WORKSHEET/ SOLUTION: OXFORD MATH / NEW COUNTDOWN5 SECOND EDITION (OXFORD UNIVERSITY PRESS OUP ISBN 9780199061853)
WORKSHEET/ SOLUTION: OXFORD MATH / NEW COUNTDOWN5 SECOND EDITION (OXFORD UNIVERSITY PRESS OUP ISBN 9780199061853)
PART ONE
P: 1 GETTING READY
1NUMBER PARMIDS.
Complete these pyramids.
a  b  c  d  e  
18  
24  6  11  6  12  8  
44  79  23  18  12  2  9  48  10  5  
24  10  2  17  3  
2Maths in your head! Work out the answers in your head, then write them in your notebook.
aThe LCM of 6 and 9 =———————–
bIf a square carpet covers an area of 25 ml, each side is —————————– m long.
cA rectangle I I.5 cm long and 11.5 cm wide has a perimeter of ——————cm.
dIn AABC, ABAC = 70°, and LABC = 45°. What will BCA be equal to?
eWhat is the fraction form of (i) 0.2? (ii) 0.057 (iii) 0.00821
fIf five pens cost Rs 20.25, how much do two pens cost?
gVI + III =——————– in Arabic numerals.
h8650 + 100 = r——————
iA room 13 m long and 11 m broad has an area of —————————m^{2}.
j2+ 4=———————– in decimal form.
kThe HCF of 28 and 56 =—————
P: 2
3Copy and fill in the missing numerals (think carefully)
a  49—— 81  b  4379——  c  ——6504  d  56——52 
9719  2193  7923  4348 
4Write the number in words.
a  4,50,219  
b  9,00,675  
c  1,60,524  
d  18,301 
5Write symbols for *s (>, <, =)
a  10.023————10.21  b  14.31 kl———–14310 kl 
c  10————–10  d  +————–+ 
e  0.035m———350m 
6Divide by I0, then by 100
A  2,65,030  
B  8398  
C  3,07,296  
d  94,351 
 Give the value of the coloured digit.
a329064  b9.172  c1,04,943  d25.038  e18.064  f35.111 
 Write vertically and complete.
a  3849×32  b  9.134×15  c  637×146 
d  8.356×20  e  1.032×7  f  1.83×43 
9 Write as 24 hour clock times.
a  4.25 p.m.  b  11.12 p.m.  c  12.14 p.m.  d  9.18 p.m.  
10 Write in ascending order.
a  3.51, 3.15, 3.165, 3.55  
b  0.112, 0.02, 0.001, 0.121 
11 Write as fractions.
A:14.01  B:625.3  C:10.005  D:497.02  E:84.038  F:596.357 
P: 3
12 Write in long division form and complete.
a  693÷47  b  16848÷8 
47  8  
c  875÷56  d  109.15÷3 
56  3 
13Write in order, starting with the smallest.
a  m,3.5cm,25mm,20cm  
b  m,1.7 m, 120cm, 35cm  
c  l,27 l, 430 l,3.2 l 
14Write the HCF of:
a27 and 45  b. 56 and 72  c25 and 35  d. 60 and 40 
15Tick the numbers that are divisible by 9.
a3,06,051  b. 30,1106  c1,18,275  d. 2,57,08 
16Add or subtract.
a  3+2  b  10 – 4 
c  5+6  d  91 
17Write as decimals.
a 8  b 7  c 6  d 9  e 4  f18 
I8. Write vertically and complete.
a  2,68,03 + 53,458 + 174  b  I6 + 75,034 + 759 +1632  c  1845 + 9 + 64,038 + 1,01,295 
19 Using your protractor or set square, draw rectangles with sides of these lengths.
a. 5.8 cm and 3.7 cm  b. 9.3 cm and 5.1 cm  c. 8.4 cm and 4.5 cm 

 Draw these angles using a protractor. (Your angles can open in either direction.)
a  20°  b  110°  c  I30° 
d  90°  e  45°  f  125° 
21 Now draw these angles and label them.
a. ∠ PQR =85°  b. ∠ ABC=145°  c ∠RST = 90°  d. ∠EFG = 25°  e. ∠JKL = 120° 

P: 4 MORE ABOUT GRAPHS: THE 4NE GRAPH
1Look carefully at the 4ne graph at the bottom of the previous column, and answer these questions.
aWhat was the height of the plant on the 1^{st} day?
bHow many cm did the plant grow between the 2nd and 5th days?
cHow many cm did the plant grow between the 2nd and 3rd days? .
dBetween which days did the plant grow the fastest?
2Study this 4ne graph and answer the questions.
a What is the cost of 3 pizzas?
bIf Sid Space walker has a Rs 500 note, how many pizzas can he buy?
cIf Sid needs 25 pizzas for a party, how much money must he spend?
P: 5
LINE GRAPHS
1Copy and complete this Line graph.
Number of bars of chocolate
4Study the graph, then answer the questions that follow.
Number of Litrebottles of Lemon squash
aWhat is the cost of 31 of lemon squash?
bIf you have two Rs 20 notes can you buy 4 l of lemon squash?
cHow much change will you get from Rs 100 when you buy 2 l of lemon squash?
Journey of brown car from Karachi to Lahore
Brown car time (in hours) A
Journey of black’ car along Rawalpindi,
Black car time (in hours)
 Use the graphs given above to answer these questions.
 How much farther did the brown car travel than the black car?
 Between which hours did the driver of the black car stop for lunch?
 At the end of the 3rd hour, how far had each of the two cars travelled?
 In which hour did the black car travel the farthest?
P: 6 LINE GRAPHS
The graph tells us about Sara Spacewalker’s ride on her spacemoped.
Time (24hour clock)
 Study the graph, then answer these questions.
How many km had Sara travelled by 11.00 hours?
 At what time did Sara begin her trip?
 What was the total length of her journey in km?
 At what time did Sara stop for a rest? How long was it before she resumed her journey?
 How far had Sara still to go at 11.3O h?
 At what time did Sara complete exactly half the distance of her journey?
This Line graph tells us about people arriving at Qaddafi Cricket Stadium, Lahore, to watch a test match between Pakistan and England.
7Now answer these.
>>>How many people arrived in the stadium by 9 a.m.?—–1000
aWhen the match started at I0 a.m., how many people were in the stadium watching it?
bHow many people arrived in the stadium between i0 a.m. and 4 a.m.?
cHow many people were in the stadium when the play stopped at noon for lunch?
P: 7
PLOT YOUR OWN 4NE GRAPH!
 Draw this graph on a sheet of paper.
 Answer these questions about the graph you have just drawn.
 What length of the scarf had Sara knitted by I0 a.m.7
 What length of the scarf was already knitted when Sara began work at 8 a.m. 7
 By how many cm did the length of the scarf increase before Sara stopped for lunch at I p.m.?
 During which hour did Sara knit the most?
 Aleem sells ice cream between I0 a.m. and 3 p m .The table below shows how many ice creams he has sold at the end of each hour:
Think and plot a graph to show his sales. As Sara does in her graph, make the bottom, horizontal arm of your graph showing the time, and the vertical arm showing the number of ice creams sold.
P: 8 REMEMBERING 5DIGIT & 6DIGIT NUMBERS
1Write the value of the coloured digit.
>>>42,851… 2 thousands or 2000
A  23,116  
B  120,493  
C  94,017  
D  2,84,327 
2Write in expanded form. 2, 56,139= 2, 00,000 + 50,000+6,000+ 100+30+9
A  40,024  
B  11,204  
C  4,211,502  
D  6,01,751 
3Write the number, placing your commas correctly.
Two lakh, sixteen thousand four hundred and two =2, 16,402
aSeven lakh, five hundred and thirtyeight=
bEight hundred and two thousand, and seventyfive=
cOne hundred and eleven thousand, and one=
dFive lakh, five hundred and fiftyfive=
4Put these numbers into International periods. l,60,029= l60,029
a  5,93,I62  b  6,05,0I6  c  8,I7,724′  d  2,I2,2I2 
5Change these numbers from International to Pakistani periods. 398,402= 3, 98,402
a  I00,253  b  999,094  c  412,0811  d  358,1I2 
6Write the successor of each number.
aI,09,029  b3,99,999  c2,45,499  d3,49,999 
7Write the correct symbol (>, <, =). in each blank.
>>>2, 84, 169————2, 84, I69 2, 84, 169=2, 84, I69
a3,25,00 1—————–3,52, 100
b3,84,292 10————3,84,283
c9,00,0 I 0 “I 00———8,99,900
d3,58,666 X 2 —————–7, I 7,342
P: 9 THINKING ABOUT 7 DIGIT NUMBERS: TEN LAKH
1Write the number names. 40, 00,000 = forty lakh
a15,00,000  b60,00,000  c48,00,000 
2Write the number, placing your commas correctly. Twentythree lakh=23, 00,000
a Nineteen lakh  b Eightyfour lakh  c Seventy lakh 
3Place these 7digit numbers in Pakistani periods and write their names.
19, 60,283 = nineteen lakh, sixty thousand, two hundred and eightythree
A  3 1,19,624  
B  47,03,955  
C  60,30,158  
D  80,00,206 
4Write the numbers, placing your commas carefully.
Sixtyfour lakh, two thousand and sixty = 64, 02,060’
Seventyone lakh, twelve thousand, and fortytwo
Thirtythree lakh, ninety thousand five hundred, and sixtyseven
Eighteen lakh, four thousand two hundred, and seventytwo
P:10 TEN LAKH EQUALS ON ONE MILLION
1Place these in periods, ‘first in the Pakistani Way, second in the International Way
8324967 ——— 83, 24. ‘167 = 8,324,967
A  2905384  
B  64703 I7  
C  320059  
D  4305016 
2Write the number names. 2,000,000 two million
a.4,000,000  b.6,500,000  C.90,000,000  d.5,620,000  e.8,000,000  f. 2,840,000 
3Write the number, placing your Commas correctly. Five million 5,000,000
Two million, five hundred thousand=
Five million, seven hundred and forty thousand=
Eight million, six hundred thousand=
Nine million, nine hundred thousand=
4Change these numbers into International periods. 14,67,015 = 1,467.015
a.60,29,347  b.19,03,001  c.25,00,123  d.8,49,016  e.81,07,869  f.14,03,970 
P:11 7DIGIT NUMBERS; PLACE VALUE
1Look carefully at the numbers, then write the value of the coloured digit. 49,648,123 = six hundred thousand or 600.000
a  14,79,623  
b  1,090,900  
c  3,495,631  
d  8,049,315  
e  28,04,925  
f  9,116,661 
2Read aloud, then write in words.
75,00,065 =seventyfive lakh and sixtyfive
a  702,019  
b  60,03,007  
c  6,750, 1142  
d  96,52,095 
3Write the number. One million, two hundred and fortyseven thousand,
three hundred and sixtytwo , l,247,362
a  Twentyeight lakh, sixty thousand, seven hundred and thirteen  
b  Five million, eight thousand and twentythree  
c  Thirtyfive lakh, fortyone thousand and eighteen 
4Write in expanded form.
6, 482, 1 I3 =6,000,000 + 400,000+ 80,000 + 2000+ 100 + I0 + 3
a  4,532,481  
b  6,093,048  
c  28,16,019  
d  37,05,131  
e  17,53,224  
f  3,629,503 
5Arrange in ascending order.
9,248,517; 9,240,715; ‘9, 2208,751 9,208,75I; 9, 2110, 715; 9,248,517
a18,06,295; I8,60,995;18,06,259 
b4,053,6I2; 4,035,8I2; 4,530,2I6; 4,033,065 
c24, I 5,396; 24,51,996; 24,05,031 
6Write the predecessor. 32,00,000 31,99,999
I 8,20,200  6,243,000  53,60,000  49,50,000  4,632,450  I 2,02, 100 
P:12
7DIGIT NUMBERS: PLACE
Write the number that matches each of these expanded forms.
2,000,000 + 88,000 + 400 + 2 = 2,088,402
44,00,000 + 6000 + 300 + I0  a  
67,00,000 + I0,000 + 2000 + 500 + 4  b  
3,000,000 + 700,000 + 40,000 + 2000 + 60 + 9  c  
8,000,000 + 500,000 + 3000 + 700 + 40  d  
90,00,000 + 40,000 + 6000+ 100 + 90 + 1  e  
1,000,000 + 80,000 + 5000.+ 800 + 50 + 8  f 
8Read aloud, then write in words.
8,096,432  a  
1, 100,001  b  
64,03,1 I5  c  
5,700,300  d  
10,01,100  e  
9,123,312  f 
9 Arrange in descending order. 1,293,401; 1,923,401; 1,239,104
I.‘123,40I; I ,2‘l3,l»0 I; 1,239, I 04
a. l5,00,62fI; 15,00,962; 15,00,266 
b. 23,14,038; 23,41,380; 23,I4,38I 
c. 5,690,410; 5,691,4I0; 5,69I,44I 
I0 Write the correct symbol In each blank (>, <, =).1 ,250, 13 1—— 1,250, 1 31
I2,50,311 < I2.50,311
 4,084,620—————4,084,260
 18,50, 119————— 18,51,119
 23,62,731—————–23,26,731
 5, 116,290—————51,16,290
 64,033,495————–64,04,495
 73,02,220—————7,302,220
P:13
THINKING EVEN BIGGER : 8DIGIT NUMBERS
Write the number names—————8,00,00,000 8 crore
4,00,00,000  6,00,00,000  2,00,00,000  10,00,00,000  5,00,00,000  9,00,00,000 
2Write the numbers.
Three crore 3,00.00.000
Eight crore  One crore  Eleven crore  Four crore  Five crore  Twenty crore 
3The following list gives the total number of votes won by seven constituencies in Pakistan. Place each number in Pakistani periods. Which constituency received most votes?
a  Constituency A:2470 I 6322,47,0I,632  b  Constituency B: 380 I 9478 
c  Constituency C: 3932630I  d  Constituency D: l2753I7 
P:14
MORE ABOUT CRORES
 Place these numbers in Pakistani periods and write their names.
4,06,06,85,012=Four crore, six lakh, eightyfive thousand and twelve
 67300I59———————————————————————————————— b. 32456900————————————————————————————————
 30846002 ———————————————————————————————–
 17018037————————————————————————————————
 Write the numbers, placing your commas carefully.
>>Five crore, one lakh and sixteen =5,0I,00,0l6
 Three crore, eleven lakh, fortytwo thousand, three hundred=
 Eight crore, thirty lakh, nineteen thousand, four hundred and sixtyone=
 Four crore, eightysix lakh, fifty thousand and ninetytwo=
 Six crore, fortynine thousand, seven hundred and three=
 Seven crore and three hundred =
2Write the value of the coloured digit, 4, 10, 62, ‘938 ten lakh or 10, 00,000
a8, 1 5, 67,032=
b5,00,92,475=
c4, 73, 85,693=
d9, 87, 32,777=
4Write in expanded form.
5,26,49,032 = 5,00,00.000 + l20.00,000 + 6,00,000 +40,000 + 9,000 + 30 + 2
a6, 18,30,596=
b 5, 94, 03,075=
c7,05,12,847 =
d 3, l12, 01,690=
e1,I0,‘i5,738 =
fl1,00,67,143=
5Write the successor.
1,22,16,999 1,22,17,000
P:15
1Write the number names.
116,030, 100 fortysix million, thirty thousand, one hundred
a38, 100,580 =
b 60, I 74,005=
c5 I ,069, I 20 =
d 25,430,756=
eI9,405,328=
f I0, I 65,032=
2Place these in periods, first in the Pakistani way, second in the International way.
1103961425 (i) l1,03,‘l6,l125 (ii) 40,396,425
a38106259 =
b60054291=
cM965478=
d 56030201=
e2450031=
f 93768325=
3Write the number, placing your commas correctly.
eighteen million, four thousand and twentyseven =I8,0011,027
aThirtyone million, five hundred and ten thousand, six hundred and three
bSeventyeight million, four hundred thousand, eight hundred and twelve
cEightyeight million and fifteen
dTwelve million, nine hundred and, sixtyfour thousand, two hundred and one
eFifty million, three hundred and ninety thousand, seven hundred and eightyseven
P:16
8DIGIT NUMBERS: PLACE VALUE
1Change these numbers into International periods.11,02,59,603 40,259,603
a6,18,‘I2,079  b8,00,69,464  c3,54,06,295  d4,27,01,695 
2Read aloud, then write in words. 1,90,l12,1 I0 =one crore ninety lakh, fortytwo thousand, one hundred and ten
a  85,623,005  
b  8,I5,l6,075  
c  7,l18,01,623  
d  30,585,624 
3Write the number. Seventeen million, six hundred thousand and eightynine 17, 600, 08‘4
Four crore, ten lakh, fifteen thousand, eight hundred and four
Eightysix million, twentyseven thousand, three hundred and twenty
One crore, ninetyfour lakh, six thousand, four hundred and thirteen
4Write the predecessor. 35,000,000 predecessor 34,999,999
a15,350,000  b1,38,12,100  c3,04,00,000  d16,800,000 
5Write in expanded form.
47,625,105= 40,000,000 +7,000,000 + 600.000 + 20.000 + 5000 + 100 + 5
a52,018,623
 1, 29, l12, 060
c4,53,08,492
d I 1,958,121
6Think and write!
a If one crore equals—————— million, ten crore equals —————–million.
bOne crore rupees divided equally between two charity homes equals—————lakh rupees each.
P:17
7Arrange in ascending order
a49,603,298; 49,630,928; 49,6 I 3,829
b3,4I,06,235; 3,4I,60,532; 3,4 I ,59,332
c85,0 I 4,623; 85,004,632; 84,04I,362; 85,011, 184
8Write the successor.43,599,999 successor 43,600,000
a8,07,49,999  b301,999,999  c24,100,009  d2,48,39,999 
9Skipcounting in hundreds, write numbers in the blanks.
aI9,643,298  
b65,0303 I 6  
c37, I 91834  
d2,08,52,6 I 5 
10Write the correct symbol in each blank (<, >, =).
al,29,3O, 142———12,930,421 
b481 63,538————4,82,63, 528 
c7,00, 1 5,033—————1 70,015,033 
d61 2,21,438—————61,221,348 
e8,64,30,292—————86,430,295 
f27,040,628————2,71,41,628 
11Write numbers in the blanks to complete each series (be very careful!).
a  19,999,997  19,999,998  
b  57,999,800  57,999,900  
c  20,600, I07  20,700, I07  
d  6, 18,09,799  6, 18,09,899  
e  46, I 00,895  46, I 00,995  
f  37,560,899  37,560,999 
P:18 USING BIG NUMBERS:LAKHS, CRORES OR MILLIONS
1 Given below are some sentences you might read in Pakistani newspapers or magazines. Change them so that visitors from abroad can understand the numbers.
Example: Two crore people voted in the elections, yesterday. —–Twenty million people voted in the elections, yesterday.
aAbout 4 crore children in Pakistan aged between 5 and 9 go to school.
bNearly five lakh people attended a giant po4tical rally in Lahore yesterday.
cAbout thirteen lakh students are enrolled in colleges and universities in Pakistan.
dAccording to a census, the population of Karachi is now more than one crore.
ePunjab is the largest province, with more than 8 crore 25 lakh people.
fIn 1990, Pakistan produced I crore 67 lakh tonnes of wheat.
P:19
 Copy and complete.
a 01,408,156
+2,015,346 
b–
23,569,231 +5,694,325 
c
I4,07, I56 +25,92,843 
d
4,468,57 I +2,865,149 
e
3,407,862 +I,374,I09 
f
I 5,650, I92 +73,029,999 
g
24,67,333 +18,05,438 
h
3,48,36, 117 +I,05,62,431 
2Write in vertical form and complete (be careful with columns!)
A  3,564, 121 + 2,473,565  e

465 + 2,4‘1,00,321 + 1002

B  2,655,132 + 2984 + 34, 103  f

5,62,43,018 + 32 + 51,673

C  1,030,49‘71 + 38,324 + 5687  g

84,65,321 + 7495 + 1,18,626

D  39,862 + 410,364 +2,003, 145 


3Write the number which is:
Example: 4000 more than 3,487, 103= 3,491,103
a5000 more than 20,045,624  
b800 more than 1,26,95,382  
c20,000 more than 14,62,834  
d12,000 more than 2,695, 148  
e900 more than 5,624,540 
P:20 USING BIG NUMBERS: SUBTRACTION
 Copy and complete.
a
I,496,953 205,343 
b–
45,647,329 14,538,142 
c
4875648 1232537 
d
16400825 7936172 
e
1864932 1418725 
f
50100032 28052164 
g
5195438 3841654 
h
27003029 10816420 
2Now write sums to answer these.
aFrom the greatest 7digit number (Pakistani system), subtract the smallest 6digit number. 

bFind the difference between the greatest 8digit number (International system) and the greatest 5digit number. 

cFrom the smallest 8digit number (Pakistani sgstem), subtract the greatest 6digit number. 

3Write in vertical form and complete.
a85,23 1 ,569 – 1 6,829,293  
b2,00,00,360 – 38,745  
c4,000,35 1 – 25,689  
d8,60,03,8 1 4 – 65, 17,298  
e 1 0,000,000 – 45,692  
f32,034,629 – 1,465,1 17 
4Write the number which is:
a2000 less than 49,840,328  
b700 less than 7,593,400  
c5000 less than 52,I3,864 
P:21 ADDITION AND SUBTRACTION: WORD PROBLEMS
1Now answer these, thinking carefully whether you should add or subtract.
aHow many more people live in Sindh than in Khyber Pakhtunkhwa? 

bAfter Punjab, which province has the most number of people? How many people altogether, 4ve in this province and in the Punjab? 

cWhat is’ the total population of FATA and Sindh? 

dWhich province has the least number of people? What is the difference in population between this province and the Punjab? 

eIf the population of Balochistan is added to that of Islamabad, how many people are there altogether? 

P:22 ROUNDING OFF
1Round off these numbers to the nearest 10. 138 … 140
a51  b 1 I2  c 999  d49  e 147  f 1253 
2Round off these numbers to the nearest 10O. 563 (nearer to 600 than 500) 600
al79  b 2430  c 9679  d241  e 6274  f 4031 


P:23 ROUNDING OFF
Sprog Spacewalker has 145 stamps. He wants to round off this total to the nearest
145 comes exactly halfway between
 Round off to the nearest I0 335 340
a. 105  b. 2335  c. 15395  d. 115  e. 1555  f. 6939 
 Round off to the nearest 100 Remember: halfway numbers are rounded upwards. * 1750 1300
a. 350  b. 1650  c. I4, 039  d. 150  e. 2550  f. 19,650 
 Round off each price to the nearest Rs I 00: Rs 1149….. Rs 1100
a. Rs 22I6  b. Rs I0,4141  c. Rs 3481  d. Rs 8550 
 Copy and complete this table.
village  Population  Population to the nearest 1000 
A  2721  300 
B  4500  
C  9764  
D  317 
7 Round off these bills to the nearest Rs 1000_ Rs 14,384 RS 141,000
a. Rs 25,500  b. R5 98,964  c. Rs 64,692  d. RS 103,2I9 
P:24 MORE ABOUT ROUNDING
 Round off these times to the nearest 5 minute. 8.22 a.m. 8.20 a.m.
a. 12.I4 p.m.  b. 1.01 p.m.  c. 11.18a.m.  d. 12.19p.m. 
 Round off these ages to the nearest year. 9 years 2 months 9 years
a. 10 years 6 months  b. 8 years 5 months  c. 7 years 6 months 2 dogs 
 Measure these 4nes, write down their exact Length, then round off to the nearest cm.
A  ____________ 
B  __________________ 
C  ________________ 
11 Copy and complete the table
Mountain  Height  Mountain Height in rounded off metres to nearest 
Mt Everest  8848  8800 
K2  86I0  
Nanga Parbat  8l26  
Tirich Mir  7690 
12 Work out approximately answers to these sums by rounding off to the nearest 10. 45+71+38= 50+70+40
a. 27+42+19  
b. 56+38+41  
C. 25+34+16 
P:25
13Round these off to the nearest l0,000. 386,I I4 —————390.000
a265,000  b. 1,432, 1 61  c148,732  d. 2, 123,‘945 
e384,239  f. 5,648,02  g752, 169  h. 6,01 1,933 
14 Round these off to the nearest I 00,000: 1,462,315 1.500,000
a. 2,637,002  b. I,918,727 
15 Copy and complete this table:
Item  Cost in Rs  Cost of the nearest Rs million 
Hospital  6,500,000  7,000,000 
Stadium  7,362,000  
Hotel  5,964,310  
School  1,093,999 
I6. Refer to page 21 and answer these questions. Example: What is the population of Sindh rounded off to the nearest I0, 000? 30,400,000
 What is Baluchistan’s population rounded off to I the nearest 1000?
 What is Punjab’s population rounded off to the nearest million?
 What is the population of FATA rounded off to the nearest I00,000?
 What is Islamabad FCA’s population rounded off to the nearest I00?
P:26
MORE WORK WITH BIGGER NUMBERS: MULTIPLICATION
1Copy and complete:
a1231x540  b6099x487  c3614x353  d7536x396 


e6148x469  f2984x455  g2405x321  h1879x628 

2Write vertically and complete.
a3847 X 431  b. 7346 X 398  
c9625 X 855  d. 5174 X 872  
d6098 X 627  f. 10,193 X 243 
3Solve the problems, making complete statements.
aIf a toy factory produces 2850 toy _cars everyday, how many cars will be produced in a year of 296 working days? 

bIf Naseem Hameed runs 6500 m every day as part of her training programme, how many metres will she run in the course of one year? How many km is that altogether? 

cA school uniform at Ameen High School costs Rs I325. If there are 567 children at the school, what will the total bill for all the children’s uniforms be? 

P:27
1Copy and complete, working very carefully:
a29)32,497  b19) 281,425 
c24)18,726  d23)425,662 
e35)51,972  f45)884,695 
2Write each in long division form and complete.
a6295÷31  b85,177÷81 
c14,038 ÷ 87  d 47,072 ÷ 67 
e35,764 ÷ 59  f 8706 ÷ 95 
3Write quotients in the blanks after solving each division mentally.
5200 ÷ I0 =
3800 ÷ I9 =
6600 ÷ 66 =
7200 ÷ 24 =
l0,000 ÷ 50 =
65,000 ÷ 100 =
4Now solve these.
2,603,420 ÷ 25

3,1l2,633 ÷ 27  5,753,l I9 ÷ 43 
P:28
1Copy and complete working as carefully as you can:
a248)32,561

b187) 29,364 
c330)45,695

d485) 50,678 
 Write in long division ‘form and complete.
 46,028÷384
 52, I69 ÷416
 75,673÷649
 34,396÷457
 28,932 ÷535
 1i721÷464
 56,430 ÷719
 49,868÷ 384
 Work out the division in your head, then write quotients in the blanks.
 360,000 ÷200=
 480,000 ÷400=
 69 5,000 ÷695=
 560,000 ÷140=
 738,000 ÷1000=
 2 I 0,000 ÷700=
Write your answers as fractions.
P:29 WORD PROBLEMS
1Read these carefully, and decide whether you should multiply or divide in each case. Then, solve the problems, making complete statements.
aJumbo Fancy Stores Wants to place an order for firecrackers. If one box contains I44 firecrackers, how many boxes must the shop order for a stock of 100,080 firecrackers?  
bThe Punjab Government wants to build new homes for 382 homeless fami4es. If each home costs ‘Rs lr,00,960, how much will the project cost altogether?  
cSchool children in Karachi raise Rs 40,575 through a sponsored marathon race. If the collection is shared between 520 needy families, how much does each family get, and how much money will be left over?  
dSuperpop soft drinks factory employs 267 people. If each worker receives Rs 2384 as wayes every month, I what is the total waye bill (i) for one month, (ii) for the whole year. 
2Help Sid work out these word problems, making complete statements.
aIf Sid’s rocket travels a distance of 756,600 km in 240 hours, how many km does it travel in one hour?  
bDuring his trip, Sara knits a bright, orange scarf i at the rate of 469 mm every hour. If her trip lasts 8 days and if Sara sleeps only 5 hours a day, how much scarf will she have knitted by the end of the trip?  
cIf each of the 6I4 Super globe residents eats 83250 g of vegetables in a year, what is the total weight of vegetables eaten (in kg)? 
P:30 REVIEW
1Using graph paper, plot o 4negraph to show the number of people who visited Lahore Zoo during the first six months of 2004.
No. of Visitors  1000  2500  3000  3500  4500  5000 
Month  Jan  Feb  Mar  Apr  May  june 
 Why do you think so many people visited the Zoo in May and June?
 What is the difference between the number of visitors in February and May?
 What is the total number of visitors in January and February?
2Write in expanded form.
a. 962,430  
b. 1 0,720,482  
c. 2,464,209  
d. 4,67,30, 141 
3Write each number in Pakistani periods.
a6050038  b85324861 
4Rewrite each number in International periods.
a462456I  b60405645 
5Write vertically and complete
a. 4,695,132 + 69,549 + 59051  
b16,80,51,1 – 833,745 1  
c. 16,213×264 
6Write in Long division form any complete.
a. 462,391 ÷ 384  b. 381, 684 ÷465

7Round off to the nearest 10.
a. 269  b. 8490  c. 7851 
8Round off to the nearest 100.
a. 506  b. 6052  c. 45,023 
9Round off to the nearest IO00
a. 11,425  b. 438,421  c. 6,846,680 
P:31 BILLS WORKING WITH LARGER SUMS OF MONEY
1Prepare bills for these customers at Galaxy Superstore.
a  Manyy Moon: 6 kg of rice at Rs 75 per kg, 3 kg of grapes at Rs 40.00 per kg;25 packets of washing powder at Rs 80 per pocket; 3 l of oil at Rs 125 per l

b  Linda Lightyear: 8 kg of wheat flour at Rs 36 per kg; 8 packets of biscuits at Rs 23 per packet; 2 kg of carrots at Rs 25 per kg; I .75 kg of potatoes at Rs 30per kg.

2Now prepare bills for customers at SuperZoom Garage. Make your bills wider than before, because you will be working with larger sums of money.
a  Sara Spacewalker: 2 space_bikes costing Rs 12,6Il¢each; ci new lamp costingRs 85150; 23 I of petrol at Rs 48.40 per l

b  Veena Venus: I Lunar moped costing Rs I4,832.50; is space helmets costingRs 2I9.60′ each; 6 spare wheels at Rs 347.50 each.

3This bill has a mistake! Find the mistake, then rewrite and work out the correct amounts.
Customer:Sara S. dated:1.11.1999  
Quantity  Item  Cost per unit  Total cost 
8 kg  Rice  Rs 64.00  Rs 604.00 
4 l  Oil  Rs 86.00  Rs 244.00 
4kg  Tomatoes  Rs 30.00  Rs 047.00 
12 kg  Mangoes  Rs 50.00  Rs 400.00 
Grand Total Rs 1295.50 
P:32 THE FOUR OPERATIONS: ORDERING (SIMPLIFICATION )
1Using the simplification rule, DMAS solve these.
Example: (9+3×4)=(multiply before adding)
3×4 (next add)
9+12=21
Answer:21
a)8 + 4 – 3  b)8 ÷ 2 + 12 
c)6 x 5 – 5  d)10 – 3 ÷ 3 
e)11 +2 x 8  f)12 ÷ 4 x 5 
g)30 + 6 ÷ 3  h)16 + 8 ÷ 2 
P:33 SIMPLIFICATION
a) 12 x 6 + 3  b) 15 x 42 + 14 
c) 84 + 7 x 10  d) 108 + 12 + 46 
e) 14 + 21 + 3  f) 20 16 + 4 
g) 58 – 24 + 8  h) 17 + 5 x 20 
3Now simplify these:
a) 3 x 2 + 8 – 5  b) 128 ÷ 4 +12 x 5 
c) 6 x 5 +12 ÷ 4  d) I8 x 6 ÷ 2 – 24 
2 Remember your DMAS rule and simplify these:
a) 7 + 6 + 2 x 18  b) 5 x15 + 3 + 49 
c) 121 + 11 + 5 x 20  d) 8 x14 + 7 10 
e) 844 12 x 3 – 6 
5 Think carefully, then simplify:
a) 18 + 4 x 6 + 2 – 9  b) 25 + 5 x 8 + 6 – 12 
c) 31 + 24 ÷ 8 x 9 39  d) 45 ÷ 5 +7 x1120 
P:34 SIMPLIFICATION : USING BRACKETS
Name: Worksheet countdown5 date:
P:35 SIMPLIFICATION : USING BRACKETS
6Copy and complete these. Work out the operations inside the brackets first.
4+(8×3) 4+(24)
= 28
a(3×7)+ I2  b(9+22)x4  c8xl2+16)  d14+(18×3) 
7Now copy and complete these.
(93)x8…(93)=6
(6)x8=48
a(5×8 1)  b. 6×18÷9)  c(6×9)I8  d. (9xl0)÷45 
8Now simplify these sums involving fractions, using the brackets to help you.
+()–=
=
a (+) –  b ( – ) + _{ } 
c – ( – )  d + ( – ) 
9Work the same way with decimal fractions.
(0.5 + 0.2) X 4 (0.7) X 4
= 2.8
a  (5.0 – 0.5) x 2  c  (9.6 – 7.2) X 4 
b  8 X (4.0 – 3.5)  d  16 + (8.3 – 4.3) 
10Think carefully. Put brackets in the correct places t6 make these statements true.
a2 X 2 X 2 – 2 = 0  b2+2+2+2=5  c 186+3=4 
P:36 SIMPLICATION:BRACKETS
11Working carefully, copy and simplify.
4 + [15 – {7 + (6 + 2)}]
= 4 + [15 – {7 + (3)}]
=4+ [ I5 – {7+3}]
= 14 + [15 – {l0}]
= 4 + 5
= 9
a24[5+{8(96)}] 
b2x[18(6+(9÷3)}] 
c[100 – {80 ÷ (20 X 2)}] + 3 
d80 + [IO x {l6 – (8 ÷ 2)}] 
e39[6+{5(63)}] 
f I0 ÷ [3 + {5 – (12 ÷4)}] 
12Now simplify these. Remember that while adding and subtracting un4ke fractions, you need to find the common denominator.
Example: + ( + ) = + ( + )
= +
= + =
a  + ( + ) 
b  ( + ) + ( – ) 
c  + ( – ) 
d  + ( – ) 
P:37 SIMPLIFICATION : BRACKETS
 Simplify these and reduce your answer to its Lowest terms.
a  10 + [ 4 – { + ( + ) } ] 
b  6 – [ + { 3 – ( + ) 
c  3 – { + ( 2 – ) 
14Now,simplify these:
15Now simplify these sums involving decimal fractions. Remember to place your decimal points carefully.
2.8 + {3.6l – (1.12 + 2.34)}
1.12 + 2.34 = 3.46
= 2.8 + {3.6 – (3.46)}
= 2.8 + {0.15}
2.8 + 0.95 = 2.95
a7.3 – {1.4 + (0.92 + I.63)} 
b{3 X (1.59 + 2.01)} + l00.22 
c100 x [12 – (6.2 + (1.3 + 2.6)}] 
16Simplify these.
a. Arif Shares, a chocolate bar with his two brothers. He gives one brother got the bar and ‘the other brother of the bor. How much does he keep for himself? 
Solution: 
b In a special offer at Sid’s supermarket, music CDs ‘ which usually cost Rs 32.50orfe reduced in price by Rs 5. If a customer buys Six CDs, how much will they cost him? 
Solution: 
P:38 REVIEW
AREA
 Write the area, in cm^{2}, of each shape shown below.
 On a paper with centimetre squares, draw these shapes.
a. A rectangle with an area of 8 cm^{2} 

b. Any shape with an area of 10 cm^{2} 

c. A square with an area of I6 cm^{2}. 

d. A rectangle with an area of 15 cm^{2} 

3Copy and complete this table.
Rectangle  Area  Perimeter  
Length  Breadth  
5 cm  2 cm  
16 cm  10 cm  
21 cm  3 cm 
4Use multiplication to work out the area of these gardens.
5Solve these problems in your note book.
a. If the area of a carpet is 32 m^{2} and its breadth is 4 m, what the length? 

b. A builder has enough bricks to construct a rectangular compound wall with aperimeter of 16 m. One side of the wall is 30 m, what is the width of the other side? 

P:39 MORE ABOUT AREA: COMPOSITE SHAPES
1 Work out these floor areas by dividing the shapes into rectangle s.
 Manyy Moon, who is an architect, has designed a new school building. Work out the area of each room in it.
What is the total area covered A by the school building?
P:40 Area: Triangles
 Work out the area of each triangle shown on a centimetre grid below.
P:41
 Work out the area of each coloured triangle.
5Copy these shapes carefully on to a centimeter grid. Then work out the area of each shape by dividing it into Squares, rectangles and Triangles.
P:42 AREA: PARALLELOGRAMS
6Copy these parallelograms carefully on a centimeter grid. Change each parallelogram into a rectangle or square of the same area and calculate
the area:
7Measure the length and breadth of each of these parallelograms, and then
work out the area.
8Measuring carefully, work out the area of each parallelogram and the area of each coloured triangle.
P:43 MORE ABOUT TRINAGLES
9 Now find area of triangle
P:44 MORE ABOUT TRINAGLES
10 Calculate the area of each coloured triangle , using your ruler if necessary?
11Draw two straight 4nes from point A to divide the shaded area into a square and three Triangles. Find (a) the total area of the shape, and (b) the area of the three shapes formed.
aArea of Large square = 64 cm2
Area of blank squares =————————–
Area of shaded squares =———————–
b Now cut the shape into a square and three Triangles. Calculate area of each. Does it tally with (a)?
P:45
1Look at these pairs of objects then tick the object you think has greater volume.
2Look at these shapes made out of cubeshaped building blocks, Work out how many cubes have been used to make each shape.
3Do the two cuboids in each pair have the same volume? Write “yes” or “no”.
P: 46 THINKING ABOUT VOLUME
P:47 VOLUME: THE CUBIC CENTIMETRE
I Look at page 96 again. Look carefully at the open cube made by Sid. Now draw a cube of your’ own, making each edge 4 cm long.
 How many cubes with each edge of 1cm can be fitted on to the base of your cube?
 How many such layers ore needed to fill the cube?
 Look at the cuboids below, then copy and complete the table.
cubiod  No. of cubes in each layer  No. of layers  No. of cubes in cubiod 
a  3×2=6  3  18 
b 
P:48 VOLUME: THE CUBIC CENTIMETRE
 The layers below have been mode with centimetre cubes. Write the volume of each Luger, using the rule.
 Now, find the volume of each of these cuboids mode of centimetre cubes.
Q 5. Work out the volume of each box.
 Copy and complete the table.
cubiod  Area of base  height  Volume 
22 cm^{2}  4cm  88 cm^{3}  
a  20 cm^{2}  6 cm  
b  16 cm^{2}  7 cm 
P:49 VOLUME
7Calculate the volume of cuboid each with these measurements.
I= I2cm,b=4cm,h=3cm
Volume = (l2 cm xl»cm)x 3 cm
= 48x 3 cm = l44cm^{2}
al=9cm, b= i.5cm, h=hcm 
bl=6cm, b= 2.5cm, h= 8cm 
cI= 11cm, b=7cm, h=9cm 
8Look at these boxes. Sid knows the volume of each of them, but does not have one of the measurements. Help him find out the missing measurement by using division.
9Now copy and complete this table. length Breadth Height Volume
cubiod  length  breadth  Height  volume 
9 cm  8 cm  5 cm  360 cm^{3}  
12 cm  7 cm  924 cm^{3}  
6 cm  6 cm  288 cm^{3}  
11 cm  3 cm  396 cm^{3} 
10Solve these word problems in your notebook, making complete statements.
aIf a fish tank is 50 cm long, 20 cm wide and I5 cm high, how many cubic centimeters of water will it hold?

bMondy Moon designs a classroom cupboard with a volume of 6 cubic metres (6 m^{3}). If the cupboard is 3 m high and I m long, what is its breadth?

cThe aquarium in Sid Spacewalker’s home has a volume of I2,000 cm^{3}. If itis 30 cm long and 20 cm wide, how high is it?

P:50 VOLUME: 4NKING VOLUME WITH CAPACITY
1Write the volume and then the capacity of each box:
P:51 REVIEW
1Using graph paper, pat a 4ne groph to show the number of children present of Modern School during a week in July I99l. Here is the data.
children  450  500  550  600  650 
Day  Mon  Tue  Wed  Thu  Fri 
2Change these numbers into Pakistani periods.
a1,249,000,938  b51,670,324 
3Round off to the nearest I00.
a15,550  b. 84,472 
4Copy and complete.
a. 384,691 + 372  b. 605,827 + 453

5Round off to the nearest cm.
a. I6.5 cm  b. 23.4 cm 
6Simplify these, using the DMAS rule.
a. 8 x 6 + I0 + 2

b. 23 + I6 + 4 X 2

c. 48 + I2 + 6 X 4

d. 30 + 6 x 2 + 2

7Now simplify these.
a. (8.3 7.1)x 9

b. [90 – {50 + (30 ÷ 3)}] – 28

c. ( – ) + ( + )

d4 – { + ( 3 – )}

8Calculate the area of each of these shapes.
9Calculate the volume of each of these boxes. Then give the capacity in ml.
a. I=7cm, b=8.5cm, h=6cm 
b. I= I0.5cm,b=6cm, h=7cm 
c. l=9.2cm, b=7cm, h= l0cm 
P:52 PART TWO REMEMBERING MULTIPLES AND FACTORS
HELP SID COMPLETE THIS REVIEW
CluesAcross
 4, 6, 8, 10 and 12 are all —————of the number 2.
 Two numbers which have only I as their common factor are called————————— numbers.
 All even numbers are multiples of this number.
 Every number is a factor of —————————.
9On a number 4ne II0, the next greatest prime number after five is————— .
I0. The number eight has a total of ———————factors.
CluesDown
2A number with only two different factors (itself and I) is called —————————–a number.
3————————–numbers have more than two different factors.
5A multiple is a number which can be divided by another number without any——————————
6The LCM of4 and 6 is ——————————–
8Number I is a—————————– of every number.
9I2, 48, 18 und 30 are all multiples of the number———————–
P:53
1Find the LCM of these pairs.
I0 and I5… I0=2×5
l5=3X5
LCM of I0 and I5 = 30
a. 8, I2  b. 3,7  c. 9, I5 
2Copy and complete the table.
I X———– = 28
————x I4 = 28
11 X———— = 28
7 x————— = 28
Now write all the factors of 28.
3How many factors does each number have?
I8 6 factors (I, 2, 3, 6,9 I8)
a. 24

b. 56  c. 75 
d. 25

e. 100  f. 91 
4By 4sting the factors of each number, find the HCF of these pairs.
ir 20, 25 20: I, 2, ll, 5 IO, 20
25: I, 5, 25
HCF of 20, 25 = 5
a. I5, 39  b. 2I, I7

5Tick the pairs of coprime numbers.
5 and 11… 5=1×5,
11=1 x11
a. 56 and I4  b. I00 and 25  c. 23 and 29  d. 81and 7 
6Are these statements true or false? Write T or F, explaining your answer.
I8 is a factor of 72
T(18 x 4 = 72)
 15 and 35 are coprime numbers.
 The HCF of 16 and 24 is la.
 The LCM of 1 1 and 9 is 99.
 Among prime numbers, only the number 2 is an even number.
 1030 is divisible by 3.
 48,605 is divisible by 5.
7Think carefully, then answer these.
Write a few pairs of numbers with HCF 7
14 and 21; 28 and 49
 Write two 4digit numbers divisible by 9.
 What is the smallest prime number?
 Draw factorization trees to show the prime factors of (a) 32 and (b) 45.
d If the LCM of a pair of numbers is 190 and one of the numbers is I0, what is the other number?
P:54 MORE TESTS OF DIVISIBI4TY
1Sid Space walker is trying to remember his rules of divisibi4ty.
Help him fill in the blanks:
 Any number with 0 in the column is divisible
 An——————— number is always divisible by 2.
 A number where digits add up to a multiple of 3 is divisible by——————–
 All numbers which are divisible by 9 have digits that add up to a multiple of———.
 An example of a number which is divisible by 5 and by I0 is————————
 Which of these numbers is divisible by 3?
a. 149  b. 5481  c. 19,410 

3 Which of these numbers is divisible by 5?
a. 16,495  b. l7,03,760  c 705 

4Write down six 7digitnumbers which are divisible by 9.
 Tick the numbers which are divisible by I0:
a. 4960  b. 5010  c720395 
 Which of these are divisible by 4?
a. 1096  b. 2000  c. 23,606 
P:55 MORE TESTS OF DIVISIBILTY
7Copy these numbers and see which of them are divisible by 6.
a8622  b. 47,0 I 8  c1463  d. 39,582 

8Look at “these numbers carefully. Tick those which are divisible by 3 but not
by 6.
a14707  b. 801  C.1,59,65l1 

9 Check to see whether these numbers are divisible by 8.
a. l1189  b. 1,17,000  c. 6408  d. 1,4‘13,600 

P:56
11 Check to see if these numbers are divisible by I2
a24,430  b. 1080  c.81,156 

P:57 REMEMBERING THE DIVISION METHOD
 Find the prime factors of these numbers, using the division method. Then,
check your answers.
a. 156  b. 66

c. 475 
d. 2l2  e. 94  f. 164

2 Use brackets to help you. All the prime factors of 90 are given below.
2x3x3x5=(2×5)x(3×3)
= 10×9
We have used groups of IO to help us. Now, write the numbers with these factors:
a. 2x2x5x5  b. 2x2x5x7  c. 3x3x5  d. 2x2x3x3x5 
3 Write the HCF of:
I2, I6 and 20 HCF=4
a. I8, 27, 36  b. I2, 30  c. 27, 54, I8  d. 38, 16, I4 
P:58 THE DIVISION METHOD AND HSF
4Break these pairs of numbers into their prime factors, then find their HCF and LCM.
a64 and 148  b. 63 and 108 
c26 and 96  d. 27 and 130 
5These are numbers that have already been broken down into their prime factors. Quickly find the HCF of each pair.
2x3x7x5 and 2x5x2
CF = 2 and 5
HCF= 2×5= I0
a2x2x2x5 and 2x2x3x5  b2x3x3x5 and 2x3x5x7  c2x3x5x5 and 3x5x5x7 
6Now find the HCF of each set of three or more numbers.
2x2x3, 2x3x3 and 2x3X3
Common factors = 2X 2 X 3
2X 2 X 3
2X 2 X 3
HCF = 2 X 3 = 6
a2x3x3;2x2x2; and2x2x3  b2x2x3x5;2x2x5 and2x3x3x5 
P:59 THE HCF OF LARGER NUMBERS
1FIND THE HCF AND LCM OF:
132 and 220  180 and 252  120 and 168

175, 300 and 425  70, 147 and 98

P:60 THE HCF OF LARGER NUMBERS: LONG DIVISION METHOD
2 Use Sid’s method to find the HCF of these pairs.
a. 105 ; 93  b. Z72 ; 1278 
c. 999 ; 851  d. 513 ; 40 
3Now find the HCF and LC of these pairs.
a. 1100 ; 1490  b. 722 ; l406

c. 1272 ; 90l  d. 2272 ; 127

P:61 THE DIVISION METHOD AND LCM
1Using the division method, find the lcm of these pairs.
a42; 126  b20; 56

2These pairs of numbers are broken down into their prime factors. Quickly find the LCM of each pair.
2 x 2 x 3 and 2 x 2 x 5
LCM= (2×2) x 3 x 5=60
a2 x 2 x 3 and 2 x 7  b2 x 2 x 2 and 2 x 2 x 3  c2 x 2 x 5 and 5 x 5 

3Look at the pairs of numbers in Exercise 2 above. As quickly as you can, change the numbers back into whole numbers.
2 x 2 x 3 and 2 x 2 x 5
I2 and 20
a2 x 2 x 3 and 2 x 7  b2 x 2 x 2 and 2 x 2 x 3  c2 x 2 x 5 and 5 x 5 

4Match each pair of numbers shown on the left to the correct LCM (use your
rough notebook to make your calculations).
a16 and I2b27and 45
c36 and 24 d55 and 66 e40 and 32 f15 and 125 g70 and 98 h30 and 40 
16072
490 48 120 375 135 330 
P:62 LCM OF THREE NUMBERS
1Find the LCM of these of numbers.
a. 6, 9 and 15  b. I0, 12 and 20  c. I2, I5 and I8 

2 Using a coin, draw Venn diagrams to show the prime factors and common prime factors of these pairs of numbers. Then work out the LCM.
a2x3x5 and 2x2x5  b2x2x2x3 and 2x2x3 

 Repeat Exercise 2, this with three numbers and three circles.
a2 x 3 x 5 and 2 x 2 x 5  b2 x 2 x 2 x 3 and 2 x 2 x 3 

P:63 HCF&LCM
P:64 REVIEW
1Tick only those numbers which are divisible by 4.
a. 624  b. 308,005  c. 3060  d. 864,442 
2Circle those numbers, which are divisible by 6.
a. 1572  b. 18,060  c. 43.034  d. 66.603 
3Write any 4digit number which is divisible by 3 but not by 6.
4Tick only the numbers which are divisible by 8.
a. 846,000  b. 22,408  c. 1318  d. 903,000 
5Which of these numbers can be divided by 12?
a. 80,505  b. 215,205  c. 86,300  d. 4′1,050 
6Can these numbers be divided by I2? Write ‘yes’ or ‘no’.
a. 8132  b. 45,265  c. 10,248  d. 594,156 
7Write the numbers whose prime factors are shown, using brackets to help you.
a. 2x2x2x3x3X5  b. 2 X 3 X 3 X 7 

8Break down these numbers their prime factors, using the division method.
a. 148  b. 210  c365 

9Find the HCF of these sets, using the division method.
a. 36 and 108  b. 24,112 and 72  c. 38,95 and 114 

10Find the LCM of these pairs of numbers, remembering to include common factors only once.
a. 2×2 x3 and 2 x 2 x 2 x 3  b. 3 x 3 x 5 and 3 x 5 x 7  c. 5 x 5 x 7 and 2 x 5 x 7 

11Find the LCM of these sets.
a. 9, I8 and 21

b. I0, I4 and 30

c. I2, I6 and 20

d. 24, 30 and 40

12Copy the sentences and fill the blanks.
a. If the product of two numbers is 756 and their HCF is 6, their LCM will————— 

b. If the LCM of two numb is I05, their HCF 3, and of the numbers I5, then other number is————— 

P:65 FABULOUS FRACTION FUNFAIR
P:66 MORE FRACTIONS
I Reduce these fractions to their lowest terms.
a  b  c 
 Complete the equivalent fractions.
a =  b =  c =  d = 
 Write these us mixed numbers.
a  b  c 
 Write these as improper fractions.
a 5  b 7  c 10  d 12 
 Fill in the missing numbers.
a =  b =  c = 
6Reduce these to their lowest terms, then change into mixed numbers.
a  b  c 

7Rewrite these fractions so that they have a common denominator.
and = and
a and  b and  c and  d and 
8Complete these, making sure each answer is in its lowest terms.
a +  b 5 + 2  c 1 +  d 2 + 
9Now, subtract carefully, making sure each answer is in its lowest terms.
a 5 – 3  b 7 – 3  c 8 – 4  d 12 6 
P:67 MULTIPLICATION OF FRACTIONS: FIRST IDEAS
1 Complete these using repeated condition (The diagrams will help you).
a5 x  
b 4 X  
c 3 x  
d 4 x 
2 Now complete these, using multiplication instead of repeated addition.
a x4  b 7 x  c x 3 
d x 7  e 5 x  f 6 x 
Q 3. Complete these, making sure your answer is in its lowest terms.
a x6  
b x 8  
c x 2  
d 4 x  
e x 3  
f 7 x 
P:68 MULTIPLYING A FRATION BY A FRACTION
1Look at these multiplication s. Copy and complete them in your notebook.
a x 4=  x = = 2 
b 3 x =  
c x 2=  
d 5 x =  
e x = 
2Draw pairs of diagrams to show these statements.
a of of  b  of of  of of 
P:69 MULTIPLYING A FRATION BY A FRACTION
3Write statements to match these diagrams.
4Now draw diagrams to match these multiplications, and write the product of
each.
a x  b x  c x  d x 

5Use multiplication to find the products, then draw diagrams to check.
a x  b x  c x  d x 
 Now find the products of these, using multiplication only.
a x  b x  c x 
d x  e x  f x 
7 Solve these multiplications:
a x  x

c x  d x

e x  f x

g x  h x

P:70 MULTIPLYING A FRACTION BY A FRACTION
8 Draw diagrams to Show these multiplications, then write each product.
a x  x

c x  d x

e x  f x

9Write multiplication sums to match these statements.
* Twothirds of = x
 Twofifths of =
 Threeeighths of =
10Use multiplication to find the products, then draw diagrams to check.
a x  x

c x  d x

e x  f x

11Now find the products of this using multiplication only.
a x  x

c x  d x

P:71 MULTIPLICATION OF FRACTION: LOWEST TERM: BRACKETS
I Solve these multiplications, writing each production its lowest terms.
a x  b x  c x  d x 
 Solve these, using brackets to help you.
a x x  b x x  c x x  d x x 
P:72 MULTIPLICATION OF MIXED NUMBERS: CANCELLING
I Solve these multiplication s making sure each product is in its lowest terms.
a 2 x 3  b 4 x

c 1 x 2  d 5 x 4

e 3 x

f 2 x 1 
g 2 x 6  h 2 x

i 3 x 2  j x 2

k 3 x 1  l 5 x 1

P:73 MULTIPLICATION OF FRACTIONS: WORD PROBLEMS
1 Think Carefully, then solve these word problems, writing complete statements.
a In a class of 44 pupils, are girls. How many girls are there altogether? Howmany boys? Answer in (i) numbers and (ii) fractions.

b. Ayesha’s grandmother buys m of lace for her handkerchief. She uses onlyof the Luce. What length of lace has she used?

c. If the geography textbook for Class 5 is cm thick, how tall will a pile of 9 such textbooks be?

2Now solve these, think carefully and make complete statements.
a On Purple Grass Farm in Super globe, of the land is used for growing vegetables. Spacefingers are grown on of this portion. What fraction of the total farm area is devoted to spacefingers? 
bThe racetrack in Planet City Stadium is 1 km long. If Sprog Spacewalkermanages to run around it 4 times before collapsing, how many km has he run?

P:74 SID’S MAGIC FRACTION PAGE
P:75 DIVISION WITH FRACTIONS: FIRST IDEAS
1 Copy and complete this table, remembering your rules of division.
Division sum  Words we say  Quotient 
72÷ 9  How many nines make 727  8 
2500÷ 50  
324÷4  
391÷ 17 
2 Write in numbers.
* How many twelves make l44?
144 ÷ 12 = 12
 How many 16s make 832?
 How many 21s in 903?
 How many 19s make 1083?
 How many 35s in 595?
 Now solve these, using words to help you.
a 1÷  b1 ÷  c 3÷ 


d 1÷  e 2  f 3 ÷ 

P:76 DIVISION WITH FRACTIONS: FIRST IDEAS
4Copy and complete this table, thinking very carefully.
Division sum  In words  Quotient  
2 ÷  How many thirds make 2 wholes?  
a  3 ÷  
b  9÷  
c  12 ÷  132  
d  14 ÷ 
5Write division sums to match these diagrams.
a  
b  
c  
d 
6Now complete these with the help of diagrams.
a 6÷  b 30 ÷

c 13 ÷ 
d28 ÷  e 18 ÷  f 7 ÷

g32÷  h 17 ÷  i 14 ÷

j 23 ÷  k 11 ÷  l 43 ÷

7Write the reciprocals of the following.
a  b  c 
8Find the reciprocals of these.
a 1  b 2  c 1 
P:77 MORE ON RECIPROCALS
1Write these whole numbers as fractions.
a 4  b 12  c 100 
2Write these numbers as fractions and then write the reciprocal of each.
a 10  b 21  c 2397 
3 Rewrite the numbers as fractions, and solve.
a 12 ÷ 2  b 36÷ 12  c 100 ÷ 25 

 Now solve these.
a 12 ÷  b 100 ÷  c15 ÷  d96 ÷ 

5Use the ‘division by fraction’ rule to solve these.
a3 ÷  b24 ÷ 

P:78 RECIPROCALS: DIVIDING FRACTIONS BY WHOLE NUMBERS
6 Now solve these.
a8 ÷ 6  b 3 1

c ÷ 4  d ÷ 4

DIVIDING A FRACTIONAL NUMBER BY A FRACTIONAL NUMBER
7Solve these sums, using the division by o fraction’ rule
a ÷  b ÷  c ÷ 

8Now, work out the following.
a  b ÷ 

9Copy and fill in the blanks
a Dividing by is the some is multiplying by———————————
bDividing by is the some as —————by
P:79 DIVIDING MIXED NUMBERS
1Now, solve these divisions
a 10 ÷ 5  b 8 ÷ 6 


c 5 ÷ 2  d18 ÷ 3 


e 16 ÷ 4  f3 ÷ 1 


g4 ÷ 2  h12 ÷ 4 

2Now, solve these.
a 8 ÷ 3  b 5 ÷ 2 

3True or false? Think carefully, then write T or F.
aThe reciprocal of ÷ is I2.
b ÷ means ‘how many halves make twothirds.
cThe reciprocal of 2 is 2
dThe product of any two fractional numbers is always less than either of the two numbers.
eThe product of a fractional number and its reciprocal is always zero.
fEach fractional number has only one reciprocal.
gThe reciprocal of is 1000.
h ÷ is the some as of
P:80 MORE FRACTION MAGIC
P:81 DIVISION WITH FRACTIONS: WORD PROBLEMS
1Now solve these problems, making complete statements.
aA pile of maths textbooks on a table is exactly iiié cm high. If each book is ig cm thick, how many books make up the pile?

bMaham has 36 chocolates. She gives 9 of them to her best friend, Laila, then ‘ shares the rest between herself and 4 other friends. How many chocolates does Maham get?

c A piece of ribbon is 5% m long. If it is cut into I4 e9ual pieces, how long will each piece be? Write your answer (i) in fractions (ii) in m and cm.

dIn the Shooting Star Restaurant, Outer Space, a pancake takes just é °f U minute to cook. How many pancakes can be cooked in the space of 1% hours?

P:82 SIMPLICATION WITH FRACTIONS
 Using the DMAS rule to help you solve these.
a 3 +5 – 1

b 4 ÷ 2 – 1

c5 x 1 + 10

d18 6 ÷ 4

e 5 ÷ 2 x 10

f 4 x 1 + 10

2 Working very carefully, solve these:
a (1 + 2 ) x(3 + 2 )

b 4 + { ( 3 – 1 )x 5}

c[{( 18 ÷ 6 ) + 14 } – 2 ]

d20 + [ 5 x {9 – ( 1 x )

e24 + [ 3 x { 10 – ( ÷ )} ]

f[ 12 + { 3 x ( + ) } ] – 2

g{ 4 + ( 5 x 3 ) } 2

P:83 REVIEW Fractions
 Copy and complete the table.
of  is the same as  x  =  
a  of  =  
b  of 2  =  
c  of  = 
 Solve these, making safe each answer is in its lowest terms.
a x x 1  b x x0 
c 1 x  d3 x 
 Write the reciprocals of the following.
a21  b10  c2  d  e 100  f15 
4 Solve these.
a18 ÷  b ÷  c ÷ 3  d 1 ÷

5Solve these, thinking carefully about which operation you need to use. Make complete statements.
a. Babar starts the dag with I5 kg of potatoes for sale in his shop. He sells 4 kg before I0 a.m. and 6 kg between I0 a.m. and noon. What weight is left over for the afternoon? Give your answer (i) in fractions; (ii) in kg and g. 

b. Selvi Spacewalker took hours to draw a picture of Venus. Sid took only of the same period of time to draw a picture of Saturn. How long did Sid take to complete his picture? Give you answer (i) in minutes; (ii) as a fraction of an hour. 

6Solve these, working very carefully.
a (6 + 2 ) – (1 x )

b {3 x ( 1 ÷ ) } – 2

c 3 + [ 5 x { 16 – ( 3 – 2 )}]

P:84 SID AND SARA’S DECIMAL REMINDER PAGE
P:85 DECIMAL AND FRACTIONS: REVIEW PAGE
1Write these common fractions as decimals by changing them into equivalent fractions with denominator I0, when necessary.
a 3  b  c2  d 100  e 10  f 3 

2Change into common fractions.
a  10.01= 
b  18.05= 
c  35.75= 
d  25.25= 
e  33.04= 
f  100.2= 
3Write these lengths in cm.
a 6 cm 5 mm  b15 cm 9 mm  c 10 cm 1 mm  d8cm 7 mm 
4Copy and fill in the missing symbols (+, , x or +).
a0.06 —————I0= 0.6
b5.91—————10= 0.591
c 9.1 —————–2.1 = 7
d2.02 ——————1.01= 3.03
5Write numbers to match the statements.
>>>8 in the hundredths place, in the ones place, 3 in the tenths place. I.38
a9 in the ones place , 4 in the tens place, 6 in the hundredths place, O in the tenths place. 
b0 in the hundredths place,5 in the thousandths place, 0 in the tenths place, 9 in the ones place. 
6Write as decimals.
a 2  b8  c200  d4  e  f15 
7Write the place of the coloured digit.
a14.032  b 492.032  c25.174  d 645.53 
8Write these as decimals by first changing them into equivalent fractions with denominators of I0, I00 or I000.
a3 = 
b8 = 
c14 = 
P:86 COMPARING DECIMALS: RIEW PAGE
1 Copy in your notebook, then fill in <, > , or =.
a ——————
b ——————
c0.004—————— 0.040
d1.75——————1
2Look carefully of these sets, then rewrite them in ascending order.
a  , ,, 
b  18.413, 18.143,18.341, 18.431 
c  0.012, .12, 0.002, .001 
d  , , , 
 Now place the numbers in these sets in descending order.
a  5.063 , 5.6 , 5.003 , 5.36 
b  11.064 , 11.604 , 11.406 , 11.1 
c  , , , 
 Tick (./) the largest decimal number in each set.
a  18.95, 18.90, 18.05 
b  600.60, 600.65, 606.05 
 Think carefully, then tick (√) the shortest length in each set.
 4cm, 4.5 cm, 0.4 m
 1cm, 100 cm, 1002 m
P:87 ADDITION & SUBTRACTION DECIMALS: REVIEW
1 In your notebook, draw a placevalue chart, then put these numbers into it carefully.
a 39.51  b. 110.064  c. 14.5 

2Now, work out these, making sure you write numbers in correct columns.
a302.48 – 208.24  b 619.052 + 341.006  cR5 I 16.35 – RS 89.74 

3 Complete these first making sure you turn all numbers into like decimals.
a. 1182.11 + 653.938  
b. 3.19 + 27.974 + 8.8  
c. 49.34 – 8.7  
d. 732.1 1 – 28.932 
P:88 MULTIPLICATION AND DIVISION WITH DECIMALS
1 Copy and complete:
a. 234.11 X 18  b. Rs 625.50 x 25

c. 2707.68 ÷ 16  d. RS 1929.90 X 11

e. 2213.40 ÷ 68  f. 861.1121 ÷ 11

2 Find the value of the following.
a. 2.4 X 3  b7.905 x 3

c. 10.5 x 2  d 4.672 x 5

e. 5.6 X 7  f 3.187 x 9

g. 19.56 x 8  h0.998 x 15

i. 21.33 x 9  j1.767 x 21

k. 2I2.35 x 5  l2.438 x 18

m. 8.96 x I2  n8.752 x 26

3 Now find the value of these.
a. 13.6 ÷ 4  b. 14.56 ÷ 7 
c. 14.5 ÷ 5  d. 21.95 ÷ 5 
e. 27.2 ÷ 8  f. 72.84 ÷ 4 
g. 5.2 ÷ 4  h. 42.07 ÷ 7 
i. 2.79 ÷ 3  j. 1.2s ÷ 6 
k. 1 13.88 ÷12  l. 3.75 ÷ 5 
m. 83.93 ÷ 11  n. 76.86 ÷ 9 
0l2.08 + 2  p149.85 ÷ 15 
P:89 MULTIPLYING DECIMAL NUMBER
 Multiply the following numbers by I0.
a9. 59.6

b. 129.8  c. 364.8  d. 730.1 
e. 469.78

f. 341.0  g. 3463.7  h. 734.9 
2 Multiply the numbers after changing decimal numbers into common fractions.
a. 5.3 x 100  b. 4.96 X I00  c. 1 .9 X 1000 
d. 395.678 x I000  e. 0.08 x I000  f. 70.01 x 100 
g. 35.635 x 1000  h. 0.002 x 10  i. 29.3 x 10 
P:90 DIVIDING A NUMBER WITH A DECIMAL POINT BY I0
1Copy and complete the divisions.
a. 3.18+10  b. 6.51+1

c. 6.24 + I0  d. 6.94 + I0

e. 8.3+100  f. 4.83+10

g. 4.1+1000  h. 4.5+100

2Think carefully then fill the blanks.
a 3.6 ÷ —————= 0.36 
b4.8 ÷ —————= 0.048 
c1.92 ÷ —————= 0.192 
d8.74 ÷ —————= 0.0874 
3Which number should replace the question mark?
100  43.5  0.0435 
100  13.2  ? 
10  4.7  0.47 
P:91 MULTIPLYING BY A DECIMAL (TENTHS ONLY)
 Help Sid work out the area of these pieces of graph paper, (i) in mm^{2} and (ii) in cm.
(i) 32 mm X 22 mm= 704 mm^{2}
Area=704 mm^{2}
(ii) 3.2 cm X 2.2 cm=
= x cm^{2}
= = 7
Area=704 mm^{2}
 Work out these areas, (i) in mm^{2} and (ii) in cm^{2}.
a.16 mm x 112 mm  b. 57 mm X 28 mm  c. 84 mm X 65 mm 

P:92 MULTIPLYING BY A DECIMAL (TENTHS ONLY)
3 Work out the area of shaded portion of each square, (i) in cm^{2} and mm^{2}.
4 Complete these multiplications (i) by changing decimals into common fractions, (ii) changing decimals into whole numbers, multiplying, then dividing your answer by 100.
a. 0.66×0.7  b. 7.1 x1.9

c. 0.4 x 0.6  d. 6.4 x 0.8

e. 1.3 X 0.6  f. 3.7 X 2.4

P:93 MULTIPLYING A DECIMAL FRACTION BY HUNDREDTHS
1 Now, work out these multiplications.
a. 2.4 x l.58  b. 3.62 X 1.5 
c. 3.62 x 4.3  d. 7.6 x 4.84 
2 Solve these by first changing decimal fractions into common fractions.
a. 1.732 X 0.5  b. 0.482 X 1.9

c. 2.415 X 1.4  d. 7.325 X 0.4

e. 1.86i X 2.2  f. 4.09 X 7.3

3 Copy and write denominators for *s. Then complete the sums.
 1.62 x 5.3 =
 3.8 x 7.72 =
 8.45 X 2.7=
4 Copy and write denominators in place of *s. Then multiply.
 2.621 x 0.7 =
 0.939 x 6.3 =
 7.9 x 8.64 =
 0.68 X 7.7 =
 9.368 X 5.2 =
P:94 DIVIDING BY A DECIMAL FRACTION
P:95 DIVIDING BY A DECIMAL FRACTION
1Copy and complete the table.
Division sum(decimal divisor)  Equivalent to (whole number divisor)  Answer  
*  1.8 ÷ 0.2  18 ÷ 2  9 
a  0.84 ÷ 0.12  
b  21.9 ÷ 0.3  
c  0.63 ÷ 0.21  
d  0.85 ÷ 0.5 
2 Look at the example and work out the divisions.
a2.8 ÷ 0.7  b0.49÷ 0.7

c 3.2 ÷0.8  d9.5 ÷1.9

e 0. 72 ÷ 0.9  f0.55 ÷ 0.5

3Now, work out these divisions.
a 9.6 ÷ 0.048  b 556÷6.95

c64.2 ÷ 1.07  d0.9 ÷ 0.018

P:96 USING DIVISION TO CHANGE COMMON FRACTIONS INTO
1 Solve these.
a 5÷ 10  b6 ÷ 300  c 7 ÷ 14

2 Now change these into decimal fractions.
a  b  c

d  e  f

3 Solve the following.
a. While playing in the field, Sprog and his three friends find a ten rupee note. They decide to divide the note among themselves. How much does each get?

b. Spook gets a nice big chocolate on his birthday. At school he decides to share it with four of his friends. How much does each get?

P:97 SIMPLIFICATION DECIMAL FRACTIONS
1Using the DMAS rule to guide you, simplify each expression.
a. 6.8X0.14+ 14.63 
b. 8.56 + 0.08 + 2.4 – 1.72 
c. 10.01 X 3.5 – 6.881 
d. 0.95 + 0.05 X 3.3 
e. 20.14 X 0.6 + 100.933 
2Simplify these.
4.2 – (6.85 – (4.72 – 1.68))
4.2 – (6.85 – (3.04)}
4.2 – (6.85 – 3.04)
4.2 – 3.81 = 0.39
a9.5 – (2.03 x 1.6) 
b 7.41 + (O.18 + (6.29 – 4.81) 
c (0.74 x i.3) + (i.50i – 0.72) 
d l1x[0.7 + (1.6 + 3.8 – (1.1 x 0.75))] 
e 9.7 – (6.38 – (18.l7 – I4.39)} 
f 2 X (l.6 + (33.9 – 2.4 + (0.3 X 0.4)}] 
3Copy and fill in the blanks.
a6.9l X 4.385: the answer will have——————— decimal places.
bTo change 0.753 into a whole number, I must multiply by————
c14.73 – 8.645 =——————–
d6.49 + I0 =—————–
e——————x 100 = 23.69
f ———— in decimal form.
g 6.2 X 3.85 =——————
h 0.119 x—————– = 11.9
P:98 REVIEW
1 Rewrite these in descending order.
a. 3.01 1, 3.101, 3.001, 3.301 
b , , , 
2Write vertically and complete.
9. 6.8l11 13.962  b. 482.04 + 75338 + 1.2 

3Rewrite these groups of decimals as like decimals.
4.058, 6.0, 7.29, 17.3 
4Work out the multiplications.
a. 1.769 x 100  b. 1.3 X 7.9

c. 72.034 x 24  d. 0. I17 x 0.3

5Work out the divisions.
a. I15.02 ÷ 18  b. 0.42 ÷ 0.14

c. 621.l7 ÷ 100  d. 3.2 ÷ 0.04

6Change these into decimal fractions.
a  b  c 
7Solve these problems, making complete statements.
a. Spray Spacewalker has a strip of wood 52 cm long. For a model spaceship he is making, he needs small pieces of wood 2.6 cm long. How many can be cut from his long strip?

bHow many 0.25 litre cups can be filled from a 4.5 I jug of lemonade?

cSid Spacewalker finds 12.25 kg of flour in the cupboard. To bake oneapple pie, he needs l.75 kg of flour. How many pies can he bake?

dIn the beginning of July, Sara Spacewalker weighed 51.25 kg. By the end of the month, she weighed 5l1.I5 kg. How much weight had she gained?

eAt an endofterm party, I2 chocolate cakes are shared equally between 40 children. How much does’ each child get? Give your answer as a decimal fraction.

fThe string attached toy Sprog Spacewalker’s kite is 20.65 m long If Sprog lengthens it by 7.5 m, how long will the string be?

P:99 PART THREE MORE ABOUT ROUNDING OFF
P:100 ROUNDING OFF WITH DECIMALS: TO 1 DECIMAL PLACE
 Round off to one decimal 2 place.
6.85 6.9; 3.01 3.0
a 7.05  b. l5.43  c. 26.25  d. 10.15  e. 27.07  f. 40.03 
 Rewrite vertically and solve. Then round off your answers to the nearest whole number.
a. 37.l1 + 16.8 
b. 16414 + 2.384 + 162.9 
c. 1003.5 – 869.9 
d. 1423 + 238.6 + 14.7 
e. 2061.4 – 1453.8 
 Write the length of the shaded part of the line. Then, round it off to the nearest whole number.
a 
b 
P:101 ROUNDING OFF WITH DECIMALS: TO 2 DECIMAL PLACES
1Round off to 2 decimal pieces. 8.015 8.02
a.132  b. 14.109  2.494  d. I 48.003  e8.027  f. 1792.007 
2Rewrite vertically and solve. Then round off you answer to 2 decimal places.
a10.049 + 3.1 I7 + 8.632  b28.032 – I4.595

c94.128 + 13.3 + 6.497  d72.064 – 18.967

e52.135 – 29.772

3Multiply or divide, then round off your answer to 2 decimal places.
a 4.3 x 6.21  b38.15 x 7.8 
c24. I8 X 5.7  d 4.9 + 0.7 
e14.4 ÷ 1.8  f32.1 ÷ 10.7 
P: 102 ROUNDING OFF: THE RECURRING OR UNENDING DECIMAL
1 Change these fractions into decimals, rounding off you answers to 3 decimal places.
a  b

c  d

e  f

2 Change these into decimals, rounding off you answer to 3 decimal places.
a  b  c 
d  e  f 
P: 103 ROUNDING OFF DIVISION QUOTIENTS
1 Solve these divisions, rounding off you answers to 2 decimal places.
a. 15,623 ÷ 49  b. 472,689 ÷ 64

c. 78,309 ÷ 62  d. 508,933 ÷ 72

Q 2. Now solve these, rounding off your answers to 3 decimal places (Remember: keep dividing till you have four places of decimals, then round off).
a. 53,997 ÷ 48  b. 78,632 ÷ 145

c. 90,455 ÷ 67  d. 65,339 ÷ 28

P: 104 PERCENTAGES: A SPECIAL KIND OF FRACTION
P: 105 PERCENTAGES: A SPECIAL KIND OF FRACTION
1Change these fractions into equivalent fractions with denominator 100
a  b –  c – 
d –  e –  f – 
2Express these as fractions of 100, rounding off to 2 decimal places where necessary.
a of100  b. of100  C of 100  d. of100 
Answers:
P:107
1Write each fraction as a percentage.
——=36 per cent
2 Write each fraction as a percentage, using the special symbol.
——=36 %
3Write each percentage fraction, reducing it to its lowest terms where possible.
=
30%  45%  89%  24%  32%  100% 
4Change these fractions into percentages, rounding off your answers to 2 decimal places where necessary:
——————= X =11.11%
of 100  
b. of 100  
c. of 100  
d. of 100  
e. of 100  
f. of 100 
P:108
Q 1. Change these mixed numbers into percentages.
——————=x =x=320%
b.  
c.  
d.  
e.  
f. 
Q2: Change these into Percentages.
a.6  
b.17  
c.58  
d.9  
e.23  
f.79 
Q 3. Change these into percentages.
a.0.23  
b.7.394  
c.7.01  
d.4.69  
e.3.9  
f.3.00 
P:109
CHANGING PERCENTAGES INTO FRACTIONS OR DECIMALS
Q4: Change these percentages into fractions, mixed reducing where gou can.
a.75%
 300%
 21%
d.38%
 135%
 800%
Q5: Change these percentages into decimal numbers:
24% ——————= =0.24
 35%
 1.8%
 98%
 140%
 6%
 16.3%
Q6: Change these decimal numbers into percentages:
0.05——————==5%
 0.39
 0.6
 l.0
 0.04
 0.55
 1.52
7: Copy and complete Sid’s table.
Sara’s Performing
% Percentages %
%  Fraction with denominator  decimal  Fraction in lowest terms 
50%  0.50 or 0.5  
10%  
1%  
4.5  
P:110
Q8: Look at the price board. Help Sid bg working out the special price of:
A: the plastic bucket 
B: the ‘Klikit’ camera 
C: the toothpaste 
Q9: Calculate each percentage of the quantity given.
20% of 650 km = x 650 km
= 130 km
A:10% of Rs 50
B:l0% of 75 g
C:50% of 000 km 1
D:12% of 6001
E:7.5% of 60 m
10: Solve, making complete statements.
A:Mrs Shah earns Rs 8500 every month from her work as a computer operator. If her boss gives her a10% increase in salary, how much will she now earn every month? And how much will she earn in one year? 
B:Moonshine earns an astronomical sum of Rs 3,500,000 per month as director of Super shine space station. He sends 40% of salary to his wife on space station Zebra. How much that? 
P:111
USING PERCENTAGES
Q11 Rewrite these newspaper stories, changing fractions into percentages.
A:Super globe, 14 January 24 out of 48 cows on Moon View arm are suffering from toothache. On Space Field farm, 32 out of 60 cows are suffering from the same complaint. 
B:Tauland, 27 March On yesterday’s rocketbus from Super globe, 240 out of 500 seats were occupied. On the bus from Tauland to Venus, 325 out of 600 seats were occupied. 
Q12: Now solve these, making complete statements.
A:In her end»ofterm exams, Salima got 33 out of 50 marks in Urdu and 7 out of 10 marks in History. What were her two marks in percentages? In which subject did she do better? 
B:In a TV quiz programme, Sid answers 65 questions and gets 32 answers right. Sara answers 80 questions and gets 56 correct answers. Give their scores in percentages and find out who is better at quizzes! 
P:112
PROFIT AND LOSS
Q1 Work out Steve’s profit on each of these rocket soles.
C.P=Rs 14,500….. Rs 16000
S.P. =RS 16,000 – Rs 14500
Profit=Rs 1500 Rs 1500
A: C.P.= Rs 13,250S.P.= Rs 15,800

B: S.P.= Rs 30,000C.P.= Rs 24,075

C:C.P.= Rs 8900S.P.= Rs 12,450

D:C.P.= Rs 12,450S.P.= Rs 14700

Q2: WORK OUT THE PERCENTAGE PROFIT ON THESE SALES.
C.P =Rs 5000
Profit =Rs2500
Profit = x 100== 50%
A: C.P.= RS 6000Profit= RS1200

B:C.P= RS4500Profit= RS1500

C: S.P.= RS850Profit= RS90

D: C.P.= RS565Profit= RS50

P:113
PROFIT & LOSS
 Work out Steve’s loss on each of these sales.
C.P. = RS 3600… RS 3600
S.P.=RS 1950 – Rs H50
Rs 1650
Loss = Rs 1650
a. C.P. = Rs 4700S.P. = Rs 3850 
b. S.P. = Rs 7225C.P. = Rs 10000

c. C.P. = Rs 16,5ooS.P. = Rs 14,750

4Work out (i) the loss; (ii) the percentage loss on these sales.
C.P= Rs 1000 …..Rs 1000
S.P.= Rs 800 – Rs 800
Loss = Rs 200
% Loss = % x 100
a)C.P= R5 2500S.P= RS 2000

b) S.P= RS 3250C.P= RS 4500 
c) C.P= R5 7250S.P= RS 6000 
P:114
PROFIT & LOSS
Q1: Find the profit or loss on each of these sales.
C.P. = Rs 240; S.P. =Rs 80
S.P. is less than C.P.
Loss = Rs 60
a) C.P. = Rs 500 
b) C.P. = Rs 1764 
c) C.P. = Rs 2730 
Q2: Find the selling price.
a)C.P. = Rs 429 
b)C.P. = Rs 2500 
c)C.P. = Rs I770 
Q 3: Find the cost price.
a) S.P. = Rs 756 
b) S.P. = Rs 2460 
c) S.P. = Rs I265 
Q 4: Work out (i) the profit; (ii) the percentage profit on these sales.
C.P. = Rs 60 Rs 200
S.P. = Rs 200 Rs 60
Profit = Rs 40
Profit % !L6e x mo
= % or 25%
a) C.P. = Rs 900 
b) C.P. = Rs 3200 
c) C.P. = Rs 480 
Q5: Find the profit or loss as a percentage of the cost price.
Sara buys a TV for Rs 8000. She later sells it for Rs 6500.
C.P = RS 8000
S.P. = Rs 6500
Loss = Rs 1500 %
= 1500%
Loss % =
Loss % = 18.75%
a) Sid bought a motorcycle for Rs 7000. After three accidents, he sold it for Rs 4500. 
b) The Jamal’s bought a refrigerator for Rs 20,000. Five years later they sold it for Rs 27500. 
c) At Wholesale Cloth Centre, Alam buys cotton cloth at Rs 50 per metre. He sells it to his customers at Rs 75 per metre. 
d) Rehan bought a cycle for Rs 2600. After using it for a year, he sold it for Rs 2200. 
e) Adil buys apples for his stall at Rs 40 per dozen. He sells them at Rs 56 per dozen. 
P:115 SIMPLE INTEREST
P:116
SIMPLE INTEREST
1Work out the amount in these bank accounts after one year.
Principal = Rs 2000
Interest = 5%
Amount = P + I
=Rs 2000 + E6 X Rs 2000
= Rs 2000 + Rs 100
= Rs 2100
a) Principal = Rs 3000interest = 20%

b)Principal = Rs 1000Interest = 7.5%

c)Principal = Rs 600interest = 15%

2Work out the amount owed to the bank after one year.
Principal = Rs 4500
Interest, = 9%
Amount = P + I
= Rs 4500 + 9/100 x Rs 4500
= Rs 4500 + Rs 405
= R5 H905
a) Principal = Rs 12,000Interest = 6% 
b) Principal = Rs 20,000Interest = 12.5% 
c)Principal = Rs 18,500Interest = 8% 
P:117
SIMPLE INTEREST
3Calculate the interest where:
Principal (P) = Rs 600
Rate (R) = 9%
Time (T) = 4 years
Interest = Rs
=Rs 216
a)P=Rs 106R=3%
T=3years

b)P=Rs 500R=8%
T= 5 years

P:118
c)Rs 250P=4%
T=5 years

d)Rs 2000P=7.5%
T=3 years

e)Rs 12,000P=6%
T=4 years

f) Rs 28,750P=5%
T= 5 1/2 years 
Rs 25,000P=12%
T=6 years

g) Rs 6,600R=12%
T=2 years

) Rs 2400P=15%
T=4 years

4Work out these problems.
(a) Mick Moon deposits Rs 4000 in a bank account for his daughter Meg. How much money will be in the account after 5 years if the bank pays Mick a \2% % rate of interest? 
(b) Mrs Siddiqi deposits Rs 3000 in a fixed deposit account. She agrees not to withdraw any money before 3 years are over. In return, the bank will pay her a 16% rate of interest. How much interest will Mrs Siddiqi earn during this period? How much money will be in her account at the end of 3 years? 

P:119
REVIEW
1 Round off to 2 decimal places.
 18.494 b. 143.0°19 c. 475.199
2Change into decimals, rounding off to 3 decimal places.
a.  b.  c. 
3Write as percentages (to 2 decimal places, if necessary)
a)  b) 2  c) 0.51 
d)  e) 4  f) 1.2 
g)  h) 8  i) 1.032 
4 Write as fractions in their lowest terms:
a. 28%  b. 72%  c. 600% 
5Change into decimals.
a. 48%  b. 2.5%  c. 142% 
6Calculate:
a. 40% of Rs 480  b. 75% of 6001  c. 5% of 7000 km 
7Work out the price of these items on special offer.
a. Softy Soap: 10% off at Rs 5.50  b. Transistor radio: 20% off at Rs 260  c. School bog: 15% off at Rs 125 
8Calculate the interest payable where.
a. P=R5300R = 4%
T=6 years 
b. P=Rs7500R = 11 %
T= 9 months ( years) 
c. P = RS 2500R=7
T=3 years 
d. P = Rs 3600R = 14%
T=2 years 
9 Solve these problems.
a. Sue Spacewalker borrows Rs 7550 to buy a spacemoped. The bank asks her to pay the money back over 3 years at 15% rate of interest. Find (i) the interest she must pay, and (ii) the total amount of money she must repay at the end of 3 years. 
b. Which of these bank customers will earn the largest sum ot interest every year?(i) Usman: P = Rs 6000, R = 7%
T = 4 years (ii) Zeba: P = Rs4500, R = 8% T= I0 years (iii) Rashid: P = Rs 7250, R = 6% T = 2 years 
P:120
REMEMBERING ANGLES
Sid remembers that there are five different types of angles, but he can’t remember their names. Help him complete the crossword by naming each angle shown in the clues.
Clues Across
Clues Down (pic)
Q2 Draw and label an angle that matches the name.
∠PQR (obtuse angle)
a∠ABC (right angle)

b∠STU (acute angle)

c∠EFG (reflex angle)

3 Copy and fill in the blanks.
a)There are ———————degrees in a complete turn.
b)An acute angle is any angle greater than 0° but less than——————
c)The halfcircle protractor has a total of ——————marked on it.
d)An angle which is greater than a right angle but less than I80° is called an—————— angle.
 e) 3/4 circle =—————— degrees.
f)A reflex angle is any angle which is greater than ——————but less than——————
P:121
REMEMBERING ANGLES
Q4: Use your protractor to measure these angles. Think carefully which row of markings on the protractor you should use.
Q5: Draw these angles in your notebook, using a protractor.
a.40°

b. 90°  c. 55° 
d. 60°

e. 115°  f. 145° 
Q6: Draw these angles adding an interior or exterior point in any suitable place.
∠XYZ = 80° exterior point /A
a)∠PQR = 25°; interior point C
 b) ∠STU = 115°; exterior point J
Q7: Look at this angle. Then write words in the blanks.
 a) The angle is made up of two line segments, ————————and——————
b)They meet at a common point ——————which is called the ——————
 c) Point R is in the——————
d)Point X is in the——————
Q122: USING THE PROTECTOR REFLEX ANGLES
1 Calculate these reflex angles, using your protractor
2 Draw these reflex angles, using your protractor.
Reflex ∠XYZ = 305°
— (360° 305° = 55°) = 305
a) Reflex ∠PQR = 320° 
b) Reflex ∠WXY = 290° 
c) Reflex ∠CDE = 335° 
P:123
USING THE PROTRACTOR: COMPASS & BEARINGS
P:124
MORE ABOUT CIRCLES
P:125
MORE ABOUT CIRCLES
Q1: Measure the diameter of each circle
Diameter = 3.2 cm



Q2: Now calculate the radius of each circle in Exercise1.
Diameter = 3.2 cm
Radius = cm = 1.6 cm
Q3: Complete these.
 a) If a circle has a diameter of 9.64 cm, it’s radius will be——————cm.
 b) If the radius of a circle equals 5.845 m, its diameter is——————m.
 c) A quarter circle is also known as a ——————
d)The diameter of a circle always passes through the—————— of the circle and joins together 2 points on its——————
Q4: Using a small plate or the bottom of a tumbler, draw a circle in your notebook.
Mark a point on its circumference and label it A.
Draw as many chords as possible, using point A as one of the end points. Make one of your chords pass through the centre of your circle. Label your chords (AB, AC, AD, etc.) and measure each of them. Which is the longest of the chords you have drawn?
P:126
MAKING CIRCLES: USING COMPASSES
P:127
MAKING CIRCLES: USING COMPASSES
Q 1. Using your ruler and compasses, draw circles with these radii (radii say ‘raydeeeye’is the plural form of radius).
a. 4 cm  b. 7 cm  c. 3.3 cm 


d. 5 cm  e. 4.5 cm  f. 4.1 cm 

Q 2. Without using your ruler, state the diameter of each of the circles you have drawn in Exercise A.
Circle a: radius = 4 cm
diameter = 8 cm
Q3: Look at this circle.
 Name all the radii of the circle.
 Measure the lengths of the diameters.
 Name all the arcs marked on the circumference.
P:128
MORE ABOUT TRIANGLES
Q1. Measure the sides of this triangle with your ruler. Record your findings in the table. Then, with your protractor, measure the angles of the triangle and record your findings.
Length of side (cm)  Size of angle (°) 
AB  ∠CAB 
BC  ∠ABC 
AC  ∠BCA 
What type of triangle is this? What do you observe about its angles?
Q 2. Now measure and record the sides and angles of this triangle.
Length of side (cm)  (Size of angle (°) 
PQ  ∠RPQ 
QR  ∠PQR 
PR  ∠QRP 
What type of triangle is shown? What do you notice about its angles?
Q3: Measure and record the sides and angles of this triangle.
Length of Size of side (cm) angle (°)
Length of side (cm)  (Size of angle (°) 
ED  ∠FED 
DF  ∠EDF 
EF  ∠DFE 
What type of triangle is this?
What is special about its angles?
Q4 Measure each triangle (sides and angles), then name the triangle family to which it belongs. Present your findings in the form of a table.
Sides  Angles  
WY  5cm  ∠WXY  72 
YX  5cm  ∠XWY  72 
XW  3cm  ∠WYX  36 
Δ Family = isosceles



Q 5. Take a blank sheet of paper or cardboard. Draw a triangle on it, and mark each angle with dots, thus.
Cut out your triangle, then cut the three angles from the triangle thus:
Arrange the three angles so as to make a straight line:
You have just shown how the three angles of a triangle make a straight angle or 180° !
Q6: Without using your protractor, calculate the size ofthe angles marked with letters.



Q7: Here is a page from Sprog Spacewalker’s geometry notebook. He has measured the angles of some As, but not very carefully. Make a list of the triangles whose angles have been measured incorrectly.
Triangles
a.∠ABC = 90°∠BAC = 70°
∠ACB = 20° 
b. ∠CDE 25°∠CED 115°
∠DEC 43° 
c.∠POR = 110°∠PRO = 40°
∠RPO = 40° 
d. ∠JLK 85°∠JKL 45°
∠KJL40° 
e.∠STU = 35°∠SUT = 47°
∠TSU =100° 
f. ∠XYZ 35°∠XZY 110°
∠ZXY40° 
P:131
CONSTRUCTING TRIANGLES
We can construct a triangle if we know:
(a) the length of all 3 sides
or (b) the length of 2 sides plus the size ofthe angle between them
or (c) the size of 2 angles plus the length of the sides between them
To construct a triangle when all 3 sides are given:
for example, AABC where AB = 5 cm, AC = 4 cm and CB = 3gcm.
Step 1
With ruler and pencil, draw line AB (5 cm).
Step 2
Keeping the pivot of your compasses on the 0 cm mark, stretch out the pencil arm till the pencil point touches the 4 cm mark. Now point the pivot on point A of line AB. Mark an arc with your compass.
Step 3
Readjust your Compasses so that the arms are 3 cm apart (use your ruler) Place the pivot on point B and draw a second arc:
Step 4
The point where the two arcs cross marks the third vertex, C, of your triangle. Join C to A and then to B using your ruler.
You have constructed Δ ABC!
Q1. Construct these triangles, using your ruler and compass.
a. Δ ABC: AB = 6 cm, AC =3cm and CB =4cm 
b. Δ POR: PQ = 7 cm, QR =5cm and PR = 4cm 
c. Δ RST: RS = fi cm, ST =7.5 cm and RT = 3 cm 
P:132
CONSTRUCTING TRIANGLES
Q2: Tick the sets of measurements which cannot be made into triangles.
 a) 3cm, 2cm, 4cm
 b) 8cm, 4cm, 1cm
 c) 4cm, 11cm, 8cm
P:133
CONSTRUCTING TRIANGLES
Q 3. Construct these triangles.
a. Δ XYZ where XY = 6 cm, XZ = 4 cm and ∠YXZ = 50° 
b. Δ EFG where EF = 5.5 cm, EG = 4.5 cm and ∠GEF=65° 
c. Δ RST where RS = 4.8 cm, RT = 6.5 cm and ∠TRS = 35° 
4Now construct these triangles.
a)∠PQR where ∠QPR = 30°∠PQR = 60° and side QP = 4cm


b)Δ ABC where side AB = 5cm,∠BAC = 45° and ∠ABC = 25°


c)Δ JKL where ∠KJL = 65°,∠JKL = 40°and side JK = l4.6cm 

d)Δ TUV where ∠UTV= 80°∠TUV= 25° and side TU = 8cm 

Q5: Construct the triangles whose measurements are given in this table
AB  BC  ∠ABC 
5 cm  2.5 cm  75° 
5.6 cm  3 cm  115° 
4.8 cm  5,2 cm  35° 
Q6: Now construct triangles with these measurements.
AB  ∠CAB  ∠CBA 
a)4.5 cm  45°  75° 
b)5.6 cm  25°  55° 
c)6.3 cm  90°  35° 
Q7: Choosing your own measurements, construct and then label.
a) any equilateral triangle  b) any isosceles triangle  c) any scalene triangle 
P:134
REMEMBERING QUADRILATERALS
Q2: Name each of these quadrilaterals. Then measures all 4 angles. What is the sum of the angles?



P:135
PERPENDICULAR AND PARALLEL LINES
Q 1. In the following figure some of the coloured lines are perpendicular to line PQ. Write their names in your notebook. (pic)
Q 2. Study this figure, then complete the sentences. (pic)
 AB is perpendicular to——————
 AE is perpendicular to——————
 DE is perpendicular to——————
 XC is perpendicular to——————
3Look carefully at line XY. Which of the lines are parallel to the coloured line? Write their names in your notebook.
P:136
CONSTRUCTING PERPENDICULAR AND PARALLEL LINES
Q1. Use your protractor to draw these perpendicular lines.
a. PQ perpendicular to QR  b. EF perpendicular to FG

 Using your set square, draw these perpendicular lines.
a. XY perpendicular to the midpoint of CD  b. QR perpendicular to the midpoint of VW 
P:137
MORE ABOUT PARALLEL LINES
Q1: Using your ruler and protractor (or set square), draw these sets of parallel lines. Don’t forget to mark arrows on them.
–Line AB parallel to line CD
I cm apart
AB
cm
C D
a)Line JK parallel Ho line LNI, 3.5 cm apart  b)Line CD parallel to line EF, 4.2 cm apart 
2Now draw these, following the instructions carefully.
Parallel lines PQ and RS, each 3.8 cm long, and I.7 cm apart
P Q
R S
a)Parallel lines AB and CD, each 4.1 cm long, and 3.4 cm apart  b)Parallel lines OP and QR, each 5.6 cm long, and 5 1.7 cm apart

Q:a. Draw three concentric circles of radii I.7 cm, 2.6 cm and 4.5 cm.  Q:b. Draw two concentric circles of radii 1.7 cm, 2.6 cm and 4.5 cm.

P:138
Q1: Work out the average of these sets.
12, 6, 21, 13 Total = 52
Addenda = 4
Average = I3
a)14, 27, 5, 19, 10  b)Rs36, Rs 14, Rs 17, Rs 42, Rs 101  c)8 cm, 25 cm, I5 cm, 32 cm, 10 cm

2Copg and complete these.
a)The average of f, 2, 3, 4 and 5 is——————
b)The average of I0, I00 and I,00 is——————
c)To find the average of 18, 14, 5, and 7, we divide by 4
P: 139
AVERAGE
Q3: Below are the weights recorded for four I0gearold children test. Work out the average weight of the children
NAME  WEIGHT 
Mona  34.0kg 
Kashif  36.2kg 
Aslam  35.8kg 
Insia  40.0kg 
Q4: Solve these word problems, making complete statements.
a. Sid bugs a kilogram of spacefingers on 6 different dags. The prices he pages are R5 8, Rs 10, Rs 7.50, Rs 12, Rs 11.75 and Rs 9.25. Find the average price.  
b. Over a 4month period, Moiz’s monthly income was Rs 5000, Rs 4000, Rs 2500 and Rs 1000. What was his average income for that period?  
b. Study this table: it shows the number of girls and bogs studying at Ahsan Primary School:
Find (i) the average number of girls in each class, (ii) the average number of bogs in each class, (iii) the total number of children in the school and (iv) the average number of children in each class. 
P:140
AVERAGES AND GRAPHS
Q1: This column graph shows oneweek attendance for Class 5 at Ahsan Primary School.
Number of children
(GRAPH)
Mon Tue Wed Thu Fri
Day
Study the graph and then work out:
 The total attendance for each day of the week.
 On which days the attendance was below the average.
 This column graph shows the Marks by 6 children in a spelling test.
Study the graph, then work out the average marks scored by the 6 children. Which children scored above the average? This graph shows the price of 4 story books
(graph)
The dotted line shows the average price of the 4 books.
You can see that average is a number roughly halfway between the smallest number and the largest attendance.
(graph)
Q3: Here is the top part of a column graph showing 4 children’s results in a test.
Look at the graph and estimate what the average marks will be. Than work out the average exactly.
P:141
AVERGES, GRAPHS AND SPEED
Q 4: Study the graphs, then work out the average speed for each journey.
Distance (km)
Average speed = 140 km + 2 hours
= 20 km/hr
 Distance (km)
 Distance(km)
 Distance (km)
Q 5. Work out these average speeds.
90 km covered in 5 hours
Average speed= = 45 kmph
a) 105km covered in 5 hours

a) 990km covered in 3 hours

a) 445km covered in 8 hours

P:142
DISTANCE, SPEED & TIME
Q1: Find the time taken for each journey.
D = 100 km, S = 20 kmph,
T= ——————
S = 55 kmph, D = IIOkm,
T: ——————
D = SAO km, S = 60 kmph,
T:——————
Q2: Solve the following.
a)A motorcycle averages 50 kmph. How long does it take to travel 25 km? 
b)How long will a bus travelling at an average speed of 45 kmph take to cover a distance of 225 km? 
P:143
DISTANCE, SPEED AND TIME
Q3: Work out the distance travelled in each of these journeys.
a)S=30 kmph, T=5hrs,D=? 
b)S=55 kmph, T=4hrs,D=? 
c)T= 121 hrs, S= 50 kmph, D=? 
Q4: Work out the average speed of these journeys.
a)T=5 hrs, D=360 km S=? 
b)T= 16 hrs, D= 1200 km, S=? 
c)T=7 hrs, D=497 km, S=? 
Q5: Calculate values in the blanks.
a)S=40 kmph, T=D=480 km? 
b)T=5 hrs, D=72O km, S=? 
c)S=?,T = 12 hrs, D=732km 
d)D= 1350 km, s=5o kmph, T=? 
e)s=6o kmph, D=?,T=2 1/2 hrs 
f)D=?, T=4 1/4 hrs, s=70 kmph 
Q 6Copy and complete the table:
Distance  Time  Speed  
a  240 km  6 hr  
b  hr  40 kmph  
c  450 km  90 kmph  
d  1500 km 
Q7: Solve, making complete statements
a) If a cyclist travels Q0 km in 5 hours, what is her average speed? 
b) Sprog Spacewalker takes part in a marathon race I8 km long. If his average speed is 6 kmph, how long does he take to complete the race? 
c)How far will a gasfilled balloon travel in 8 hours if its average speed is 10%kmph? 
d)How long will it take Sue Spacewalker to run 12 km at 8 kmph? If Selvi takes 2 hours to run the same distance, what is her average speed? 
P:144
THINKING ABOUT TEMPERATURE
P:145
ALL ABOUT TEMPERATURE
Convert these temperatures into the other Scale (answer to 2 decimal places where necessary).
a.122°F  b. 45°C  c.77°F 
d. 40°C  e.113°F  f. 35°C 
P: 146 PART FOUR
ALGEBRA
 Look at the objects in each plate and write the initial of each object in the blank.
1apple  1 brinjal  1cauliflower 
Q 2. Now look at these boxes. Write the initial of each object.
 (2 lollipops) (3 sweets)
(2 chocolates) (4 burgers)
B: Now, write all these using different symbols of your choice. For example, ’lollipop’ can be written as w, ‘sweet’ as x and so on.
C: If x stands for one rupee, write the amount of money. each box contains, using x:
(Rupees seven) (Rupees five) (Ru5ees ten)
D: Put all the money together, and write your answer using x:
P:147
ALGEBRAIC EXPRESSIONS
Q1: Now, put all the items given in Exercise 2A, on the previous page, in one tray.
Write the contents of the tray, using the English alphabets.
Q 2. Now, write each group as an algebraic expression, using first the initial letter and then the last letter of each word.
 2 apples + 3 bananas + I mango + I watermelon
 2 (pairs of) scissors, two knives, 3 forks and I teapot
P:148
Q1: Now, write the following sets at objects as a algebric expressions using different alphabets of your choice.
 5 books, 3 notebooks and I atlas.
 3 ships, 1 boat and 2 kayaks.
 4 ink pens, 3 ballpoint pens, 12 pencils and 1 felltip pen.
Q2 Now add each set of the following expressions.
a). 2x+3y+lIz; 5x+2y+4z  b)2a+3b+4c+ ld; 5a+lIb+2c  c)p+2q+3r; 2q+3r; lIp+2q 
Q3 Take away
a) 2x+3yfrOm 5x+8y  b). 3p+2q+ rfr0m5p+2q+  c) 2a+1b+1c from 2a +1b+1c+1d 
P:149
SIMPLE MULTIPLICATION
Write in short.
a) x+x+x  b) y+y+y  c) f+f+f+f+f+f 
Q2: Now, find the perimeter of each of these figures.
a. Triangle with side x cm  b. Square with side y cm  c. Hexagon with side z cm 
Q 3: Write as an addition:
a. 3g 
b. 5q 
c. 82 
Q 4. Now, write the sum in each case.
3a+2b+c; 3a+2b+c
= 2 (3a+ 2b+c)
= 6a+4b+2c
a. 4x + 5y; 4x + 5y  b. 2p+iq+3r;2p+lq+3r;2p+1q+3r

P:150
Q1: Now find the area each of these rectangles
a. Rectangle with length of p cm, and breadth q cm

b. Square with side s cm  c. Rectangle with length f cm and breadth g cm. 
Q2: Expand and write.
5p = 5 x p (or F 5.p)
=p+p+p+p+p
a. 6m 
b. 9z 
c. pq cm2 
P:151
REVIEW
Exercise
Write out these problems in algebraic terms and work them out.
Q1: If one pineapple costs Rs 10 find the cost of:
 5 pineapples
 3 pineapples
 x pineapples
P:152
Q2:Two bags contain 3 lollipops and li sweets each. Write the sum as an algebraic expression. 
Q3: One cage has 2 parrots and 3 sparrows, and the other has 1 parrot, crow and 1 Sparrow. Birds from these two cages are put together in a larger cage. Write the sum as an algebraic expression. 
Q4: There were 4 sweets in a box; two were eaten by Adil. Write this as an algebraic term. 
Q5: There were 4 cakes and 4 sandwiches on a plate. Rabia ate one of each. Write this as an algebraic expression. 
Q6: Work these out:
 a) p+p+p+p+p+p =——————
 4k =——————
 3d – 2d =——————
 7x + 3x + 2x =——————
 80 – 2c =——————
Q7:Add:
a. (3a + Lib) + (Sb + lm + Zc) 
b (ZX + 3y) + (5y + Zy) 
Q8:Subtract:
a. (3x + 4y) – (2y + 1x)  b. (9p +8r) – (4r + 3p) 
Q9: Multiply
a.a x b  b. p x r  c. y x z

P:153
REVIEW OF THE YEAR
Q1: Place in Pakistani periods and write the number name
a. 5672318  b. 74028301  c. 6009053  d. 90755620 
Q2: Change into International periods and write the International number name.
a. 42,03,721  b. 3,16,72,049  c. 50,47,834  d. 8,02,46,1 I8 
Q3: Write the value of the coloured digit.
a. 1,627,148  b. 7,24,16,831  c. 22, 14,690  d. 84, 1172,063 
Q4: For each number, write (i) the predecessor and (ii) the successor.
a. 2,348,000  b. 6, 10,00,000  c. 14, 17,600  d. 84,000,000 
Q5: Write vertically and complete.
a. 1,40,732 + 8,64,395 +28  b. 7,640,117 – 4,584,623 
c. 8,96,23, 141+ 3292 + 764  d. 1468.29 – 979.54 
Q6: Round oft each number (i) to the nearest I0 and; (ii) to the nearest I00.
 643 b. 82,555 c. 1,29,387
Q7: Round off each number (i) to decimal place and (ii) to 2 decimal places.
a. 2.461  b. 84.099  c. 6.191  d. 100.335 
Q8: Write vertically and complete.
a. 1629×312  b. 8.I97x36  c. 8074×593  d. 10.895×75 
Q9: Solve, Writing your answer to two decimal places where necessary.
a. 97,920 ÷ 384  b. 69,482 ÷ 77 
c. 46,839 ÷ 47  d. 108,964 ÷ 98 
Q10: Prepare bills for these 33 customers.
a. Hungry Crocodile: 20 kg of rice at Rs 3.75/kg; 16%kg of fish at Rs 24/kg; 51 of cooking oil at Rs 850/I; I0 packets of biscuits at Rs I I.35/packet. 
b. Adil: 12 kg of wheat flour at Rs 4. 1 5/kg; 5.5 kg of sugar at Rs 6.25/kg; 2.51 of cream at Rs 8.60/1; 25 chocolate bars at Rs 9.85 each. 
P:154
Q11. Simplify.
a. 6X5+184  b. 11+18+3×21 
c. 9 x21+7+145  d. 8.1×0.160.6114 
 Simplify.
a. (0.38 x 4.62) + 10.5 
b. 4.61 + {2. + (3.82 – 1.75)} 
c 3+{1+(x)} 
d. [{84 (21 + 3)} + 12] + 74 
e. {31 – 16.3 + 8.6)}x 1000 
 Work out the areas.



 Work out the volume of these cuboids (in cm3 or m3):
a. l=4.2cm,b=5cm,h=1.5cm  b. I=I0m,b=3.5m,h=4.3m 
c. l=6.9cm,b=7.5cm,h=2.2cm  d. any 5digit number divisible by 4. 
Q15: Write down:
a. any 5digit number divisible by 4. 
b. any 6digit number divisible by 8. 
c. any numbers from this list which are divisible by 15:400, 7020, 1 1,620, 15,055. 
Q16: Write the numbers whose prime factors are given here, using brackets to help you.
a. 2 X 2 X 2 X 3  b. 2 x 2 x 2 x 5 x 5  c. 2x3x5xV7x7x11 
Q17: Using prime factorization, find the HCF of;
a. 56 and 140  b. 63 and 511 
Q18:Find the HCF, using the long division method.
a. 1026; 247 
b.21A6; H84 
c. 368; 1173 
d. I377; 836 
Q19: Find the LCM of each set.
a. 12, 15, 21 
b. 24, 32, 26 
c. 10, 12, 18 
d. 27, 30, 15 
P155
Q20: Fill in the blanks.
 If the product of 2 numbers is 270 and their HCF is 3, their LCM is——————
 For a pair of numbers, the HCF is 4 and the LCM is 252.
If one of the numbers is 28, the other number is——————
 Solve, giving each answer in its lowest terms
a) x  b)5 x6 
c) 3 ÷2  d) x x 
e)9 ÷ 1  f) ÷ 
Q22: Multiply each number (i) by 10 (ii) by 100 and (iii) by 1000: ,
a. 4.8 
b. 1 .47 
c. 6.87 
d. 4.535 
Q23: Solve.
a. 0.6 X 0.4  b. 3.0 x 4.5 
c. 0.63 + 0.21  d. 1.752 + 0.219 
e. 2.81X 3.6  f. 0.12 + 0.006 
Q24: Write denominators in place of its, then complete the sums.
a. 2.34X4.61 = 
b. 3.604 x 7.3 = 
Q25: Change these into decimals, giving your answer (i) to 2 decimal places and (ii) to 3 decimal places.
a) 
b) 
c) 
Q26: Write as percentages, using the % symbol.
a)  b)  c) 3 
Q27: Write as percentages (to 2 decimal places where necessary).
a) 1  b) 4  c) 3 
Q28: Change into fractions or mixed numbers, reducing where you
can,
a. 80%  b.224%  c. 16% 
d. 75%  e. 155%  f. 44% 
Q29:Change into decimals.
a. 45%  b. 672%  c. l2% 
d. 55%  e. 752%  f. 34% 
Q30 Change into percentages.
a. 0.018  b. 1.64  c. 0.143 
P:156
Calculate.
a. 20% of Rs 40.75

b. The percentage profit where C.P. = Rs 800 and S.P. = RS Q50

c. 70% of 5600 l of water

d. The percentage profit where S.P. = Rs 5000 and C.P. = Rs 3800 (to 3 decimal places)

Q32: Calculate the interest where:
a. P = Rs 11200, R = 5%,T = 3 years 

b. P = Rs 5000, R = 6%,T = 4 years 

C. P = Rs85O, R = 9%,T = 2 years 

Q33: Construct these, using the appropriate instrument.
a. Reflex LABC = 240°  
b. A circle of diameter 7.8 cm  
c. A circle of radius 6.0 cm with arc PQR marked on it. 
Q34: Complete these statements.
 If each side of Δ ABC is 4.5 cm, ∠ABC = ——————degrees,
 If two angles of an isosceles Δ PQR are 50° each, the third angle=——————.
 If a Δ has angles of 30°, 45°, and 105°, it is a—————— Δ.
 if a coral reef is due west of the golden cockroach its bearing=——————
 Construct triangles to match these dimensions.
AB  BC  AC  ∠BAC  ∠ABC  
a  4cm  5cm  3.5  –  – 
b  6cm  4cm  55^{o}  –  
c  5cm  7cm  –  –  80^{ o} 
d  7.5cm  –  –  35^{ o}  45^{ o} 
 Construct:
a. Parallel lines AB and CD, each 3.2 cm long and 2.0 cm apart.

b. Two concentric circles, one of radius 3.5 cm and the other of radius AA cm.

c. Line PQ perpendicular to the end point of line ST.

 Solve, making complete statements.
a. Over a 3 month period, Kashif’s monthly income from weaving handloom cloth was R~s 460, Rs 2000 and Rs 37liI. What was his average income for the period? 

b. If a rickshaw averages 30 kmph, how long will it take to cover 50 km? If a coral reef is due West of the Golden Cockroach, its bearing = °. 

P:107
1Write each fraction as a percentage.
——=36 per cent
2 Write each fraction as a percentage, using the special symbol.
——=36 %
3Write each percentage fraction, reducing it to its lowest terms where possible.
=
30%  45%  89%  24%  32%  100% 
4Change these fractions into percentages, rounding off your answers to 2 decimal places where necessary:
——————= X =11.11%
of 100  
b. of 100  
c. of 100  
d. of 100  
e. of 100  
f. of 100 
P:108
Q 1. Change these mixed numbers into percentages.
——————=x =x=320%
b.  
c.  
d.  
e.  
f. 
Q2: Change these into Percentages.
a.6  
b.17  
c.58  
d.9  
e.23  
f.79 
Q 3. Change these into percentages.
a.0.23  
b.7.394  
c.7.01  
d.4.69  
e.3.9  
f.3.00 
P:109
CHANGING PERCENTAGES INTO FRACTIONS OR DECIMALS
Q4: Change these percentages into fractions, mixed reducing where gou can.
a.75%
 300%
 21%
d.38%
 135%
 800%
Q5: Change these percentages into decimal numbers:
24% ——————= =0.24
 35%
 1.8%
 98%
 140%
 6%
 16.3%
Q6: Change these decimal numbers into percentages:
0.05——————==5%
 0.39
 0.6
 l.0
 0.04
 0.55
 1.52
7: Copy and complete Sid’s table.
Sara’s Performing
% Percentages %
%  Fraction with denominator  decimal  Fraction in lowest terms 
50%  0.50 or 0.5  
10%  
1%  
4.5  
P:110
Q8: Look at the price board. Help Sid bg working out the special price of:
A: the plastic bucket 
B: the ‘Klikit’ camera 
C: the toothpaste 
Q9: Calculate each percentage of the quantity given.
20% of 650 km = x 650 km
= 130 km
A:10% of Rs 50
B:l0% of 75 g
C:50% of 000 km 1
D:12% of 6001
E:7.5% of 60 m
10: Solve, making complete statements.
A:Mrs Shah earns Rs 8500 every month from her work as a computer operator. If her boss gives her a10% increase in salary, how much will she now earn every month? And how much will she earn in one year? 
B:Moonshine earns an astronomical sum of Rs 3,500,000 per month as director of Super shine space station. He sends 40% of salary to his wife on space station Zebra. How much that? 
P:111
USING PERCENTAGES
Q11 Rewrite these newspaper stories, changing fractions into percentages.
A:Super globe, 14 January 24 out of 48 cows on Moon View arm are suffering from toothache. On Space Field farm, 32 out of 60 cows are suffering from the same complaint. 
B:Tauland, 27 March On yesterday’s rocketbus from Super globe, 240 out of 500 seats were occupied. On the bus from Tauland to Venus, 325 out of 600 seats were occupied. 
Q12: Now solve these, making complete statements.
A:In her end»ofterm exams, Salima got 33 out of 50 marks in Urdu and 7 out of 10 marks in History. What were her two marks in percentages? In which subject did she do better? 
B:In a TV quiz programme, Sid answers 65 questions and gets 32 answers right. Sara answers 80 questions and gets 56 correct answers. Give their scores in percentages and find out who is better at quizzes! 
P:112
PROFIT AND LOSS
Q1 Work out Steve’s profit on each of these rocket soles.
C.P=Rs 14,500….. Rs 16000
S.P. =RS 16,000 – Rs 14500
Profit=Rs 1500 Rs 1500
A: C.P.= Rs 13,250
S.P.= Rs 15,800 
B: S.P.= Rs 30,000
C.P.= Rs 24,075 
C:C.P.= Rs 8900
S.P.= Rs 12,450 
D:C.P.= Rs 12,450
S.P.= Rs 14700 
Q2: WORK OUT THE PERCENTAGE PROFIT ON THESE SALES.
C.P =Rs 5000
Profit =Rs2500
Profit = x 100== 50%
A: C.P.= RS 6000
Profit= RS1200 
B:C.P= RS4500
Profit= RS1500 
C: S.P.= RS850
Profit= RS90 
D: C.P.= RS565
Profit= RS50 
P:113
PROFIT & LOSS
 Work out Steve’s loss on each of these sales.
C.P. = RS 3600… RS 3600
S.P.=RS 1950 – Rs H50
Rs 1650
Loss = Rs 1650
a. C.P. = Rs 4700
S.P. = Rs 3850 
b. S.P. = Rs 7225
C.P. = Rs 10000 
c. C.P. = Rs 16,5oo
S.P. = Rs 14,750 
4Work out (i) the loss; (ii) the percentage loss on these sales.
C.P= Rs 1000 …..Rs 1000
S.P.= Rs 800 – Rs 800
Loss = Rs 200
% Loss = % x 100
a)C.P= R5 2500
S.P= RS 2000 
b) S.P= RS 3250
C.P= RS 4500 
c) C.P= R5 7250
S.P= RS 6000 
P:114
PROFIT & LOSS
Q1: Find the profit or loss on each of these sales.
C.P. = Rs 240; S.P. =Rs 80
S.P. is less than C.P.
Loss = Rs 60
a) C.P. = Rs 500 
b) C.P. = Rs 1764 
c) C.P. = Rs 2730 
Q2: Find the selling price.
a)C.P. = Rs 429 
b)C.P. = Rs 2500 
c)C.P. = Rs I770 
Q 3: Find the cost price.
a) S.P. = Rs 756 
b) S.P. = Rs 2460 
c) S.P. = Rs I265 
Q 4: Work out (i) the profit; (ii) the percentage profit on these sales.
C.P. = Rs 60 Rs 200
S.P. = Rs 200 Rs 60
Profit = Rs 40
Profit % !L6e x mo
= % or 25%
a) C.P. = Rs 900 
b) C.P. = Rs 3200 
c) C.P. = Rs 480 
Q5: Find the profit or loss as a percentage of the cost price.
Sara buys a TV for Rs 8000. She later sells it for Rs 6500.
C.P = RS 8000
S.P. = Rs 6500
Loss = Rs 1500 %
= 1500%
Loss % =
Loss % = 18.75%
a) Sid bought a motorcycle for Rs 7000. After three accidents, he sold it for Rs 4500. 
b) The Jamal’s bought a refrigerator for Rs 20,000. Five years later they sold it for Rs 27500. 
c) At Wholesale Cloth Centre, Alam buys cotton cloth at Rs 50 per metre. He sells it to his customers at Rs 75 per metre. 
d) Rehan bought a cycle for Rs 2600. After using it for a year, he sold it for Rs 2200. 
e) Adil buys apples for his stall at Rs 40 per dozen. He sells them at Rs 56 per dozen. 
P:115 SIMPLE INTEREST
P:116
SIMPLE INTEREST
1Work out the amount in these bank accounts after one year.
Principal = Rs 2000
Interest = 5%
Amount = P + I
=Rs 2000 + E6 X Rs 2000
= Rs 2000 + Rs 100
= Rs 2100
a) Principal = Rs 3000
interest = 20% 
b)Principal = Rs 1000
Interest = 7.5% 
c)Principal = Rs 600
interest = 15% 
2Work out the amount owed to the bank after one year.
Principal = Rs 4500
Interest, = 9%
Amount = P + I
= Rs 4500 + 9/100 x Rs 4500
= Rs 4500 + Rs 405
= R5 H905
a) Principal = Rs 12,000
Interest = 6% 
b) Principal = Rs 20,000
Interest = 12.5% 
c)Principal = Rs 18,500
Interest = 8% 
P:117
SIMPLE INTEREST
3Calculate the interest where:
Principal (P) = Rs 600
Rate (R) = 9%
Time (T) = 4 years
Interest = Rs
=Rs 216
a)P=Rs 106
R=3% T=3years 
b)P=Rs 500
R=8% T= 5 years 
P:118
c)Rs 250
P=4% T=5 years 
d)Rs 2000
P=7.5% T=3 years 
e)Rs 12,000
P=6% T=4 years 
f) Rs 28,750
P=5% T= 5 1/2 years 
Rs 25,000
P=12% T=6 years 
g) Rs 6,600
R=12% T=2 years 
) Rs 2400
P=15% T=4 years 
4Work out these problems.
(a) Mick Moon deposits Rs 4000 in a bank account for his daughter Meg. How much money will be in the account after 5 years if the bank pays Mick a \2% % rate of interest? 

(b) Mrs Siddiqi deposits Rs 3000 in a fixed deposit account. She agrees not to withdraw any money before 3 years are over. In return, the bank will pay her a 16% rate of interest. How much interest will Mrs Siddiqi earn during this period? How much money will be in her account at the end of 3 years? 

P:119
REVIEW
1 Round off to 2 decimal places.
 18.494 b. 143.0°19 c. 475.199
2Change into decimals, rounding off to 3 decimal places.
a.  b.  c. 
3Write as percentages (to 2 decimal places, if necessary)
a)  b) 2  c) 0.51 
d)  e) 4  f) 1.2 
g)  h) 8  i) 1.032 
4 Write as fractions in their lowest terms:
a. 28%  b. 72%  c. 600% 
5Change into decimals.
a. 48%  b. 2.5%  c. 142% 
6Calculate:
a. 40% of Rs 480  b. 75% of 6001  c. 5% of 7000 km 
7Work out the price of these items on special offer.
a. Softy Soap: 10% off at Rs 5.50  b. Transistor radio: 20% off at Rs 260  c. School bog: 15% off at Rs 125 
8Calculate the interest payable where.
a. P=R5300
R = 4% T=6 years 
b. P=Rs7500
R = 11 % T= 9 months ( years) 
c. P = RS 2500
R=7 T=3 years 
d. P = Rs 3600
R = 14% T=2 years 
9 Solve these problems.
a. Sue Spacewalker borrows Rs 7550 to buy a spacemoped. The bank asks her to pay the money back over 3 years at 15% rate of interest. Find (i) the interest she must pay, and (ii) the total amount of money she must repay at the end of 3 years. 
b. Which of these bank customers will earn the largest sum ot interest every year?
(i) Usman: P = Rs 6000, R = 7% T = 4 years (ii) Zeba: P = Rs4500, R = 8% T= I0 years (iii) Rashid: P = Rs 7250, R = 6% T = 2 years 
P:120
REMEMBERING ANGLES
Sid remembers that there are five different types of angles, but he can’t remember their names. Help him complete the crossword by naming each angle shown in the clues.
Clues Across
Clues Down (pic)
Q2 Draw and label an angle that matches the name.
∠PQR (obtuse angle)
a∠ABC (right angle)

b∠STU (acute angle)

c∠EFG (reflex angle)

3 Copy and fill in the blanks.
a)There are ———————degrees in a complete turn.
b)An acute angle is any angle greater than 0° but less than——————
c)The halfcircle protractor has a total of ——————marked on it.
d)An angle which is greater than a right angle but less than I80° is called an—————— angle.
 e) 3/4 circle =—————— degrees.
f)A reflex angle is any angle which is greater than ——————but less than——————
P:121
REMEMBERING ANGLES
Q4: Use your protractor to measure these angles. Think carefully which row of markings on the protractor you should use.
Q5: Draw these angles in your notebook, using a protractor.
a.40°

b. 90°  c. 55° 
d. 60°

e. 115°  f. 145° 
Q6: Draw these angles adding an interior or exterior point in any suitable place.
∠XYZ = 80° exterior point /A
a)∠PQR = 25°; interior point C
 b) ∠STU = 115°; exterior point J
Q7: Look at this angle. Then write words in the blanks.
 a) The angle is made up of two line segments, ————————and——————
b)They meet at a common point ——————which is called the ——————
 c) Point R is in the——————
d)Point X is in the——————
Q122: USING THE PROTECTOR REFLEX ANGLES
1 Calculate these reflex angles, using your protractor
2 Draw these reflex angles, using your protractor.
Reflex ∠XYZ = 305°
— (360° 305° = 55°) = 305
a) Reflex ∠PQR = 320° 
b) Reflex ∠WXY = 290° 
c) Reflex ∠CDE = 335° 
P:123
USING THE PROTRACTOR: COMPASS & BEARINGS
P:124
MORE ABOUT CIRCLES
P:125
MORE ABOUT CIRCLES
Q1: Measure the diameter of each circle
Diameter = 3.2 cm



Q2: Now calculate the radius of each circle in Exercise1.
Diameter = 3.2 cm
Radius = cm = 1.6 cm
Q3: Complete these.
 a) If a circle has a diameter of 9.64 cm, it’s radius will be——————cm.
 b) If the radius of a circle equals 5.845 m, its diameter is——————m.
 c) A quarter circle is also known as a ——————
d)The diameter of a circle always passes through the—————— of the circle and joins together 2 points on its——————
Q4: Using a small plate or the bottom of a tumbler, draw a circle in your notebook.
Mark a point on its circumference and label it A.
Draw as many chords as possible, using point A as one of the end points. Make one of your chords pass through the centre of your circle. Label your chords (AB, AC, AD, etc.) and measure each of them. Which is the longest of the chords you have drawn?
P:126
MAKING CIRCLES: USING COMPASSES
P:127
MAKING CIRCLES: USING COMPASSES
Q 1. Using your ruler and compasses, draw circles with these radii (radii say ‘raydeeeye’is the plural form of radius).
a. 4 cm  b. 7 cm  c. 3.3 cm 


d. 5 cm  e. 4.5 cm  f. 4.1 cm 

Q 2. Without using your ruler, state the diameter of each of the circles you have drawn in Exercise A.
Circle a: radius = 4 cm
diameter = 8 cm
Q3: Look at this circle.
 Name all the radii of the circle.
 Measure the lengths of the diameters.
 Name all the arcs marked on the circumference.
P:128
MORE ABOUT TRIANGLES
Q1. Measure the sides of this triangle with your ruler. Record your findings in the table. Then, with your protractor, measure the angles of the triangle and record your findings.
Length of side (cm)  Size of angle (°) 
AB  ∠CAB 
BC  ∠ABC 
AC  ∠BCA 
What type of triangle is this? What do you observe about its angles?
Q 2. Now measure and record the sides and angles of this triangle.
Length of side (cm)  (Size of angle (°) 
PQ  ∠RPQ 
QR  ∠PQR 
PR  ∠QRP 
What type of triangle is shown? What do you notice about its angles?
Q3: Measure and record the sides and angles of this triangle.
Length of Size of side (cm) angle (°)
Length of side (cm)  (Size of angle (°) 
ED  ∠FED 
DF  ∠EDF 
EF  ∠DFE 
What type of triangle is this?
What is special about its angles?
Q4 Measure each triangle (sides and angles), then name the triangle family to which it belongs. Present your findings in the form of a table.
Sides  Angles  
WY  5cm  ∠WXY  72 
YX  5cm  ∠XWY  72 
XW  3cm  ∠WYX  36 
Δ Family = isosceles



Q 5. Take a blank sheet of paper or cardboard. Draw a triangle on it, and mark each angle with dots, thus.
Cut out your triangle, then cut the three angles from the triangle thus:
Arrange the three angles so as to make a straight line:
You have just shown how the three angles of a triangle make a straight angle or 180° !
Q6: Without using your protractor, calculate the size ofthe angles marked with letters.



Q7: Here is a page from Sprog Spacewalker’s geometry notebook. He has measured the angles of some As, but not very carefully. Make a list of the triangles whose angles have been measured incorrectly.
Triangles
a.∠ABC = 90°
∠BAC = 70° ∠ACB = 20° 
b. ∠CDE 25°
∠CED 115° ∠DEC 43° 
c.∠POR = 110°
∠PRO = 40° ∠RPO = 40° 
d. ∠JLK 85°
∠JKL 45° ∠KJL40° 
e.∠STU = 35°
∠SUT = 47° ∠TSU =100° 
f. ∠XYZ 35°
∠XZY 110° ∠ZXY40° 
P:131
CONSTRUCTING TRIANGLES
We can construct a triangle if we know:
(a) the length of all 3 sides
or (b) the length of 2 sides plus the size ofthe angle between them
or (c) the size of 2 angles plus the length of the sides between them
To construct a triangle when all 3 sides are given:
for example, AABC where AB = 5 cm, AC = 4 cm and CB = 3gcm.
Step 1
With ruler and pencil, draw line AB (5 cm).
Step 2
Keeping the pivot of your compasses on the 0 cm mark, stretch out the pencil arm till the pencil point touches the 4 cm mark. Now point the pivot on point A of line AB. Mark an arc with your compass.
Step 3
Readjust your Compasses so that the arms are 3 cm apart (use your ruler) Place the pivot on point B and draw a second arc:
Step 4
The point where the two arcs cross marks the third vertex, C, of your triangle. Join C to A and then to B using your ruler.
You have constructed Δ ABC!
Q1. Construct these triangles, using your ruler and compass.
a. Δ ABC: AB = 6 cm, AC =3cm and CB =4cm 
b. Δ POR: PQ = 7 cm, QR =5cm and PR = 4cm 
c. Δ RST: RS = fi cm, ST =7.5 cm and RT = 3 cm 
P:132
CONSTRUCTING TRIANGLES
Q2: Tick the sets of measurements which cannot be made into triangles.
 a) 3cm, 2cm, 4cm
 b) 8cm, 4cm, 1cm
 c) 4cm, 11cm, 8cm
P:133
CONSTRUCTING TRIANGLES
Q 3. Construct these triangles.
a. Δ XYZ where XY = 6 cm, XZ = 4 cm and ∠YXZ = 50° 
b. Δ EFG where EF = 5.5 cm, EG = 4.5 cm and ∠GEF=65° 
c. Δ RST where RS = 4.8 cm, RT = 6.5 cm and ∠TRS = 35°

4Now construct these triangles.
a)∠PQR where ∠QPR = 30°
∠PQR = 60° and side QP = 4cm


b)Δ ABC where side AB = 5cm,
∠BAC = 45° and ∠ABC = 25°


c)Δ JKL where ∠KJL = 65°,
∠JKL = 40°and side JK = l4.6cm 

d)Δ TUV where ∠UTV= 80°
∠TUV= 25° and side TU = 8cm 

Q5: Construct the triangles whose measurements are given in this table
AB  BC  ∠ABC 
5 cm  2.5 cm  75° 
5.6 cm  3 cm  115° 
4.8 cm  5,2 cm  35° 
Q6: Now construct triangles with these measurements.
AB  ∠CAB  ∠CBA 
a)4.5 cm  45°  75° 
b)5.6 cm  25°  55° 
c)6.3 cm  90°  35° 
Q7: Choosing your own measurements, construct and then label.
a) any equilateral triangle  b) any isosceles triangle  c) any scalene triangle 
P:134
REMEMBERING QUADRILATERALS
Q2: Name each of these quadrilaterals. Then measures all 4 angles. What is the sum of the angles?



P:135
PERPENDICULAR AND PARALLEL LINES
Q 1. In the following figure some of the coloured lines are perpendicular to line PQ. Write their names in your notebook. (pic)
Q 2. Study this figure, then complete the sentences. (pic)
 AB is perpendicular to——————
 AE is perpendicular to——————
 DE is perpendicular to——————
 XC is perpendicular to——————
3Look carefully at line XY. Which of the lines are parallel to the coloured line? Write their names in your notebook.
P:136
CONSTRUCTING PERPENDICULAR AND PARALLEL LINES
Q1. Use your protractor to draw these perpendicular lines.
a. PQ perpendicular to QR  b. EF perpendicular to FG

 Using your set square, draw these perpendicular lines.
a. XY perpendicular to the midpoint of CD  b. QR perpendicular to the midpoint of VW 
P:137
MORE ABOUT PARALLEL LINES
Q1: Using your ruler and protractor (or set square), draw these sets of parallel lines. Don’t forget to mark arrows on them.
–Line AB parallel to line CD
I cm apart
AB
cm
C D
a)Line JK parallel Ho line LNI, 3.5 cm apart  b)Line CD parallel to line EF, 4.2 cm apart 
2Now draw these, following the instructions carefully.
Parallel lines PQ and RS, each 3.8 cm long, and I.7 cm apart
P Q
R S
a)Parallel lines AB and CD, each 4.1 cm long, and 3.4 cm apart  b)Parallel lines OP and QR, each 5.6 cm long, and 5 1.7 cm apart

Q:a. Draw three concentric circles of radii I.7 cm, 2.6 cm and 4.5 cm.  Q:b. Draw two concentric circles of radii 1.7 cm, 2.6 cm and 4.5 cm.

P:138
Q1: Work out the average of these sets.
12, 6, 21, 13 Total = 52
Addenda = 4
Average = I3
a)14, 27, 5, 19, 10  b)Rs36, Rs 14, Rs 17, Rs 42, Rs 101

c)8 cm, 25 cm, I5 cm, 32 cm, 10 cm

2Copg and complete these.
a)The average of f, 2, 3, 4 and 5 is——————
b)The average of I0, I00 and I,00 is——————
c)To find the average of 18, 14, 5, and 7, we divide by 4
P: 139
AVERAGE
Q3: Below are the weights recorded for four I0gearold children test. Work out the average weight of the children
NAME  WEIGHT 
Mona  34.0kg 
Kashif  36.2kg 
Aslam  35.8kg 
Insia  40.0kg 
Q4: Solve these word problems, making complete statements.
a. Sid bugs a kilogram of spacefingers on 6 different dags. The prices he pages are R5 8, Rs 10, Rs 7.50, Rs 12, Rs 11.75 and Rs 9.25. Find the average price.  
b. Over a 4month period, Moiz’s monthly income was Rs 5000, Rs 4000, Rs 2500 and Rs 1000. What was his average income for that period?  
b. Study this table: it shows the number of girls and bogs studying at Ahsan Primary School:
Find (i) the average number of girls in each class, (ii) the average number of bogs in each class, (iii) the total number of children in the school and (iv) the average number of children in each class. 
P:140
AVERAGES AND GRAPHS
Q1: This column graph shows oneweek attendance for Class 5 at Ahsan Primary School.
Number of children
(GRAPH)
Mon Tue Wed Thu Fri
Day
Study the graph and then work out:
 The total attendance for each day of the week.
 On which days the attendance was below the average.
 This column graph shows the Marks by 6 children in a spelling test.
Study the graph, then work out the average marks scored by the 6 children. Which children scored above the average? This graph shows the price of 4 story books
(graph)
The dotted line shows the average price of the 4 books.
You can see that average is a number roughly halfway between the smallest number and the largest attendance.
(graph)
Q3: Here is the top part of a column graph showing 4 children’s results in a test.
Look at the graph and estimate what the average marks will be. Than work out the average exactly.
P:141
AVERGES, GRAPHS AND SPEED
Q 4: Study the graphs, then work out the average speed for each journey.
Distance (km)
Average speed = 140 km + 2 hours
= 20 km/hr
 Distance (km)
 Distance(km)
 Distance (km)
Q 5. Work out these average speeds.
90 km covered in 5 hours
Average speed= = 45 kmph
a) 105km covered in 5 hours

a) 990km covered in 3 hours

a) 445km covered in 8 hours

P:142
DISTANCE, SPEED & TIME
Q1: Find the time taken for each journey.
D = 100 km, S = 20 kmph,
T= ——————
S = 55 kmph, D = IIOkm,
T: ——————
D = SAO km, S = 60 kmph,
T:——————
Q2: Solve the following.
a)A motorcycle averages 50 kmph. How long does it take to travel 25 km? 
b)How long will a bus travelling at an average speed of 45 kmph take to cover a distance of 225 km? 
P:143
DISTANCE, SPEED AND TIME
Q3: Work out the distance travelled in each of these journeys.
a)S=30 kmph, T=5hrs,D=? 
b)S=55 kmph, T=4hrs,D=? 
c)T= 121 hrs, S= 50 kmph, D=? 
Q4: Work out the average speed of these journeys.
a)T=5 hrs, D=360 km S=? 
b)T= 16 hrs, D= 1200 km, S=? 
c)T=7 hrs, D=497 km, S=? 
Q5: Calculate values in the blanks.
a)S=40 kmph, T=D=480 km? 
b)T=5 hrs, D=72O km, S=? 
c)S=?,T = 12 hrs, D=732km 
d)D= 1350 km, s=5o kmph, T=? 
e)s=6o kmph, D=?,T=2 1/2 hrs 
f)D=?, T=4 1/4 hrs, s=70 kmph 
Q 6Copy and complete the table:
Distance  Time  Speed  
a  240 km  6 hr  
b  hr  40 kmph  
c  450 km  90 kmph  
d  1500 km 
Q7: Solve, making complete statements
a) If a cyclist travels Q0 km in 5 hours, what is her average speed? 
b) Sprog Spacewalker takes part in a marathon race I8 km long. If his average speed is 6 kmph, how long does he take to complete the race? 
c)How far will a gasfilled balloon travel in 8 hours if its average speed is 10%kmph? 
d)How long will it take Sue Spacewalker to run 12 km at 8 kmph? If Selvi takes 2 hours to run the same distance, what is her average speed? 
P:144
THINKING ABOUT TEMPERATURE
P:145
ALL ABOUT TEMPERATURE
Convert these temperatures into the other Scale (answer to 2 decimal places where necessary).
a.122°F  b. 45°C  c.77°F 


d. 40°C  e.113°F  f. 35°C 

P: 146 PART FOUR
ALGEBRA
 Look at the objects in each plate and write the initial of each object in the blank.
1apple  1 brinjal  1cauliflower 
Q 2. Now look at these boxes. Write the initial of each object.
 (2 lollipops) (3 sweets)
(2 chocolates) (4 burgers)
B: Now, write all these using different symbols of your choice. For example, ’lollipop’ can be written as w, ‘sweet’ as x and so on.
C: If x stands for one rupee, write the amount of money. each box contains, using x:
(Rupees seven) (Rupees five) (Ru5ees ten)
D: Put all the money together, and write your answer using x:
P:147
ALGEBRAIC EXPRESSIONS
Q1: Now, put all the items given in Exercise 2A, on the previous page, in one tray.
Write the contents of the tray, using the English alphabets.
Q 2. Now, write each group as an algebraic expression, using first the initial letter and then the last letter of each word.
 2 apples + 3 bananas + I mango + I watermelon
 2 (pairs of) scissors, two knives, 3 forks and I teapot
P:148
Q1: Now, write the following sets at objects as a algebric expressions using different alphabets of your choice.
 5 books, 3 notebooks and I atlas.
 3 ships, 1 boat and 2 kayaks.
 4 ink pens, 3 ballpoint pens, 12 pencils and 1 felltip pen.
Q2 Now add each set of the following expressions.
a). 2x+3y+lIz; 5x+2y+4z  b)2a+3b+4c+ ld; 5a+lIb+2c  c)p+2q+3r; 2q+3r; lIp+2q 
Q3 Take away
a) 2x+3yfrOm 5x+8y  b). 3p+2q+ rfr0m5p+2q+  c) 2a+1b+1c from 2a +1b+1c+1d 
P:149
SIMPLE MULTIPLICATION
Write in short.
a) x+x+x  b) y+y+y  c) f+f+f+f+f+f 
Q2: Now, find the perimeter of each of these figures.
a. Triangle with side x cm  b. Square with side y cm  c. Hexagon with side z cm 
Q 3: Write as an addition:
a. 3g 
b. 5q 
c. 82 
Q 4. Now, write the sum in each case.
3a+2b+c; 3a+2b+c
= 2 (3a+ 2b+c)
= 6a+4b+2c
a. 4x + 5y; 4x + 5y  b. 2p+iq+3r;2p+lq+3r;
2p+1q+3r 
P:150
Q1: Now find the area each of these rectangles
a. Rectangle with length of p cm, and breadth q cm

b. Square with side s cm  c. Rectangle with length f cm and breadth g cm. 
Q2: Expand and write.
5p = 5 x p (or F 5.p)
=p+p+p+p+p
a. 6m 
b. 9z 
c. pq cm2 
P:151
REVIEW
Exercise
Write out these problems in algebraic terms and work them out.
Q1: If one pineapple costs Rs 10 find the cost of:
 5 pineapples
 3 pineapples
 x pineapples
P:152
Q2:Two bags contain 3 lollipops and li sweets each. Write the sum as an algebraic expression. 
Q3: One cage has 2 parrots and 3 sparrows, and the other has 1 parrot, crow and 1 Sparrow. Birds from these two cages are put together in a larger cage. Write the sum as an algebraic expression. 
Q4: There were 4 sweets in a box; two were eaten by Adil. Write this as an algebraic term. 
Q5: There were 4 cakes and 4 sandwiches on a plate. Rabia ate one of each. Write this as an algebraic expression. 
Q6: Work these out:
 a) p+p+p+p+p+p =——————
 4k =——————
 3d – 2d =——————
 7x + 3x + 2x =——————
 80 – 2c =——————
Q7:Add:
a. (3a + Lib) + (Sb + lm + Zc) 
b (ZX + 3y) + (5y + Zy) 
Q8:Subtract:
a. (3x + 4y) – (2y + 1x)  b. (9p +8r) – (4r + 3p) 
Q9: Multiply
a.a x b  b. p x r  c. y x z

P:153
REVIEW OF THE YEAR
Q1: Place in Pakistani periods and write the number name
a. 5672318  b. 74028301  c. 6009053  d. 90755620 
Q2: Change into International periods and write the International number name.
a. 42,03,721  b. 3,16,72,049  c. 50,47,834  d. 8,02,46,1 I8 
Q3: Write the value of the coloured digit.
a. 1,627,148  b. 7,24,16,831  c. 22, 14,690  d. 84, 1172,063 
Q4: For each number, write (i) the predecessor and (ii) the successor.
a. 2,348,000  b. 6, 10,00,000  c. 14, 17,600  d. 84,000,000 
Q5: Write vertically and complete.
a. 1,40,732 + 8,64,395 +28  b. 7,640,117 – 4,584,623 
c. 8,96,23, 141+ 3292 + 764  d. 1468.29 – 979.54 
Q6: Round oft each number (i) to the nearest I0 and; (ii) to the nearest I00.
 643 b. 82,555 c. 1,29,387
Q7: Round off each number (i) to decimal place and (ii) to 2 decimal places.
a. 2.461  b. 84.099  c. 6.191  d. 100.335 
Q8: Write vertically and complete.
a. 1629×312  b. 8.I97x36  c. 8074×593  d. 10.895×75 
Q9: Solve, Writing your answer to two decimal places where necessary.
a. 97,920 ÷ 384  b. 69,482 ÷ 77 
c. 46,839 ÷ 47  d. 108,964 ÷ 98 
Q10: Prepare bills for these 33 customers.
a. Hungry Crocodile: 20 kg of rice at Rs 3.75/kg; 16%kg of fish at Rs 24/kg; 51 of cooking oil at Rs 850/I; I0 packets of biscuits at Rs I I.35/packet. 
b. Adil: 12 kg of wheat flour at Rs 4. 1 5/kg; 5.5 kg of sugar at Rs 6.25/kg; 2.51 of cream at Rs 8.60/1; 25 chocolate bars at Rs 9.85 each. 
P:154
Q11. Simplify.
a. 6X5+184  b. 11+18+3×21 
c. 9 x21+7+145  d. 8.1×0.160.6114 
 Simplify.
a. (0.38 x 4.62) + 10.5 
b. 4.61 + {2. + (3.82 – 1.75)} 
c 3+{1+(x)} 
d. [{84 (21 + 3)} + 12] + 74 
e. {31 – 16.3 + 8.6)}x 1000 
 Work out the areas.



 Work out the volume of these cuboids (in cm3 or m3):
a. l=4.2cm,b=5cm,h=1.5cm  b. I=I0m,b=3.5m,h=4.3m 
c. l=6.9cm,b=7.5cm,h=2.2cm  d. any 5digit number divisible by 4. 
Q15: Write down:
a. any 5digit number divisible by 4. 
b. any 6digit number divisible by 8. 
c. any numbers from this list which are divisible by 15:
400, 7020, 1 1,620, 15,055. 
Q16: Write the numbers whose prime factors are given here, using brackets to help you.
a. 2 X 2 X 2 X 3  b. 2 x 2 x 2 x 5 x 5  c. 2x3x5xV7x7x11 
Q17: Using prime factorization, find the HCF of;
a. 56 and 140  b. 63 and 511 
Q18:Find the HCF, using the long division method.
a. 1026; 247 
b.21A6; H84 
c. 368; 1173 
d. I377; 836 
Q19: Find the LCM of each set.
a. 12, 15, 21 
b. 24, 32, 26 
c. 10, 12, 18 
d. 27, 30, 15 
P155
Q20: Fill in the blanks.
 If the product of 2 numbers is 270 and their HCF is 3, their LCM is——————
 For a pair of numbers, the HCF is 4 and the LCM is 252.
If one of the numbers is 28, the other number is——————
 Solve, giving each answer in its lowest terms
a) x  b)5 x6 
c) 3 ÷2  d) x x 
e)9 ÷ 1  f) ÷ 
Q22: Multiply each number (i) by 10 (ii) by 100 and (iii) by 1000: ,
a. 4.8 
b. 1 .47 
c. 6.87 
d. 4.535 
Q23: Solve.
a. 0.6 X 0.4  b. 3.0 x 4.5 
c. 0.63 + 0.21  d. 1.752 + 0.219 
e. 2.81X 3.6  f. 0.12 + 0.006 
Q24: Write denominators in place of its, then complete the sums.
a. 2.34X4.61 = 
b. 3.604 x 7.3 = 
Q25: Change these into decimals, giving your answer (i) to 2 decimal places and (ii) to 3 decimal places.
a) 
b) 
c) 
Q26: Write as percentages, using the % symbol.
a)  b)  c) 3 
Q27: Write as percentages (to 2 decimal places where necessary).
a) 1  b) 4  c) 3 
Q28: Change into fractions or mixed numbers, reducing where you
can,
a. 80%  b.224%  c. 16% 
d. 75%  e. 155%  f. 44% 
Q29:Change into decimals.
a. 45%  b. 672%  c. l2% 
d. 55%  e. 752%  f. 34% 
Q30 Change into percentages.
a. 0.018  b. 1.64  c. 0.143 
P:156
Calculate.
a. 20% of Rs 40.75

b. The percentage profit where C.P. = Rs 800 and S.P. = RS Q50

c. 70% of 5600 l of water

d. The percentage profit where S.P. = Rs 5000 and C.P. = Rs 3800 (to 3 decimal places)

Q32: Calculate the interest where:
a. P = Rs 11200, R = 5%,T = 3 years 

b. P = Rs 5000, R = 6%,T = 4 years 

C. P = Rs85O, R = 9%,T = 2 years 

Q33: Construct these, using the appropriate instrument.
a. Reflex LABC = 240°  
b. A circle of diameter 7.8 cm  
c. A circle of radius 6.0 cm with arc PQR marked on it. 
Q34: Complete these statements.
 If each side of Δ ABC is 4.5 cm, ∠ABC = ——————degrees,
 If two angles of an isosceles Δ PQR are 50° each, the third angle=——————.
 If a Δ has angles of 30°, 45°, and 105°, it is a—————— Δ.
 if a coral reef is due west of the golden cockroach its bearing=——————
 Construct triangles to match these dimensions.
AB  BC  AC  ∠BAC  ∠ABC  
a  4cm  5cm  3.5  –  – 
b  6cm  4cm  55^{o}  –  
c  5cm  7cm  –  –  80^{ o} 
d  7.5cm  –  –  35^{ o}  45^{ o} 
 Construct:
a. Parallel lines AB and CD, each 3.2 cm long and 2.0 cm apart.

b. Two concentric circles, one of radius 3.5 cm and the other of radius AA cm.

c. Line PQ perpendicular to the end point of line ST.

 Solve, making complete statements.
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