 CM
B. 9/10 CM = .9 CM

5-WRITE THESE AS DECIMALS.
101/10 4/10 153/10 14 5/10 1 7/10 21 1/10
10.1
.4 15.3 14.5 1.7 21.1

6-THINK CAREFULLY, THEN WRITE THESE US DECIMALS SECOND FRACTIONS.
21 tenths
I8 tenths
A. 2.1 = 2 1/10
B. 1.8 = 1 8/10

7. IN YOUR NOTEBOOK, DRAW I0 SQUARES JUST LIKE THIS. THEN DIVIDE EACH SQUARE INTO I0 EQUAL STRIPS.
NOW COLOUR THE PART OF THE SQUARE INDICATED, SECOND WRITE THE CORRESPSECONDING FRACTION SECOND THE DECIMAL: (USE A NEW SQUARE FOR EACH.)
a. 0.4
b. 3/10
c. one tenth
d. five tenths
e. 9/10
f. 0.6

8. IN YOUR NOTEBOOK, COPY THE TABLE SHOWN BELOW (MAKING YOURS LONGER).
THEN PUT THE NUMBERS BELOW INTO YOUR TABLE (THE FIRST ONE HAS BEEN DONE FOR YOU IN THE
TABLE ABOVE.)
a. 283 3/10 b. 24 5/10
c. 410 1/10 d. 100 2/10
e. 500 9/10 f. 800 7/10
H T O t
A 2 8 3 3
B 0 2 4 5
C 4 1 0 1
D 1 0 0 2
E 5 0 0 9
F 8 0 0 7
P:94 DECIMALS: THE DECIMAL POINT, ADDITION, SUBTRACTION
9- WRITE THESE NUMBERS IN WORDS, THEN SAY THEM OUT LOUD.
a. 606.2
b. 1204.3
C. 495.8
d. 2619.6
e. 220.1
f. 3990.4
g. 899.9
h. 8029.7
a. Six hundred and six point two.
b. On thousand ‘two hundred and four point three.
c. Four hundred and ninety five point eight.
d. Two thousand six hundred and nineteen point six,
e. Two hundred and twenty point one.
f. 1Three. Thousand nine hundred and nine pointnfeur.
g. Eight hundred and ninety nine point nine.
h. Eight thousand and twenty nine point seven.
a. 653.4 + 122.5
465.3 + 284.6
SOLUTION: 509.1 + 482.3
SOLUTION:
SOLUTION:
653.4
+ 122.5 SOLUTION:
465.3
+ 284.6 SOLUTION:
509.1
+ 482.3
775.9 749.9 991.4

1 1. NOW SUBTRACT THESE CAREFULLY.
a. 985.6 – 139.5 b. 702.7 – 484.3 C. 521.8-199.1 d. 619.9 – 487.4
SOLUTION: SOLUTION: SOLUTION: SOLUTION:
985.6
– 139.5 702.7
– 484.3 521.8
-199.1 619.9
– 487.4
846.1 218.4 322.7 132.5
12. NOW WRITE THESE VERTICALLY AND COMPLETE
a. 329.4 + 614.7 b. 759.8+196.9 C. 477.7+378.6 d. 1269.3+1769.8
SOLUTION: SOLUTION: SOLUTION: SOLUTION:
329.4
+ 614.7 759.8
+196.9 477.7
+378.6 1269.3
+1769.8
944.1 956.7 856.3 3039.1

13-WRITE VERTICALLY AND COMPLETE.
a. 602.3-455.4 b. 750.1-289.3 C. 808.4-662.7 d. 513.2-377.6 e.1219.5-846.9
SOLUTION: SOLUTION: SOLUTION: SOLUTION: SOLUTION:
a. 602.3
-455.4 b. 750.1
-289.3 C. 808.4
-662.7 d. 513.2
-377.6 e.1219.5
-846.9
146.9 460.8 145.7 135.6 372.6

P:95 DECIMALS: MULTIPLICATION & DIVISION
14- COPY AND COMPLETE.
a. T O . t b. T O . t
3 8. 3
x 5 8 4 . 9
3 . 2
191.5 1698
+25470
2716.8
c. T O . t d . T O . t
9 3 . 7
X 7 6 0 .9
X 4 . 3
655.9 1827
24360
26187

a. If a monkey eats 3.4 kg of bananas every day, how much will it eat in one week?
SOLUTION:
304
X7
23.8

b. A swimming pool is 23.5 m long. If Bina swims 4 lengths, how far is that altogether?
SOLUTION:
23.5
X4
94.0

I6. COPY AND COMPLETE.
a. H T O . t
2 4 0 . 8 ÷ 8 b. H T O . t
8 1 2 . 4 ÷ 6
SOLUTION: SOLUTION:

8 30.1
8 135.4
240.8
24 812.4
6
00
00 21
18
08
08 32
30
00 24
24
c. H T O . t
6 5 4 . 6 ÷ 3 d. H T O . t
9 6 0 . 3 ÷ 9
SOLUTION: SOLUTION:
3 218.2 9 106.7
654.6
6 960.3
9
05
3 60
54
24
24 63
63
06
06 0
0

I7. WRITE IN LONG DIVISION FORM SECOND COMPLETE.
a. I82.7 + 9 b. 6098.4 + 6
SOLUTION: SOLUTION:

9 20.3
5 1016.4
182.7
18 6098.4
6
027
27 009
6
0 38
36
24
24
00
c. 4601.2 + 3 d. 1472.1 + 7
SOLUTION: SOLUTION:
3 156.4 7 210.3
469.2
3 1472.1
14
16
15 07
07
19
18 021
021
12
12 0
0

a. What length is 1/4 of 84.8 m?
SOLUTION:
1/4 of 84.8 = 21.2 m
= 1/4x 84.8 =21.2 m
b. How much is 1/5 of 750.5 g?
SOLUTION:
1/5 of 750.5
=
1/5 x750.5 = 150.18
c. Mr Shah had 27.6 1 of petrol in his car. He had used 1/6 liters f petrol on a drive. How many litres of petrol had he used? How much petrol was left over?
SOLUTION:
1/6 of 27.6
=
1/6 x27.6 = 4.6 L
Petrol left over
= 27.6 – 4.6
= 23.0 L
P:96
DECIMALS:TENTH & HUNDREDTHS
1. SHOW THE COLOURED PART OF THESE SQUARES AS A FRACTION AND AS A DECIMAL.
a.
4/100 = 0.04 b.
0/100 = 0.0 c.
7/100 =0.07 d.
3/100 =0.03
e.
21/100 =0.21 f.
23/100 = 0.23 g.
65/100 = 0.65 h.
55/100 =0.55
(i) WRITE THESE IN ASCENDING ORDER.
ANSWERS: b, d, a, c, e, f, h, g
(II) FIND THE SUM OF O1ND G. B. & E.
4/100 + 65/100 = 69/100 = 0.69
b+e = 0/100 + 21/100 =
21/100 = 0.21
(III) WHICH IS BIGGER; F. OR H.? BY HOW MUCH?
h – f = 55/100 – 33/100
= 22/100 = 0.22
P:97
DECIMALS: TENTHS SECOND HUNDREDTHS
2- COLOUR SQUARES TO MATCH THE DECIMAL NUMBERS.

0.03 0.18 0.51 0.75

3- ASK YOUR TEACHER FOR SQUARED PAPER (GRAPH PAPER) SECOND DRAW SQUARES OF DIFFERENT SIZES. DIVIDE EACH SQUARE INTO HUNDREDTHS. THEN COLOUR THEM TO SHOW THESE DECIMALS; USE A DIFFERENT SQUARE FOR EACH.
a0.47 b. 0.88 C. 0.09 d. 0.07 e. 0.50 f. 0.94

4-WRITE THESE AS DECIMAL NUMBERS.
46/100 7/100 16/100
46/100 =0.46 7/100 = 0.07 16/100= 0.16

5. WRITE THESE AS FRACTIONS.
a. 0.15 b. 0.56 C. 0.10 d. 0.03 e. 0.01 f. 0.33
SOLUTION:
15/100 56/100 10/100 3/100 1/100 33/100

Q 6. THINK CAREFULLY, THEN FILL IN >, <, OR = (USE YOUR HUNDRED SQUARES TO HELP YOU.).
a. 0.05 ———————- 0.50
b. 0.19——————-0.91
c. 50/100——0.5
d. 0.08 ——————- 0.1
e. 0.6 ——————- 0.60
f. 0.75 ——————-75/100
7. WRITE AS DECIMAL NUMBERS. If 7 tenths2 hundredths 0.72
a. 3 tenths5 hundredths
b. 0 tenths 9 hundredths
c. 8 tenths 0 hundredths
d. 1 tenth 4 Hundredths
P:98
TENTHS AND HUNDREDTHS : THE PLACE- VALUE TABLE

8. IN YOUR NOTEBOOK, COPY THE PLACE-VALUE TABLE SHOWN BELOW (MAKING YOUR TABLE LONGER).
H T O T h
4 8 2 0 3
SOLUTION:
H T U t h
B 5 0 0 5 1
C 6 0 5 5 0
D 3 2 8 0 1
E 9 9 9 9 9
F 6 9 5 6 5

THEN PUT THE NUMBERS BELOW INTO YOUR TABLE (THE FIRST ONE HAS BEEN DONE FOR YOU IN THE TABLE ABOVE.).
a. 482 3/100
b. 500 51/100
c. 605 5/10
d. 328 1/100
e. 999 99/100
f. 695 65/100
9. WRITE THESE IN ASCENDING ORDER.
1.85, 1.58, 1.79, 1.43
1.43, 1.58, 1.79, 1.85
a. 1. 2.47, 2.43, 2.48, 2.45
b. 8.76, 7.86, 6.78, 8.78
c. 3.81, 8.31, 8.30, 3.80

10. LOOK AT THESE CAREFULLY, ‘THEN WRITE THE MISSING DECIMAL.
0.1, ——–, 0.3 0.2
a. 15.4, ——–, 15.6
b. 17.8, ———-, 18.0
C. 18.10,———— 18.12
d. 49.99, ———–, 50.01
e. 70.98,————-, 71 .00
11. WRITE THE DECIMALS AS FRACTIONS.
a. 19.94
b. 493.1
c. 24.2
d. 738.08
e. 35.9
f. 41 5.85
P:99
DECIMALS AND FRACTIONS

1- WRITE THESE FRACTIONS AS DECIMALS BG CHANGING THEM INTO EQUIVALENT FRACTIONS WITH DENOMINATORS I0 OR IOO.
1/4 = 25/100 = 0.25
3/20 = 15/100 = 0.15
9/25 = 0.36
2/5 = 4/10 = 0.4
2/25 = 8/100 = 0.08
8/25 = 40/100 = 0.4
4/5 = 8/10 = 0.8
6/20 = 3/10 = 0.3
3/4 = 75/100 = 0.75

Q 2. WRITE THESE AS FRACTIONS OR MIXED NUMBERS IN THEIR LOWEST TERMS.
0.25 = 25/100 = 1/4
0.75 = 72/100 = 18/25
5.1 = 5 1/10
0.3 = 3/10
1.55 = 155/100 = 111/20
6.4 = 64/10 = 62/3

P:100
DECIMALS AND MONEY
Q 1. WRITE THESE SUMS OF MONEY AS DECIMALS. .
* Rs 46 second twenty paise ——-Rs 46.20
a. Rs 60 and ten paise
b. Rs 5 and five paise (think carefully!)
c. Rs 100 and eighty-five paise
d. Rs 6025 and twenty-five paise
e. Rs 300 and fifty paise
f. Rs 873 and five paise
ANSWERS: (a-Rs.60.0)(b- Rs.5.05)(c- Rs.100.85)(d- Rs.6025.25)(e- Rs.300.50)(f- Rs.873.05)
2. SID SPACEWALKER HAS BEEN ASKED TO CALL OUT THESE PRICES. WHAT WORDS SHOULD HE USE?
Rs 60.05 sixty rupees an five paise
a. Rs 105.50
ANSWER: one hundred and fifty paise
b. Rs 4820.2
ANSWER: four thousand eight hundred twenty and twenty paise
c. Rs 310.10
ANSWER: three hundred ten and ten paise
d. Rs 1659.5
ANSWER: one thousand six hundred fifty nine and fifty paise

HELP SID ADD UP HIS SHOPPING BILLS.
Sweet shop : Rs 20.15
Bakery : Rs 18.50
Video library : Rs 30.50
Total : Rs 61.15

a. Fruit shop : Rs 47.75
Toy shop : Rs 59.60
Fish shop : Rs 53.25
SOLUTION : Rs160.60
b. Newsagent : Rs 32.10
Popcorn shop :Rs 16.50
Clothes shop : Rs110.95
SOLUTION : Rs 159.55
c. Snack bar : Rs 22.35
Shoe shop : Rs 171.85
Socks shop : Rs 28.70
SOLUTION: Rs 222.90

P:101
DECIMALS SECOND MONEY:
DECIMAL SECOND MONEY : THE FOUR OPERATIONS
1. COPY AND COMPLETE.
a. Rs 618.75 + RS 1593.55
SOLUTION:
Rs 618.75
+ RS 1593.55
RS 2212.30

b. Rs 9008.15 – RS 489.75
SOLUTION:
Rs 9008.15
– RS 489.75
Rs 8518.40

c. Rs 593.55 x 7
SOLUTION:
Rs 593.55
x 7
Rs 4154.85
d. Rs 814.40 ÷ 8
SOLUTION: 101.8
e Rs 1216.75 x 12
8 814.40
8
SOLUTION:

1216.75
x 12
14
8

243350
1216750
64
64

1460100
f. Rs 1881.90 ÷ 9
SOLUTION: 209.10
9 1881.90
18
81
81
9
9

2. ARRANGE THESE SUMS OF MONEY IN DESCENDING ORDER
Rs 100.10, Rs 101.90
Rs 100.10
Rs 101.90. Rs 100.90.
Rs 100.90

a. Rs 302.20, Rs 320. I0, Rs 320.05
b. Rs 99.90, Rs 100.05, Rs 100.00
c. Rs 418.80, Rs 418.85, Rs 417.95
3. ANSWERS: THESE QUESTIONS MAKING COMPLETE STATEMENTS.
a. A new T\/ costs Rs 24,065 Q0 Samina has only Rs 10,78O 50 in her bank account. How much more money must she save before she can buy the TV?
SOLUTION:
24064.90
10780.50
Rs 13285.40

b. Danish needs a maths book costing Rs q8.75, an English book costing Rs 67.50, an ‘ atlas costing Rs 125, second a new lunch box costing Rs 105.75. How much money will all this cost his parents? ”
SOLUTION:
Rs 98.75
Rs 67.50
Rs 125.00
Rs 105.75
Rs 397.00

P:102
DECIMALS AND MONEY: More about Bills
1-PREPARE BILLS FOR SID’S SHOPPING AT THESE DIFFERENT SHOPS. (WRITE YOUR BILLS AS NEATLY AS POSSIBLE.)
Quantity Description Cost of one Total cost
2 Shorts 225 Rs 450
12 table tennis balls 9.15 Rs 109.80
5 sports caps 35.75 Rs 178.75
Grand total Rs 738.55
a-Sports shop: 2 pairs of shorts at Rs 225.00 each; I2 table tennis balls at Rs 9.1 5 each; 5 sports caps at Rs 35.75 each.
SOLUTION:
Name Sid Date 01.01.2016
Quantity Description Cost of one Total cost
2 Paris of shorts Rs 225.00 Rs 450.00
12 Table tennis balls Rs 9.15 Rs 109.80
6 Sports caps Rs 35.75 Rs 178.75
Grand total Rs 738.55

b-Bookshop: 7 comics at Rs 32.35 each; 2 ‘Famous Five’ books at Rs 87.25 each; 3 books about magic at Rs 36.35 each; a new diary costing Rs q4.65.
SOLUTION:
Name Sid Date 01.01.2016
Quantity Description Cost of one Total cost
7 Comics Rs 23.25 Rs 232.75
2 Ff books Rs 87.25 Rs 175.50
3 Books of magic Rs 36.35 Rs 109.05
1 Diary Rs 94.65 Rs 94.95
Grand total Rs 610.95

c-Bakery: A doughnuts at Rs 15.65 each; 2 chocolate cakes at Rs 27.25 each; 6 chicken puffs at Rs I4.85 each.
SOLUTION:
Name Sid Date 01.01.2016
Quantity Description Cost of one Total cost
4 Doughnuts Rs 15.65 Rs 62.60
2 Chocolate cakes Rs 27.25 Rs 54.50
6 Chicken puffs Rs 14.85 Rs 89.10
Grand total Rs 206.20

2-NOW PREPARE THESE BILLS, WORKING OUT THE SUMS VERY CAREFULLY.
a. Mrs Shahid: 3 packets of tgping paper at Rs ‘i8.5O per packet; 2 books on electronics costing Rs I I2. each; a new pen costing Rs 28.95.
SOLUTION:
Name Sid Date 01.01.2016
Quantity Description Cost of one Total cost
3 Packets of typing Rs 98.50 Rs 295.50
2 Books Rs 112.50 Rs 225.00
1 Pen Rs 28.95 Rs 28.95
Grand total Rs 549.45
b. Mr Aamir: 5 packets of soap at Rs 26.85 each; 4 packets of biscuits at Rs 19.40 each, 3 cookery books costing Rs 130.50 each; 2 music CD at Rs 41.75 each.
SOLUTION:
Name Sid Date 01.01.2016
Quantity Description Cost of one Total cost
5 Soap Rs 26.85 Rs 135.25
4 Packets biscuits Rs 19.40 Rs 77.60
3 Cookery books Rs 130.50 Rs 391.50
2 Music CD’s Rs 41.75 Rs 94.95
Grand total Rs 686.85
c. Mrs Khan: 4 books on computers costing Rs I80. each; a new lamp for her room costing Rs 200.75; 6 tickets for a concert at Rs I l5.00 each.
SOLUTION:
Name Sid Date 01.01.2016
Quantity Description Cost of one Total cost
4 Books Rs 180.45 Rs 721.80
1 Lamp Rs 200.75 Rs 200.75
6 Tickets Rs 115.00 Rs 690.00
Grand total Rs 1612.55
3-USE THE UNITARY METHOD TO FIND THE COST OF:
A. 4 notebooks, if I0 notebooks cost Rs 80.50.
SOLUTION:
Cost of 10 notebooks =80.50
Cost of 1 notebooks =80.50/10
Cost of 4 notebooks = 8.05 x 4 = 32.20 Rs

B.3 kg of wheat, if I0 kg Rs 320.50.
SOLUTION:
Cost of 10 kg wheat = 320.50
Cost ofi‘1 kg wheat = 320.50/10
Cost of 3 kg wheat = 32.05 x 6 = 96.15 kg

C. 6 tickets to the evening show, if 8 tickets cost Rs 720.80.
SOLUTION:
Cost of 8 tickets = 720.80
Cost of 1 tickets =720.80/10 = 90.10
Cost of 6 tickets = 90.10 x = 540.60 Rs

D.5 tennis balls, if 3 tennis balls cost Rs 62.70.
SOLUTION:
Cost of 3 tennis balls = 62.70
Cost of 1 tennis balls = 62.70/3 = 20.90
Cost of 5 tennis balls = 20.90x 5 = 100.45

P:103
DECIMALS: METRES AND CENTIMETRES
1. WRITE THESE HEIGHTS IN METRES
2 m 61+ cm 2 64 m
3 m 87 cm = 3.87 m
405 cm = 4.05 m
1 m 15 m = 1.15 m
1102 cm = 11.02 m
2. WRITE THESE LENGTHS IN SECOND CM
13.05m ……13 m 5 cm
a. 2.75 m = 2 m 75 cm
b.16.83 m= 16 m 83 cm
c. I0.02 m= 10 m 2 cm
d. 240.03 m = 240 m 3 cm
3. WRITE AS MIXED NUMBERS.
* 25 02 m ………..25 2/100
a. 18.59 m = 18 59/100
b 103.08 m = 1038/100
c 44.07m = 447/100
d. 36.10 m = 361/10
4. COPY AND COMPLETE (LOOK CAREFULLY FOR + OR –
a. m b. m
l2.75
+ 3.86 143.62
+ 78.59
16.61 222.21
c. m d. m
24.63
– 18.92 103.41
– 67.58
5.71 35.83

5. WRITE VERTICALLY SECOND COMPLETE.

a. 28.65 m + 16.32 m +9.49 m b. 52.86 m + 243.95
SOLUTION: SOLUTION:
28.65
16.32
9.49 52.86
+ 243.95
54.46 296.81
c. 202.22 m – 87.93 d.614.18 m – 39.77 m
SOLUTION: SOLUTION:
202.22
– 87.93 614.18
– 39.77
114.29 284.41
e. 38.92 m + 74.58 + 64.73 m
SOLUTION:
38.92
+ 74.58
64.73
178.23

a. Sumir’s desk is 1513 m long
while Rahim’s desk is I.67 m
long. How long ore the two
desks when placed end to end? SOLUTION:
1.93
1.67
3.60
b. A door is 2.14 m high second
Javed is 1.89 m toll. How much space will there be between Javed’s head second the top of the door if he goes through it? SOLUTION:
2.14
– 1.89
0.25

P:104
DECIMALS AND METRES: THE FOUR OPERATIONS
1. COPY THIS TABLE IN YOUR NOTEBOOK SECOND COMPLETE.
Length of rope Length of cut off Length left
42.63 m 5.19 m 37.44 m
A 56.18 m 29.35 m 26.83 m
B 81.24 m 48.57 m 32.67 m
C 67.15 m 26.96 m 40.19 m

2. COPY AND MULTIPLY.
a. m b. m
18.62
X 5 102.35
X 7
93.10 717.15
c. m d. m
43.58
X 9 35 I .68
X 20
392.22 7033.6

3. WRITE VERTICALLY AND MULTIPLY.
a. 73.15 m x I0 b. 58.29 m x I5 c. 84.37 m x 20 d. 110.05 m x 25
SOLUTION: SOLUTION: SOLUTION: SOLUTION:
73.15
x I0 58.29
x I5 84.37
x 20 110.05
x 25
0000
43150 29145
58290 0000
16874 55025
22010
431.50 874.35 1687.40 2751.25
e. 214.10 m x 31 f. 93.145 m x 22
SOLUTION: SOLUTION:
214.10
x 31 93.45
x 22
21410
64230 18690
186900
6637.10 2055.90

4. COPY AND COMPLETE.
a. 252 ÷ 4 m b. 75.66÷ 6 m
SOLUTION: 6.31 SOLUTION: 12.61
4 25
24 6 75.66
6
12
12 15
12
4 36
36
6
6
c. 10.55 ÷ 5 m d. 38.07 ÷ 9 m
SOLUTION: 2.11 SOLUTION: 4.23
5 10.55
10 9 38.07
36
5
5 20
18
5
5 27
27
0 0

5. NOW COMPLETE THESE.
a. 66.57 m÷7 b. 307.89m÷9 c. 190.48m÷8 d. 369.39m÷3 e. 308.46m÷6 f. 124.65m÷ 9
SOLUTION: SOLUTION: SOLUTION: SOLUTION: SOLUTION: SOLUTION:
9.51 34.21 23.81 123.13 51.41 13.85
5 66.57
63 9 307.89
27 8 190.48
16 3 369.39
3 6 308.46
30 9 124.85
9
35
35 37
36 30
24 6
6 8
6 34
27
7
7 18
18 64
64 9
9 24
24 76
72
00 00 8
8 3
3 6
6 45
45
00 9
9 00 00

6. SOLVE THESE PROBLEMS.
a. A box is 1.15 m high. What is the total height of a stack of 6 such boxes? SOLUTION:
1.15
X6
6.90
b. A car is 4.75 m long. If 5 such cars are stuck bumper
to bumper in a traffic jam, what will be the total length? SOLUTION:
4.75
X5
23.75
c. Jamaal has a length of
string measuring 31.Q2 m.
If he cuts it into 7 equal
pieces, how long will each
piece be? SOLUTION:
P:105

a. 5 in the hundredths place
0 in the tenths place
6 in the ones place

b. 3 in the tens place
7 in the tenths place
5 in the hundredths place
0 in the ones place

c. 3 in the hundreds place
4 in the ones place
7 in the tens place
0 in the tenths place

d. 9 in the hundredths place
9 in the tens place
4 in the tenths place
6 in the hundreds place
3 in the hundredths place
8 in the ones place
Decimal Fun Page! ,
2. COPY AND WRITE SYMBOLS IN the blanks (>, <, or = ).
1.0——-0.1 1.0 > 0.l
a. 0.9 ————1
b. 3.46————–3.5
c. 2.0 ———– 2
d. 0.81————–0.8
e. 9.50————9.5
3. COPY & WRITE SYMBOLS IN THE BLANKS (X OR +).
0.4 ———-10 = 4…
0.4 x 10 =4
a. 0.01———10 = 0.1
b. 5.0———10 = 0.5
c. 9———-10 =
d. 0.85——-10= 8.5
e.3——10 = 0.3
4. USING YOUR RULER CAREFULLY, DRAW SQUARES SECOND RECTANGLES OF THESE SIZES. THEN WORK OUT THE PERIMETER OF EACH SHAPE.

Square, each side 2.3 cm
2.3 cm X 4 = 9.2 cm
Perimeter = 9.2 cm
a. Rectangle,
sides 4.2 cm second I.8 cm SOLUTION:
2(4.2+1.8) = 12cm
Perimeter =12 cm
b. Square,
each side 3.7 cm
SOLUTION:
3.7 x4 = 14.8 cm
Perimeter =14.8 cm
c. Rectangle,
sides 5.14 cm second 2.5 cm SOLUTION:
2(5.4+2.5)
=2(7.9) =15.8 cm
Perimeter =15.8 cm

P:106
DECIMALS: TENTHS, HUNDREDTHS UND THOUSANDTHS
1. Look at these numbers then Write the place value of the circled digit.
48.5 9 2………… 9 hundredths
B 19.339 9 tens
C 90.025 0 tenths
D 284.028 2 hundredths
E 157.460 0 thousandths
F 392.159 3 hundreds

P:107
DECIMALS: TENTHS, HUNDREDTHS AND THOUSANDTHS
2. IN YOUR NOTEBOOK, DRAW A PLACE-VALUE CHART. THEN PLACE THESE NUMBERS INTO IT CAREFULLY (THE FIRST HAS BEEN DONE FOR YOU.
H T O . T h th
5 0 1 . 0 1 6

a. 50l.016 b. I6.106 c. 269.428 d. 279.943 e. 84. I 59 f. 7.642

H T U t h th
B 1 6 1 0 6
C 2 6 9 4 2 8
D 2 7 9 9 4 3
E 0 8 4 1 5 9
F 7 6 4 2

3. WRITE THESE AS DECIMAL FRACTIONS.
b 1/100 0.001
c 7/100 0.007
d 4/100 0.004

4. COPY AND COMPLETE.
a 8/100 = 800/1000 b 1/100 = 50/1000
c 3/100 =30/1000 d 5/100 =50/1000

5. WRITE THE NUMBER NAMES.
10.624 ten point six two four

a. 16.081= sixteen point zero eight one
b. 212.236 = two hundred twelve point two three six
C. 40.003 = forty point zero zero three
d. 946.118 =nine hundred and forty six point one eight
6. NOW WRITE THESE AS DECIMALS.
a 18/1000 b 51/1000 c 27/1000 d 73/1000
7. WRITE THESE AS DECIMAL FRACTIONS.
a. 0.002 b. 0.008 c. 0.067 d. 0.011 e. 0.005 f. 0.090
Answer: (a- 2/100)(b- 8/100)(c- 67/100)(d- 11/1000)(e- 95/1000)(f- 90/1000)
8. WRITE AS DECIMAL NUMBERS.
* zero point zero two three ——- 0.023

a. zero point one two eight = 0.128
b. two point six zero nine=2.609
c. eleven point one six zero=1.160
d. nine point zero three nine=9.039 11
P:108 TENTHS, HUNDREDTHS, THOUSANDTHS
1. COPY & WRITE NUMBERS IN THE BLANKS.
4.12, 4.13,——– ,4.l5…4.14
a. 3.7, 3.8,———-,———— , 4.1
b. 6.29, 6.30,———,——–,——-,6.34
c. 13.498, 13.499 , 13.500,————
(a-3.9, 4.0) (b-6.31, 6.32,6.33)
(c-13.501) (d-8.120,8.122)

2. COPY & WRITE SYMBOLS IN THE BLANKS (>, <, OR =).’

100 1 l000 100 :000
a. 0.09 ———— 0.019 b. 0.04 ———— 0.040 c. 5.050 ————–5.05
d. 23.103 ——— 23.013 e. 100.001———- 100.011
3. COPY AND WRITE IN ASCENDING ORDER.
4.17, 4.061, 4.006 ————– 4.006, 4.06l, 4.17
a. 1.09, 1.04, I.10, 1.54, 1.01
b. 2.5 I4, 4.502, 4.506, 4.504
c. 0.6, 0.06, 0.8, 0.008, 1.8
d. 5.32, 5.319, 5.301, 5.33l

a. 1.01,1.04,1.09,1.10,1.54
b. 2.514,4.502,4.504,4.506
c.0.008,0.06,0.6,0.8,1.8
d. 5.301,5.319,5.320,5.331
e. 2.092,2.943,3.002,3.905

4. COPY & WRITE THE PREDECESSOR AND SUCCESSOR OF EACH.
3.682 predecessor 3.68I successor 3.683
a. 4.91 b. 10.001 c. 2.09 d. 9.320 e. 7.030 f. 12.0110

Predecessor Successor
A 4.90 4.09
B 10.000 10.002
C 2.08 2.10
D 9.319 9.321
E 7.029 7.031
F 12.039 12.041

5. COPY & WRITE IN DESCENDING ORDER.
0.l, 0.5, 0.8, 0.3
0.8, 0.5, 0.3, 0.1

5.1, 5.14, 5.0, 5.16 =5.16,5.14,5.10,5.0
3.62, 6.39, 6.4, 6.9 = 6.90,6.40,6.39,3.62
2.703, 2.7, 2.2705, 2.710 =2.710,2.703,2.700,2.2705
6.9, 5.019, 5.9I0, 6.83 = 6.9,6.83,5.910,5.019
7.035, 7.15, 7.35, 7.053 = 7.35,7.15,7.053,7.035
6. COPY & WRITE THESE FRACTIONS AS DECIMALS.
A 337/1000 0.337 B 73/1000 0.073 C 751/1000 0.751
d 264/1000 0.264 E 101/1000 0.101 f 8/1000 0.008
G 509/1000 0.509 h 62/1000 0.062 i 984/1000 0.984

P:109
1. HOW MANY DECIMAL PLACES DO EACH OF THESE DECIMAL NUMBERS HAVE?
0.I5 two decimal places
a. 0.4 =one decimal place
b. 0.099 = three decimal places
c. 0.068 = three decimal places
d. 2.14 = two decimal places
e. 4.069 = three decimal places
f. 1.103 = three decimal places
g. 0.875 = three decimal places
h. 5.21 = two decimal places

2. How many decimal places? Look carefully 12.99……. two decimal places
a. 3.504 = two decimal places
b. 26.730= three decimal places
c. 23.1 I0 = two decimal places
d. l62.090 = two decimal places
e. 103.8 = one decimal places
f. 87.50 = one decimal places

P:110
Q I. CONVERT THESE FRACTIONS INTO DECIMALS.
39/500= 39/500X2 = 78/1000 =0.078
41/250=41/250X4 =164/1000 =0.164
71/250= 71/250X4 =284/1000 =0.284
103/200= 103/200X5 =515/1000 =0.515
227/500= 227/500X2 =454/1000 =0.454
111/250= 11/250X4 =444/1000 =0.444

2. NOW CHANGE THESE MIXED NUMBERS INTO DECIMAL NUMBERS.
1 3/10= 13X10/10X10 = 1 30/100 = 1.30 = 1.3
81/5=8 1X2/5X2 = 82/10 = 8.2
627/100=627/100 6.27
1047/50 =10 47X2/50X2 = 10 94/100 = 10.94
743/1000= 7.043
7121/200= 7 605/1000 = 7.605
29/1000= 2.009
827/250= 8 108/1000 =8.108
28/25= 2 8X4/25X4 = 232/100 = 2.32

Q 3. WRITE THESE AS MIXED NUMBERS IN THEIR LOWEST TERMS. .
a. 2.6124 = 2624/1000 = (624÷8)/(1000÷8) =78/125 so 2.624= 278/125
b. 31028= 328/1000 =(28÷4)/(1000÷4) = 7/250 so 3.028=37/250
c. 5.010= 51/10 so 5.010= 51/10
d. 20.005= 205/1000 =(5÷5)/(1000÷5) =1/200 so 20.005=201/200
P:111 REVIEW
1. CAN YOU COMPLETE SID’S SPECIAL DECIMAL CROSSWORD?
CLUES ACROSS
1. When we multiply a number by I0, the digits of the number jump one place to the——————-
5. I am the name for the second place of decimals.
6. If I come of the end of o (decimal) number, do not count me as cu decimal place.
7. 1 am another name for ‘decimal point’.
9. I am ‘tenth’ in Latin.
I2. There are 100 of me in a metre.
13. 4/100=/1000
14. 0.052 equals zero——————-zero five
two. 2. 1 am the name of the column 3 places to the right of the decimal point.
3. I am the number of decimal places in 6.90.
4. 3.159 is the ——————- of 3.160.
8. For a fraction to be converted into a decimal fraction, its denominator must be a——————- of 10, 100, or 1000.
I0. 7000 paise = ——————-rupees.
11. I am the number in the tenths column of 111.695.

Clues across: (1-left)(5-hundredths )(6-dot )(7-zero)(9-)(11-centimeter)(12-forty)(13-point) Clues down (2-thousandths)(3-one)(4-predecessor )(8-factor)(10-seventy)(14- six)
2. TRUE OR FALSE?
a. 21.7 < 21.66
b. The 6 in 23.569 stands for six tenths.
c. 0.004 < 0.04
d. é is the same as O.125.
e. 0.07 can be written as 7/1000
f. The decimal value of L is
g. 3.74 > 3.7
h. 52.10 is the same as 52.1.
ANSWERS: a. false b. false c. true d. true e. false f. true g. true h. true
Page:112 DECIMAL and MEASURING
1-EXPRESS THESE LENGTHS AS KM (2486 m 2.486 km)
a. 3049 m
b. 629 m
c. 492 m
d. I 038 m
e. 10,501 m
f. 87,6O m
a. 3.049 km
b. 0.629 km
c. 0.492 km
d. I1.038 km
e. 10.501km
f. 87.6O km

2-EXPRESS THESE WEIGHTS AS KG (628 g 0.628 kg)
a.1432 g
b. 485 g
c.69,571 g
d. 832 g
e.10101 g
f. 50959
a.1.432 kg
b. 0.485 kg
c.69.571 kg
d. 0.832 kg
e.10.101 kg
f. 5.095 kg

3-CHANGE THESE KILOLITRES INTO LITRES. (1.493 kl 14931)
a.2.493 kl
b. 0.095 kl
c.10.069 kl
d. 22.608 kl
e.0.802 kl
f. 0.905 kl
a.2493 l
b. 95 l
c.10069 l
d. 22608 l
e.802 l
f. 905 l

4- CHANGE THESE MEASUREMENTS INTO KILO-UNITS. (2′ kg second 1‘80 g — 2.I80 kg)
a. 5 km & 595
b. I0 kl & 408 l
c. 4 km & 602
d. 9 kg & I I5 g
e. 10 kg and 538 g
a. 5.595 km
b. I0.408 kl
c. 4.602 km
d. 9.II5 kg
e. 10.538g

P:113
DECIMALS & MEASUREMENT

Q 5. WRITE AS KILO-UNITS.
9 kg & 3 g 51.003 kg
a. I0 km & I6 m =
SOLUTION:
16m= 16/1000 = 0.16km
10 km and 16 m= (10+0.16)km= 10.16 km
b. 28 kg & 100 g
SOLUTION:
100g = 100/1000 = 0.1 kg
28kg and 100 g = (28+0.1) kg= 28.10 kg
c. I9 km & 4 m
SOLUTION:
4 m = 4/1000 m = 0.004 km
19 km and 4 m = (19+0.004) km 19.004 km
d. 120 kg & I g
SOLUTION:
1g = 1/1000 kg=0.001 kg
120kg 1 g= (120+0.001)kg= 120.001 kg
e. 94 kl & 18 L
SOLUTION:
18L= 18/1000kl = 0.018 kl
94 kl & 18 L =(94+0.01)kl= 94.018kl
Q 6. WRITE THESE WEIGHT AS KG & G.
6.019 kg …6kg 19 g
a. 4.002 kg
b. 25.075 kg
c. 10.010 kg
d. 110.110 kg
e. 92.100 kg
f. 94.070 kg
a. 4kg 2g
b. 25kg 75g
c. 10kg 10g
d. 110kg 110g
e. 92kg 100g
f. 94kg 70g

7. COPY THIS PLACE-VALUE TABLE IN YOUR NOTEBOOK FOR ALL THE FOUR SUMS.
H T O . t h th
8 0 . 0 0 5

Look carefully at these lengths then enter them in your table in decimal form. (The first has been done for you above.)
a. 80 km 5 m b. 220 km I6 m c. 108 km 8 m d. 5 km 200 m
SOLUTION:
H T O t h th
A 8 0 0 0 5
B 2 2 0 0 1 6
C 1 0 8 0 0 8
D 0 0 5 2 0 0

8. TRUE OR FALSE? WRITE T OR F, & EXPLAIN YOUR ANSWERS:.
4905 g = 11.095 kg (F) 4905 g = 4.905 kg
a. 10kg & 1 g= 10.1kg
b. 6.295 kl = 6295 I
c. 3m 2/100 km
d. 291 – 4-1000 kl
e. 9.0I0kg =9 kg 100g
f. 5kg & 5g = 5.0059
g. 38.1 km x 10 = 381 km
h. 1 m 25 cm = I.025 m
P:114 SID’S HISTORY OF THE METRIC SYSTEM
P:115
DECIMALS & MEASUREMENT: THE METRIC SYSTEM
I. Here are some special words (or parts of words) used in the metric system

I Kilo (k) I thousand times (x 1000)
I Hecto (H) 1 hundred times (x 100)
Deca (D) 1 ten times x I0)
Deci (d) I one tenth ( ÷ I0)
Centi (c) I one hundredth (÷ I00)
I Maui (m) I one thousandth (÷ I000)
I decimeter is equal to————-m. ………..one tenth of a metre or 0.1 m
a. I hectolitre is equal to ————————-l .
b. I centimetre is equal to———————— m.
c. I milligram is equal to———————-g.
d I decalitre is equal to ———————-I.
e. I kilometre is equal to———————-m.
f. 2 hectometres are equal to—————– m.
g. I decigram is equal to —————-g.
h. I decilitre is equal to ——————I.
i. I centigram is equal to —————-g.
j. 3 kilograms are equal to ————-g.
k. A millilitres are equal to —————l.
l. 1/5 hectogram equals ———————g.
one hundred litre or 100 l .
one hundredth of a metre or 01.01 m
one thousandth of gram‘ or 0.001 g
ten times of litre or 101.
on thousand times of metre or 1000.
two hundred metre or 200m.
one tenth of gram or 0.1g.
one tenth of litre or 0.1
one hundredth of gram or 0.019.
three thousand times of gram or 3000
0 four thousandth time of litre or 0.004 l.
twenty gram or 20g.
P:116 THE METRIC SYSTEM
1. THINK CAREFULLY, THEN WRITE NUMBERS IN THE BLANKS.
40 mm = —-,cm ………..40 mm = 4 cm
200 cm = ………… m
60 mm = …………. cm
4000 m = ————— km
7000 ml = ……………I
———– mm = 21 cm

2. WRITE THESE LENGTHS IN M.
531 mm 0.531 m
a. 624 mm b. 7083 mm c.1083 mm d. 62 mm e.4002 mm f. 140 mm
a. 0.624 m b. 7.083 m c.1.083 m d. 0.062 m e.4.002 m f. 0.14 m

3. WRITE THESE LENGTHS IN CM.
629 mm …………….62.9
a. 704 mm b. 1401 mm c.1238 mm d. 5 mm e.51 mm f. 202 mm
a. 70.4 cm b. 14.01 cm c.12.38 cm d. 0.5 cm e.5.1 cm f. 20.2 cm

4. Measure these lines very carefully. Then write the length of each line in mm & then in cm.
A__________________
B__________
C_____________
D_____________________
a. 50 mm and 5 cm b. 46 mm and 4.6 cm
c. 57 mm and 5.7 cm d. 48 mm and 4.8 cm

5. NOW MEASURE THESE LINES, SECOND WRITE THEIR LENGTHS IN METRES.
A__________________
B__________
C_____________
D_____________________
a. 4.8cm or 0.048 m b. 3.7cm or 0.037 m
c. 4.4cm or 0.044 m d. 5.3 cm or 0.053 m

6. WRITE THESE LENGTHS IN MM
0.629 m ………. 629 mm
a. 0.I35 m b. 0.123 m c. 0.378 m d. 1.608 m e. 6.100 m f. 9.003 m
a. I35 mm b. 123 mm c. 378 mm d. 1608 mm e. 6100 mm f. 9003 mm
P:117 THE METRIC SYSTEM

7. WRITE THESE WEIGHTS IN kg
52 g …………..0.052 kg
a. 604 g b. 4001 g c. I5 g d. 843 g e. 8329 g f. 2 g g. 7 g h. 14930 g
a. 0.604 Kg b. 4.001 Kg c.0.0I5 Kg d.0.843 Kg e. 8.329 Kg f. 0.002 Kg g. 0.007 Kg h. 14.930 Kg

8. WRITE IN MILLIGRAMS (mg).
I0 g = 10,000 mg
a. 8 g b. 95 g c. I6 g d. 31g e. 24 g f. 50 g
a. 8 x 1000 = 8000mg b. 95g = 95 x 1000 = 95000mg c. 16g = 16 x 1000 = 16000mg d. 3g = 3 x 1000 = 3000mg e. 24g = 24 x 1000 = 24000mg f. 50g = 50 x 1000 = 50000mg

9. WRITE THESE WEIGHTS IN g.
38 mg 0.038 g
a. 52 mg b. 6 mg c. 614m mg d. 5943 mg
a. 52 mg = 52 ÷ 1000 = 0.052 g b. 6 mg = 6 ÷ 10000 = 0.006 g
c. 614 mg = 514 ÷1000 = 0.614 g d. 5943 mg = 5943 ÷ 1000 = 5.943 g

10. WRITE IN mg.
1.6 g ….. 1600 mg
a. 2.4 g b. 3.02 g c. 5516 g d. 6.801 g e. 0.01 g f. 0.004 g
2.4g = 2.4 x 1000mg = 2400 mg
3.02 g=3.02x1000mg=3020mg
5.96g=5.96x1000mg=5960mg
6.801g=6.801x1000mg=6801 mg
0.01g=0.01x1000mg=10mg
0.004g=0.004x1000mg=4mg
11. WRITE VERTICALLY & COMPLETE.
0.143 g + 1.297 g
SOLUTION:
0.143 g
+ 1.297 g 6.014 g – 4.938 g
SOLUTION:
6.014 g
– 4.938 g 7.068 g – 3.172 g
SOLUTION:
7.068 g
– 3.172 g
1.440g 1.076g 3.896g

12. WRITE THESE CAPACITIES IN ml
I.62 L 1620 ml
a. 2.04I L b. 10.004 L c. 0.634 L d. 0.96 L e. 4. I 5 L f. 11.4 L
a. 204I mL b. 10004 mL c. 634 mL d. 960 mL e. 4I50 mL f. 1140 mL

13. CHANGE THESE INTO L. 4 ml 0.004 l
a. 5 ml b. 23 ml c. I6 ml d. 908 ml
I4. EXPRESS THESE AS kl. 493 I ……….. 0.493 kl
a. 23 l b. 8 l c. 691 l d. 59 l e. 104 l f. 5 l
SOLUTION:
a. 0.023 kl b. 0.008 kl c. 0.691 kl d. 0.059 kl e. 0.104 kl f. 0.005 kl
I5. CHANGE INTO L. 69.2 kl ………. 69,200 l
a. 14.01 kl b. 20.639 kl c. 7.243 kl d. 1.05I kl e. 0.03 kl f. 8.06 kl
I6. WRITE VERTICALLY & COMPLETE.

a. 0.63I g x 5 b. 1.072 l x 4 c. 0.059 kg x I0 d. 6.432 k1 x 8
SOLUTION: SOLUTION: SOLUTION: SOLUTION:
0.63I
x 5 1.072
x 4 0.059
x I0 6.432
x 8
3.155 4.288 0000
0590 51.456
0.590

P:118 METRIC WORD PROBLEMS
1. SOLVE THESE PROBLEMS IN YOUR NOTEBOOK, MAKING COMPLETE STATEMENTS.

a. Alam cycles 4.75 km every day. How far does he cycle in 5 days?
SOLUTION:
Alam cycles every day = 4.75 km
Alarn cycles in 5 days = 4.75 km x 5
5 4.75
X5
23.75
So Alam Cycles in 5 days = 23.75 km

b. A bookcase is 80 cm high. It sits on top of a cupboard which is 1.45 m high. What is their combined height?
SOLUTION:
A book case high 1: 80cm
A Cup board high = 1.45 m
So
A cup board height =(1.45 x100) m=145cm
so Combine high = (80 + 45) cm 18

145
+80
225
so combined high = 225 cm or 2.25 m.

c. Saima’s magic rose plant grows I0 mm each month. How many centimetres will it grow in one year?
SOLUTION:
1mm =10cm
so As Saina’s magic rose grows = 10 mm
=100cm
1year =12-months
so in 1 year Saina’s magic rose =100 x12 months
1 00
x1 2
1200

So in 1 year Saima’s magic rose grows = 1200 cm

d. The perimeter of a tennis court is 69.48 m. How many metres long is the other side of the court if one side is 10.97 m?
SOLUTION:
Perimeter of a tennis court = 69.48m
one side of tennis court A = 10.97m
so other side of the court =(69.45 -10.97)
69.48
-10.97
58.51

so other side of the court 58.51 m

e. Saleem runs round a 500-metre track I5 times during a training session. How many kilometres does he run altogether?
e. Saleem runs round a track = 500m
Saleem runs on track = 15 times
so Saleem runs on track = (500 x 15)m
500
X15
7500
f. Moham broke the 3.95 m record for long jump by 20 cm. What was the new long jump record she set?
f. Old record in long jump =3.95m = 395cm
new record by Maham = (395+20)cm
=405cm=4.05m

a. 25 cm, 2 km, 150 cm, 250 cm, 30 m: Add the two longest distances together.
SOLUTION:
The two longest distance are 2 km and 30 m
so as 1 km =1000 ml
so 2 km=2000 m
2000 m
30 m
2030 m
b. If one side of a square field measures 5i.5 m, what is the perimeter of the field?
SOLUTION:
One side of a square field = 51.5 m
so perimeter of the field = 4 x 51.5 m
51.5
X4
206.0
so perimeter of the field = 206m
c. 130 g, 22 g, 10 kg, 41 g, 8 kg: Add the heaviest to the lightest of these weights.
SOLUTION:
heaviest= 10 kg
lightest = 22 kg
1kg = 1000g
10 kg =10000 g
so
10000
+22
10022 g

3. NOW SOLVE THESE, MAKING COMPLETE STATEMENTS.

a. Sid bought I kg of apples, 0.5 kg of plums, 0.75 kg of grapes, second 2.25 kg of tomatoes. What was the total weight in kg?
SOLUTION:

a. Apples 1.00 kg
0 Plums 0.50 kg
grapes 0.75 kg
tomatoes 2.25 kg
4.50 kg
So total weight = 24.50 kg
SOLUTION:
b. Rohail weighs 23.423 kg. His father weighs exactly three times Rohail’s weight. How much does Rohail’s father weigh?
SOLUTION:
Rohail’s weight = 23.423 kg
Rohail’s Father weight = 3 time RohaiI’s
so Rohail’s father weight = 23.423 kg x 3
23.423
X30
70.269
so Rohail’s father weight = 70.269 kg

c. Which is heavier-a 5-kg sack of rice or two 750 g bags of sugar? By how
much?
SOLUTION:
Sack of rice = 5 kg
Two bags of sugar = 750 g
as 1000 g = 1 kg
so two bag of sugar = 0.75 kg x 2
So one-slices weight = 0.358
so sack of nee are heavier than bag of sugar
so
5.00
– 1.50 kg
3.50 kg
3.50 kg more heavier sack of rice than bags of sugar.

d. A big chocolate cake weighs 2.864 kg. If it is cut into 8 equal slices, how much will each slice weigh?
SOLUTION:
Total weight of cake = 2.86419
It cuts into slices =8 equal
One slice weight = 2.864÷8
0.358
8 2.864
2.4
0.46
0.46
0.064
0.064
0
So one slice weight = 0.358
P:119 MORE METRIC WORD PROBLEMS
4. THINK CAREFULLY, THEN SOLVE THESE PROBLEMS IN YOUR NOTEBOOK, MAKING COMPLETE STATEMENTS.
a. Anila bought 2 l of green paint, 1% I of blue point, 250 ml of white point and 2% I of yellow paint. How much point was that altogether? (Give your ANSWERS:
green paint = 2 L
blue paint = 5/4 L
white = (250 ÷ 1000) = 0.25 L, 1/4 L
yellow paint = 5/2 L
so total paint =2 L+ 5/4 L+ 1/4 L +5/2 L
=(2 + 5/4 + 1/4 +5/2 ) L
=(8+5+1+10)/4

=24/4
=6
b. A water tanker carried 12,000 I of water. When the tanker returned, its tank was one quarter full. What quantity of water had been delivered?
SOLUTION:
Total water in tanker = 12000 L
Water left = 1/4 x 12000 L
remaining water = 3000 L
water delivered = 12000-3000 =9000 L
c. In a factory, a machine fills twenty 100 ml bottles with oil in one minute. How many litres of oil are bottled in one hour? If I.5 ml of water leaks from o tap in one minute, how much water will be wasted in g of an hour?
SOLUTION:
In L minute = 20x 100ml
In 1 hour= 20 X100 x 60ml
=(20 x 100 x 60)/1000
=120 L
d. if 1.5 ml of water leaks from a tap in one minute, how much water will be wasted in 3/4 hours?
SOLUTION:
leakage of water an one minute = 15 ml
leakage of water in = 3/4 x 60
=1.5x3x15 ml
= 22.5 x3
=67.5 ml

e. At Alamgir School, there are three fish tanks. They can hold 4.51, 6.25 l, and 4.8751 of water each. How much water would be needed to fill all three tanks?
SOLUTION:
Fish tanks = 3
Water needed =“ 4.5 L+ 6.25L + 4.875L
4.50 L
6.250L
4.8751
15.675 L

so total water needed = 15.675 L

5.NOW SOLVE THESE, THINKING VERY CAREFULLY BEFORE YOU ANSWERS:.
a. The sides of a triangle measure 4.5 cm, 3.2 cm, second 4.3 cm. Find one-half of the perimeter of this triangle. Then express your ANSWERS in metres.
SOLUTION:
Sides of a triangle are =1.5cm, 3.2c and 4.3cm
Perimeter of triangle =4.5+3.2+4.3=12 cm
1/2(perimeter)=1/2 x12=6cm
1/2 (perimeter) in meter = 6/100 m= 0.6 m

b. Four 25-cm pieces are cut from a length of wood. This leaves I.3q m. How long, was the original piece of wood? What is the difference in weight between ten I5 g packets second two 5 kg packets?
SOLUTION:
One piece length of wood=25 cm
leaves = 1.36 m
length of the wood initially =4×25 cm +1.39 m
= 100 cm + 1.39
=1 m + 1.39
= 2.39m
c. what is the difference in weight between ten 15 g packets and two 1/2
kg packets?
SOLUTION:
1 packet = 15 g
10 packet = 15 x 10g
1 packet = 1000/2 g = 500
2 packet = 2×500 g = 1000g

So difference is =(1000 – 150)g
= 850 g
d. Sana made 6 I of chocolate milkshake. Her brother, Ali, took half of this. Sana shared the rest with her 3 friends. How much milkshake did each of the four girls have?
SOLUTION:
Total milk shake = 6L
Ali’s took shake = 1/2 x 6 L = 3L
left milk shake = 6L- 3L= 3L
each girl took milkshake = 3/4 litter
there are four girls.

e. A pocket dictionary is 20 mm thick. How many of these dictionaries are needed to form o pile 48 cm high?
SOLUTION:
Thickness of one = 20 mm
=20/100 = 2 cm
A pipe height = 48cm
number of dies = 48/2=24

P:120 REVIEW
1. LOOK CAREFULLY AT THIS NUMBER:
4143.629
a. hundreds place? B. thousandths place? C. ones place? D. tenths place? E. thousandths place? F. tens place g. hundredths place?
WHAT THE DIGIT IN EACH OF THE FOLLOWING PLACES.

2. WRITE THESE AS DECIMALS.
a 3/1000 0.0003
b 9/10 0.9
c 69/1000 0.069
d 8/10 0.08
e 72/100 0.72
f 501/1000 0.501

3. COPY & WRITE SYMBOLS IN THE BLANKS (>, <, OR =).
a. 20/100 ———- 20/10
b. 200 g ———— 0.2 kg
c. 0.5 ———- 0.05
d. 1.65kl ———–170 l
e. 1.19 ———–1.90
f. 48 cm ————- 4.85 m
4. WRITE THESE AS FRACTIONS OR MIXED NUMBERS.
a. 0.35 = 35/100
b. 10.09 = 1009/100 = 10 9/100
c. 0.6 = 6/10
d. 0.93 = 93/100
e. 0.003 = 3/1000
f. 20.1O5 = 20.105/1000 = 20 105/1000

a. 24.09 + 10.13 b. 35.06 – 8.79 c. 416.45 + 2.08
SOLUTION: SOLUTION: SOLUTION:
a. 24.09
+ 10.13 b. 35.06
– 8.79 c. 416.45
+ 2.08
34.22 26.30 418.53
d. 19.165 – 9.786 e. 1.09 + 0.999 f. 5.031 – 2.875
SOLUTION: SOLUTION: SOLUTION:
d. 19.165
– 9.786 e. 1.09
+ 0.999 f. 5.031
– 2.875
8.379 2.089 2.156
6. WRITE CORRECT DECIMAL NUMBERS FOR *
a. 5946 p = Rs *
b. 4 mm = * m
c. 8cm – *m
d. I5 gm = * kg
e. 102 m – * km
f. 24 p = Rs*
g. 161 – *ml
h. 129g – *kg
i. 890p = Rs*
j. 13ml = *l
a. Rs 59.46
b. 0.004 m
c. 0.08 m
d. 0.015 kg
e. 0.102 km
f. Rs 0.24
g. 16000 mI
h. 0.129 kg
i. Rs 8.9
j. 0.013 I

7. MULTIPLY OR DIVIDE.
a. Rs49.75 X I2
SOLUTION: b. 4.968 km ÷ 8
SOLUTION: c. 0.773 g x 15
SOLUTION: d. 46.231 l x 5
SOLUTION:
49.75
X 12 4.968 km ÷ 8 0.773
x 18 16.231 L
x 5
9950
49750
8 0621 6184
7730 81.155 L
597.00
4.968
48
16
16
8
8 13.914 g
e 14.697 kl ÷ 9
SOLUTION: f. 2.076 kg ÷ 6
SOLUTION: g. l.013 kg x I0
SOLUTION: h. 2.6 cm X 100
SOLUTION:
9
1.633

6
0.346 1.013 kg
x I0 2.6 cm
X 100
14.697
9 2.076
18 10.13 260.0
56
54 27
24
29
27 36
36
27
27

P:121 LOOKING AT LINES
P:123 MAKING ANGLES
1- Cut two strips of card and fasten them with a paper fastener or paper clip at one end. You can colour them differently.

1.Turn one of the strips to make a right angle:
A right angle

2. Now make an angle smaller than a right angle by turning your strip back a little. You have now made an acute angle:
An acute angle
3. Now turn your strip beyond a right angle but not as far as a straight angle. This is called an obtuse angle:
An obtuse angle
4. Lastly, turn your strip even further, beyond a straight angle. You have made a reflex angle:
A reflex angle

Q 2. Look carefully at these angles. Then copy them in your notebook & name them.
Answer: (a- Acute)(b-right)(c- right)(d- straight)(e-reflex)(f-obtuse) (g-acute)(h-reflex)
P:124 MORE ABOUT ANGLES: THE( ∠ ) SYMBOL

3. NAME THE ARMS OF THESE ANGLES.
Answer: (a-AB and BC)(b-WX and XY)
4. NAME THE VERTEX OF THESE ANGLES.

5. Draw any angle, and label it as shown.
∠PQR (vertex Q)

a. ∠EFG (vertex F)

b. ∠JKL (vertex K)
c. ∠STU (vertex T)
d. ∠MNO (vertex N)
6. NOW DRAW ANGLES TO THE NAMES.
∠XYZ (right angle)
a. ∠PQR (acute angle)
b. ∠ABC (reflex angle)
c. ∠DEF (obtuse angle)
d. ∠WXY (right angle)
e. LRST (reflex angle)
f. LLMN (right angle)
match

P:125 FINDING THE RIGHT ANGLE!
I. Look at the angles, second tick ( ) all those that are right angles
2. Look around your classroom. How many right angles can you spot? Look at this book! Look at your desk! There are right angles all around us.
In your notebook, make a list on this pattern:
Object Location of right angle
Window

Tree Angle made by 2 sides

Angle between tree
trunk second ground

How many examples can you locate? Make sure you locate more than your neighbour does!

3.Look around your home second your school. Make a list of acute angles and obtuse angles.
Object Type of angle
Back of chair
and its seat obtuse angle

P:126 ANGLES , DEGREES AND PROTRACTOR
I. Draw a base line 6 cm long and label it AB. Now place your-protractor so that the middle of its bottom line is exactly on A .
Find the ’90’ mark on the protractor and mark it ’C’. Remove the protractor. Join C to A. What angle have you drawn?
P:127 ANGLES , DEGREES AND PROTRACTOR

2. LOOK CAREFULLY AT THE CIRCULAR PROTRACTOR ABOVE. THEN ANSWERS: THESE QUESTIONS.
How many degrees in half a circle? 360° + 2 = l80°

How many degrees in a quarter circle?
How many degrees in a right angle?
How many degrees in 1/10 a circle?
How many degrees in a straight line?
1/4circle + 1/10 circle =—————– degrees.
3/4 circle = ————- degrees.
2 right angles added together = ————- degrees.
Answer: (a-90o)(b-90o)(c- 1/10=1/10 x 360=36o)(d-180o)(e-1/4 circle+1/10 circle , 1/4 x 360= 90+36=126o)(f-3/4 circle =3/4 x 360=270o) (g-90o+90o=180o)
P:128 USING THE PROTRACTOR
1. Look at the angle you want to measure:

Is it an acute, obtuse, or a right angle?

Label the angle as ABC.
∠ ABC= acute

2. Place the centre point of your protractor on the vertex of the angle (B).

3. Put the 0 mark along the arm BC.

4. Now look very carefully to see at what number in the ‘cop row of markings the ‘AB’ arm of your angle crosses the protractor.

+

Since the ‘AB’ arm crosses at the number 30, so ∠ ABC = 30°.

P:129 USING THE PROTRACTOR: ACUTE ANGLE
Use your protractor to measure these angles. Think carefully which row of markings on the protractor you should use.

2. Look cut the protractors and write down the angles they show.

P:130 USING THE PROTRACTOR: OBTUSE ANGLES
3. Measure these obtuse angles, thinking carefully which set of markings to use.
4. Measure the angles shown in the drawing and complete the table.

∠ABC = 45o
∠ABD = 60o
∠ABE = 90o
∠ABF = 120o
∠CBE = 45o
∠DBF = 60o
5. Estimate second then measure each of the following angles. Then complete the table that follows.

6. Draw more angles in your notebook at random without a protractor second complete a similar table.
P:131 USING THE PROTRACTOR: DRAWING ANGLES

7. Draw these angles in your notebook, using 0 protractor (Your angles can open in either direction).
a. 30°
b. 65°
c.50°
d. 125°
e.70°
f. 10°
g. 90°
h. 75°
i. 10°
j. 155°
k. 45°
l. 170°
m. 130°
n. 105°
o. 25°
p. 180°

1. Measure the sides of these 4 triangles. Write equilateral, isosceles, or scalene for each one.

isosceles
2. Measure the sides of the triangles given below carefully then record your finding thus:
equilateral isosceles scalene
A

P:133 TRIANGLES & THEIR ANGLES
I. Use a set square second find out which of these are right-angled triangles.
2. In your notebook, draw a table like this. Then put the triangles shown below into the correct column.

P:134
I. Measure the angles of these triangles. Then record your findings on u table like this.
Triangle angle Total of all 3 angles
x y z
A 50° 90° 40° 180°

1. Which shapes shown above have:
4 right angles? square, rectangle

a. No right angles?
b. 4 sides of equal length?
c. Both pairs of opposite sides parallel?
d. 4 equal sides second la right angles?
e. 4 equal sides but no right angles?
Kite, .parallelogram trapezium, arrow and rhombus have no right angles.
Square and rhombus have 4 sides of equal lengths.
Square, rectangle, parallelogram and rhombus have both pairs of opposite sides parallel.
Square has 4 equal sides and 4 right angles.
Rhombus
2. Carefully measure the angles of this parallelogram and record
∠a=60
∠b=120
∠c=60
∠d=120
∠a+∠b+∠c+∠d=360
P:136
I. Test Sid’s Important Rule on page 135 by measuring the angles of these

p q r s
A

2. DRAW RECTANGLES WITH SIDES; OF THESE LENGTHS
a. 10.2 cm and 6.3 cm
b. 01.5 cm and 3.7 cm
Calculate the perimeter of each.
3. DRAW SQUARES WITH SIDES THESE LENGTHS.
a. 5.6 cm
b. 3.9 cm
Calculate the perimeter of each.
3. DRAW SQUARES WITH SIDES OF
P:137 PERPENDICULAR LINES
I. ARE THESE LINES PERPENDICULAR TO EACH OTHER? WRITE YES OR NO.

2. LOOK CAREFULLY AROUND YOU. WHAT PAIRS OF PERPENDICULAR LINES CAN YOU SEE? RECORD THEM ON A TABLE LIKE THIS.
Name of object Location of the perpendicular lines
Pencil box 2 sides of the lid

3. DRAW LINES OF THESE LENGTHS PERPENDICULAR TO EACH OTHER.
AB=3cm, CD=2cm

a. PQ=4 cm ST = 8cm
b. XY=cm, UV = 6.3 cm
c. EF =7.4 cm, JK = 4.7 cm
d. LM=cm RS = 4.8

P:138
COLUMN GRAPHS
I. LOOK CAREFULLY AT THIS COLUMN GRAPH.
Favourite Colours of Children in Class 4A

blue red Yellow green pink orange

a. How many children like red the best?
b. Which colour is least liked?
c. How many children like orange best?
d. For how many children is blue not the favourite colour?
e How many children are there in Class AA?
f How many children like green the most?
Answer: (a-8 children)(b-pink)(c-7 children)(d-27 children)(e-33 children)(f-4 children)
2. HERE IS A COLUMN GRAPH FOR 20 CHILDREN, EACH UNIT OF WHICH STANDS FOR 5 CHILDREN ALONG THE VERTICAL.
Children Absent from School
Mon Tues Wed Thurs Fr1
STUDY THE GRAPH SECOND ANSWERS: THE QUESTIONS.
a. How many children were absent from school on Friday?
b. How many more children were absent on Monday than on Wednesday?
c. How many children were not in school on Tuesday & Wednesday?

3. STUDY THE GRAPH & ANSWERS: THE QUESTIONS.
Money Collected for Homeless Families
Mon Tues Wed Thurs Fri Sat

a. How much money was collected on Wednesday?
b. How much more money was collected on Friday than on Tuesday?
c. On which day was the most money collected?
These column graphs tell us cx lot about Sid Spacewalker second his family (wife Sara & children Sue, Selvi, & Sprog
1. STUDY THE GRAPHS SECOND ANSWERS: THESE QUESTIONS.
a. What is the difference in the heights of Sprog second Sara?
b. How much older is Sue than Selvi?
c. How much lighter is Sue than Sid?
d. How old was Sara when Sprog was born?
e. Which member of the family cannot walk through a 2-m high door without bending?
f. How many stamps do Sue, Selvi, second Sprog have altogether?
g. Sid’s spaceship can carry not more than 250 kg. Can all five members of the family travel in the ship together?
h. If Sid gives % of his stamp collection to Sprog, how many stamps will Sprog now have?
i. If Sue second Selvi lie end to end, how for will they stretch?
j. If Selvi second Sprog climb together onto the scales, what weight will be shown?
Answer: (a-2-1=1m)(b-14-8=6 years)(c-80 kg -40 kg=40kg)(d-26-8=18 y)(e-Sid)(f-600+300+100=1000 stamps) (g-yes)(h- 1/4 of 600+100=150+100=250 stamps)(i-1.5 +1=2.5) (j-30+20=50 kg)
P:140 THE PIE CHART
1. STUDY THE PIE CHART, THEN ANSWERS: THE QUESTIONS.
Colours of Bangles Worn bg Teachers at Alamgir School

What colour bangles were worn by most teachers?
What colour bangles were worn by the least number of teachers?
Which colour was worn by more teachers, green or blue?
NOW STUDY THIS CHART.
Favourite Sports of Class AB
Which is the most popular sport among the students of Class 4B?
Which is their least favourite sport?
Which is more popular, football or cricket?