solved exercisemathematics 3 - javed publishers
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Text Research & Development by:
The Society for Lions Educational Research
7/4-Block E-3 Gulberg III Lahore.
Solved Exercise
MATHEMATICS VEE LL
3by: Tariq Ishaq
4 15Measurement
5 16Multiplication Facts
Through 10x10
6 23Division Facts Through 10x10
7 30Fractions
8 34Primeter and Area
1 3Numbers up to 999
2 6Addition within 999
3 10Subtraction within 999
2
Use the chart to represent the numbers:
5 thousands 7 hundreds 2 tens 8 onesTh H T O
9 thousands 2 hundreds 5 ones
8 hundreds 6 tens 3 ones
2000 + 600 + 30 + 7
500 + 8
6000 + 60 + 4
400 + 70 + 5
5 7 2 8
9 2 0 5
8 6 3
2 6 3 7
5 0 8
6 0 6 4
4 7 5
Write the place value of the digit 4:
1 2 3 41047 3406 4671 9674
Write the number:
3 thousands 6 hundreds 3 ones1
2 thousands 1 hundred 5 tens2
7 thousands 2 hundreds, 223
4000 + 80 + 1 = 6000 + 800 + 5 =4
4000 + 80 = 700 + 20 + 4 =5
1 2000 3000
2 6100 6200
Complete the pattern:
3603
2150
7222
4081 6805
4080 724
40 400 4000 4
4000 5000 6000 7000
6300 6400 6500 6600
1
Unit
Whole Numbers up to 9999Whole Numbers up to 9999Whole Numbers up to 9999
1.1 Numbers with 4-Digits
5 62367 2360 1010 1100
3 4925 920 1759 1760
1 21654 3659 2136 759
Compare. Write > or < in :
>
<
>
<
<
>
3 1100 2200
4 4010 5020
Complete the number using the cards:
7 1 8 4 6
3300 4400 5500 6600
6030 7040 8050 9060
Th H T O Th H T O
8 1 4 6 7 1 6 8
Tick ( ) the greater number:P
3 5 2
9 5
4 7 8
6 7 9
1 0 3 5
9 8 7
3 9 2 1
4 1 8 0
1 2 3 4
Tick ( ) the smaller number:P
1 5 2 0
9 8 9
5 3 3
5 3 4
9 3 2 0
9 3 2 5
1 3 5 4
4 6 3 1
1 2 3 4
Write a greater number:
1
527
2
999
3
3055
4
7199528 1000 3056 7200
Write a smaller number:1
1000
2
555
3
9350
4
3100999 554 9349 3099
3
1.2 Comparing Numbers
Write the numbers in order from least to greatest:
Use < . Write the numbers from least to greatest:
Write the greatest number:
Write the least number:
1 2650 490 395 925 952 295
3 4785 8750 8057 6022 6220 6202
21 84 90 49 300 400 700
43 346 3146 3416 6010 6100 6001
1 2986 698 896 1700 7100 7001
1 2210 120 201 4000 4100 4010
Use the digits to make the:6 7 1
395 490 650 295 925 952
785 8057 8750 6022 6220 6202
49 84 90 300 400 700< < < <
6001 6010 6100 346 3416 3146 < << <
Use > . Write the numbers from greatest to least:
1 925 9502 9052 5029
2 300 7526 5726 6725
> > >9502 9052 5029 925
> > >7526 6725 5726 300
986 7100
120 4000
greatest number 761
least number 167
Say if you would add or subtract:
Truck A weighted 9684 kgs and Truck B weighted 9864 kgs.How much more did Truck B weight?
Subtract 9864 – 9684 = 180 kg
4
1.3 Ordering Numbers
3070 6190 5913 47255 6 7 83000 6000 6000 5000
910 1321 2400 86751 2 3 41000 1000 2000 9000
910 278 366 8895 6 7 8900 300 400 900
426 69 432 6791 2 3 4400 100 400 700
1 2 3 432 77 66 10630 80 70 110
5 6 7 81032 3131 4004 3991030 3130 4000 400
Round to the nearest 10:
Round to the nearest 100:
Round to the nearest 1000:
NumberRound to the nearest
Thousand Hundred Ten1417 1420682 10003599 36004030
1000
40004000
1400700 680
36004000 4000
Complete the table:
Round the prices to the nearest 100 or 1000:
rounded toRs. 430Rs. 1865 rounded to
rounded toRs. 125 rounded toRs. 2525
2000 400
100 3000
1 Display the number. Use the chart.
Problem Solving
Th H T O
2 thousands 4 hundreds 1 ten 8 ones.
4 thousands 8 tens 2 ones.
6 thousands 3 hundreds 7 tens.
6 hundreds 9 ones.
2 4 1 8
4 0 8 2
6 3 7 0
6 0 9
5
1.4 Rounding
2About 250 persons were on the Shaheen Airlines flight fromLahore to Karachi.What is the greatest/least number that could be on the airplane?
3On a rainy day the number of students who attended school wasabout 540.What is the least number that could have attended?
4
and write the numbers that round to 500.
Use the digits 7 2 5 4
300 / 200
500/- students
524, 472, 542, 527
Add:
+
5 1 7 6
3 7 2 1
1
+
2 5 0 7
3 8 1
2
+
6 1 1 5
5 3 4
3
+
2 0 0 7
6 9 2
4
8 8 9 7 2 8 8 8 6 6 4 9 2 6 9 9
5
+
8 5 4 6
5 3
6
+
7 2 1 1
6 0 0
7
+
8 1 0 3
1 3 0
6 4 +
3 0 0 0
3 8 1
1 6
8
8 5 9 9 7 8 1 1 8 2 9 7 3 3 9 7
721 + 617 =
+ +
3000 + 799 =
1 27 2 16 1 7
1 3 3 8
3 0 0 0 7 9 9
3 7 9 9
Add:
6
2
Unit
Addition within 9999Addition within 9999Addition within 9999
2.1 Adding without Regrouping
7
Solve. Check by using a calculator:
+ 1 9 8
1 6 4 64
1 8 4 4
+ 1 4 7
1 8 6 53
2 0 1 2
+
8 6 9
1 2 8
2
9 9 7
+
6 2 7
2 5 3
1
8 8 0
Find the missing digits:
Tick ( ) the right sum:P
Complete the pattern using Thinking Math:
Collect multiples of 10:
8410 + 1379 = 1246 + 501 =
3 4
+ +8 4 1 0 1 3 7 9
9 7 8 9
1 2 4 6 5 0 1
1 7 4 7
+
2 67 1
5 8 7
5 2 6 4
8 5 8 7 2 7 7
81 5 2+ +
8 9 3
6 32 6 5+
1 2 3 413
2 33 3
11
9
2 5 4 1 2
9
5123 + 254 = 4100 + 509 =
7663 5477 5377
1 2
i ii iii i ii iii919 4609 9519P
5377
P
4609
1 3
1 9
3 2
+2 3
1 9
4 2
+3 3
1 9+4 3
1 9+5 3
1 9+1 2 3 4 5
5 2 6 2 7 2
13 + 15 + 7 = = =
= = =
= = =
14 + 7 + 6
18 + 5 + 22
(13 + 7) + 15 20 + 15 351
2
3
(14 + 6) + 7
(18 + 22) + 5
20 + 7
40 + 5
57
45
Add:
386 + 96
9 63 8 6
4 8 2
+
= 865 + 128
8 6 51 2 8+
=
1 2
9 9 3
1 1
1 1 1 1 1 1 1
1
2.2 Adding with Regrouping Twice
Add:
Use the table to fill the :
979 + 38
9 7 93 8+
= 1796 + 134
+
=
1 3 41 9 7 93 4
1 0 1 7 2 1 1 3
793 + 654 + 82
7 9 3
+
=
6 5 48 2
5
1 5 2 9
Kind of Trees
MangoApple
Orange
Cherry
Number
675
246
188
26
=The total of mango trees and orange trees is1
675 + 188 863
=The total of apple trees and cherry trees is2
246 + 26 272
=The total of all the trees is3
675 + 246 + 188 + 26 1135
Which is greater, the number of themango trees or the orange trees?
4
Mango trees
Find the missing digit:
7 8 2 1 6 5
4 8 8 72 6
5 1
7 8 6 9 7 3 1 4 2 6 2 2 3 1
++++
1 2 3 425
2 5
2
4
5 4
5
65
1 1 111
3 1 2 51 7 6 9+
6 5 4 12 0 9 4+
6 7 8 69 0 4+
6 7 6 82 5 7 4+
1 2 3 4
4 8 9 4 8 6 3 5 7 6 9 0 9 3 4 2
1111111
3 8 5 13 2 5 0+
3 1 8 51 0 9 9+
3 0 7 68 5 4+
2 3 9 08 4 7+
5 6 7 8
7 1 0 1 4 2 8 4 3 9 3 0 3 2 3 7
1 1 1 1 11 11
1 1 1 1
2
8
2.3 Adding with Regrouping
1 Complete the table. Use a calculator:
Input Output
25
Input
16
345 684
765 1346
Rule: Add 253 Rule: Add 455
Output
278
598
1018
471
1139
1801
3 A jam factory delivered 1760 cans to the Shop andSave stores, and 485 cans to the Highway Stores.
How many cans were delivered?
4 A nursery planted 595 yellow flowers and 2475 red flowers.How many flowers were planted in all?
2 Last month Ali had 1350 coins. This monthhe has 750 coins. How many total coins Alihas?
1350 + 750 = 2100 coins
1760 + 485 = 2245
2475 + 595 = 3070
+
3 6 0 38 8 71 3 7 +
1 5 7 8
3 6 59 4 6
+ 8 88 9 3
1 6 3 0
+ 1 6 3
2 4 8 05 0 5
9 10 11 12
4 6 2 7 2 8 8 9 2 6 1 1 3 1 4 8
1 1 1 1 1 1 1 2 1 1 1
Tick (P) the correct sum:
=
7444 7654
7486 + 168 7454 7554
+
1 i ii
iii iv
=6705 + 369
7014 7074
7174 7164
+
2i ii
iii iv
7 4 8 6
1 6 8
7 6 5 4
P
6 7 0 5
3 6 9
7 0 7 4
P
1 1
1 1
9
5 The number of the students in boys school is 1725.and the number of the students in girls school is 1275. How many students are in both the schools?
1725 + 1275 = 3000
Subtract. Check by adding:
–
6 8 3
5 1 –
9 5 5
2 5 0 –
6 7 0 8
1 3 0 0–
3 5 9 0
4 6 06 3 2 7 0 5 3 1 3 0 5 4 0 8
1 2 3 4
–
1 5 8 7
3 4 1–
8 6 6 6
4 5 2–
6 5 3 5
3 3 2 4–
7 6 6 8
3 5 47 3 1 4 3 2 1 1 8 2 1 4 1 2 4 6
5 6 7 8
Use the same method:
Word Problem.
The price of a new table lamp is Rs. 1650.Sara has saved Rs. 350.How many more Rs. does Sara need to buy thetable lamp?
30
400
6000
50
6000
600
1650 – 350 = 1300
10
3
UnitSubtraction within 9999Subtraction within 9999Subtraction within 9999
3.1 Subtraction without Regrouping
Subtract. Check by adding:
Subtract:
Complete the table.
Add : 45 Subtract : 55 Subtract
Add600
565
1382
973
425 370 645 675 48
632 153 26
271 828
1530
610
1427
1018
577
216
1475
627
127
74 754
– 3 6 7
1 6 5 5
–
4 7 8
3 6 9
1
–
7 8 2
3 5 8
2 3
– 1 6 9
7 4 5 34
1 0 9 4 2 4 1 2 8 8 7 2 8 4
6 18 7 12 5 14 15 3 14 13
– 7 6 8
5 3 2 15
– 3 9 2
1 7 8 56
– 8 6 9
6 5 3 77
–
8 2 5 1
2 5 7 6
8
4 5 5 3 1 3 9 3 5 6 6 8 5 6 7 5
5 14 12 17 7 11 14 11
–
8 4 3
5 7 6
843 – 576 =
1
2 6 7
–
1 3 4
7 7
134 – 77 =
2
5 7
7 13 13 0 12 14
–
8 8 8
1 9 9
888 – 199 =
3
6 8 9
–
7 7 6
4 8 8
776 – 488 =
4
2 8 8
7 17 18 6 16 16
–6 6 7
2 2 2
667 – 222 =
5
4 4 5 431 – 178 =
–4 3 1
1 7 8
6
2 5 3
3 12 11
18 61111124
11
3.2 Subtracting with Regrouping
Amount in Sara’s account
She with draws
Amount left
=
=
=
=
Rs. 6537
Rs. 869
6537 – 869
Rs. 5668
Word Problem.
Total distance
car travelled in 2 days
Remaining distance
=
=
=
=
=
750 km
243 + 335
578 km
750 – 578
172 km
1 In a safari of 750 kilometres, a car traveled 243 kilometres the first
day. On the second day it went 335 kilometres.
How many more kilometres must the car go to finish the race ?
2 In a cricket match team A makes 342 runs and team B makes 297 runs.
How many more runs are made by team A?
3 In a bank account Sara has Rs. 6537. She with draws
Rs. 869. How many rupees are left Sara account?
Runs of team A
Runs of team B
More runs by team A
=
=
=
=
342
297
342 – 297
45 runs
Solve and check by adding:
5 2 93 1 5–
1 1 5 9 04 7 3–
2 3 6 0 93 5 7–
3
2 1 4 1 1 1 7 3 2 5 2
8 10 5 10
7 8 8 09 9 9–
4 3 6 0 01 3 2 0–
5 2 7 0 51 5 0 7–
6
1 1 9 82 2 8 06 8 8 1
6 17 17 10 105 6 9 15
12
3.3 Subtracting with Regrouping (across zeroes)
Subtract.
2 =9901 – 5635
–
=5900 – 2300
–
1
5 9 00
2 3 0 0
3 6 0 0
9 9 0 1
5 6 3 5
4 2 6 6
8 9 11
4 =8600 – 5333
–
3 =9505 – 4338
–
9 5 0 5
4 3 3 8
5 1 6 7
4 9 15
8 6 0 0
5 3 3 3
5 9 10
3 2 6 7
3 5 2 52 2 5 0–
7 5 4 0 56 7 0–
8 9 0 0 24 5 5 5–
9
1 2 7 5 4 7 3 5 4 4 4 7
4 12 4 13 10 8 9 9 12
8 9 9 15 5 9 3–
10 3 3 4 42 2 6 6–
11 9 5 5 72 2 8 2–
12
3 3 9 8 1 0 7 8 7 2 7 5
8 18 11 2 13 14 4 15
6 6 0 64 7 7–
13 8 0 7 82 4 5 6–
14 7 0 0 06 2 2 2
6 1 2 9 5 6 2 2 7 7 8
15
–
5 9 16 7 10 6 9 9 10
Problem Solving
1 The number of students in school A is1765.The number of students in school B is 1352.How many more students does school B need to accept sothat the number of students in the two schools is the same.
b The sum is 6500 and the difference is 1500.
a The sum is 5000 and the difference is 1000.
2 Choose the pairs that fit:
4000 , 1000 3000 , 20003500 , 1500
4500 , 2000 4000 , 2500 5000 , 1500
1765 - 1352 = 413
13
14
3 Complete.
Add
Su
btra
ct
4725
2467
2258
4322
3688
Add
Su
btra
ct
6542
4525
3986
2867
634
9047
6155
2892 2017 1119
10528
7392
3136
Total number of students
Number of boys
Number of girls
=
=
=
=
1025
678
1025 – 678
347 girls
Price of new dress
Hina has saved
Hina need more rupees
=
=
=
=
Rs. 1550
Rs. 450
1550 - 450
Rs. 1100
a In a school the number of boys is 678.
If the total number of students in the school is 1025.
Find the number of girls in the school.
b A school library has 672 history books and 1239 language books. If
the total number of books in the library is 3000. What is the number
of science books ?
Total number of books
Number of book history
and language
Number of science book
=
=
==
Rs. 3000
672 + 1239
1911Rs. 3000 - 1911
1089
c The price of new dress is Rs. 1550. Hina has saved Rs. 450.
How many more rupees does Hina need to buy the dress?
4 Solve the following word problems.
Fill in the table with the appropriate numbers:
m 1 3 5 7 9
cm 100 300 500 700 900
Fill in the table with the appropriate numbers:
m 1 2
cm 100 200 400 600 800
4 6 8
The window is 2m wide
1m 1m
Write the length:
1 2
3 41m
The carpet is 3m long
1m 1m 1m
The desk is 1m long
The car is 1m wide
1m
15
4
Unit
MeasurementMeasurementMeasurement
4.1 Measurement Length Using Meters
Write addition and multiplication sentences:
Use the number line to find the product:
Write a multiplication sentence:
1 x 2 = 2 2 x 2 = 4 2 x 3 = 6 2 x 4 = 8 2 x 5 = 10
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
4 3 12x = 2 5x = 3 4x = 3 3x =10 12 9
+ =
x =
+ =
x =
4 4 8+ =
2 4 8x =
8 8 16
2 8 16
6 6 12
6 2 12
2 x 5So, 5 x 2=
2 rows of 5 10 = 5 columns of 2 =
21
Find the product:
10
16
5
Unit
Multiplication FactsMultiplication FactsThrough 10x10Through 10x10
Multiplication FactsThrough 10x10
5.1 Multiplication Facts Through 5x5
So, 4 x 2 2 x 4=
4 columns of 2 = 2 rows of 4 =
43
8 8
3 columns of 4 = 5 columns of 3 =
65
12 15
Write , or in > < = to complete the number sentence:
xx xx3 5 5 3 3 3 4 41 2
xx xx2 3 4 2 4 0 0 53 4
xx xx3 5 5 2 2 1 1 55 6
Write a multiplication sentence:
x =4 2 8 x =6 2 12
x =8 2 x =8 316 24
17
5.2 Multiplication Facts Through 5x9
x =6 3 18
x =7 3 21
x =7 2 14
x =9 3 27
Write < , > or = in to complete the number sentence:
7 x 3 9 x 2 3 x 8 5 x 443
5 x 2 3 x 4 2 x 6 3 x 421
Find the product. Use the figure:
7
4x
28
8
5x
6
5x
9
4x
row
column1 2 3 4
7 x 6 =
5 x 7 = 4 x 8 = 5 x 9 =
5
6 7 8
Complete:
x
15
14
27
1 2 3 4 5 6 7 8 9
2
3
10
Complete:
x 1 2 3 4 5 6 7 8 9
4
5
10
2 4 6 8 10 12 16 18 20
3 6 9 12 18 21 24 30
40 30 36
42
35 32 45
4 8 12 16 20 24 28 32 36 40
5 10 15 20 25 30 35 40 45 50
18
Word Problem.
Sami has Rs. 50.
He wants to buy 9
Does he have enough money?
Rs. 5
Yes
4 x 6 =
3 x 5 =
6 x 6 =
9 x 6 =
5 x 5 =
Use squares to make arrays. Find the product:
4 x 4 =
6 x 2 =
7 x 6 =
3 x 6 =
5 x 2 =
87
65
43
21
9 10
24
15
36
54
25
16
12
42
18
10
11 5
8x
5 x 8 =
12 5
7x
5 x 7 =
13 8
3x
8 x 3 = 40 35 24
14 6
0x
6 x 0 =
15 4
9x
4 x 9 = 0 36
x 1 2 3 4 5 6 7 8 9
6
10
x 6 = 42 x 4 = 2448 = 8 x
3 x 6 = x 2 4 x 3 = 6 xx 6 = 40 + 8
Rule: x6
Input
output
5 6 7 8 9
Rule:
Input
output 8 16 24
2 3 4 5 6
Complete:
6 12 18 24 30 36 42 48 54 60
7 6 6
9 8 2
x4
30 36 42 48 54 12 20
19
5.3 Multiply by 6
Use > , < or :=
16 x 3 4 6 50x 843
32 x 4 8 8 x 4 821
Find the product:
3 x 7 = 1 4 x 7 = 7 x 6 = 2 3
7 x 2 = 4 7 x 7 = 5 x 7 = 5 6
21 28 42
14 49 35
1
7x
78
7x
87
2x
97
9x
1010
7x
11
7 56 14 63 70
Complete:
26 3
8
547
9 9 x
40 – 5 = x 53
21 + 21 = x72
7 x 4 = + 141 14
6
7
54 27
72
45
3663
81
18
Find the product:
3 x 8 = 8 x 8 = 8 x 9 = 1 2 324 64 72
87654 8
1x
7
7x
9
6x
2
8x
8
7x
8 49 54 16 56
Complete:
x 1 2 3 4 5 6 7 8 9
8
10
8 16 24 32 40 48 56 64 72 80
>
<=
<
20
5.4 Multiply by 7
5.5 Multiply by 8
1 x 2 4x 8 8 x 4 6x 387 = =
56 x 4 9 9 64x 865 > >
Multiply these questions.
T U9
6x____________
____________
T U7
8x____________
____________
T U6
4x____________
____________
T U5
5x____________
____________
T U8
9x____________
____________
T U9
7x____________
____________
654321
5 4 5 6 2 4 2 5 6 3 7 2
By using tables, find the product of these questions:
Find the product of the following questions by carrying forward:
72
41x x____________ x____________ x____________
T
x____________
U
23
41
31
31
46
51
49
41
54321 H T U H T U H T U H T U H
____________
________________________
+ ________________________
+ ________________________
+ ________________________
+ ________________________
+
9 44 7 0
5 6 4
2 64 2 0
5 4 6
1 30
3
333
3 6
3 2 45 4 0
8 6 4
3 9 64 4 0
8 3 6
1 2 3
1
82
21x x____________ x____________ x____________
T
x____________
U
56
41
80
32
03
61
02
81
109876 H T U H T U H T U H T U H
____________
________________________
+ ________________________
+ ________________________
+ ________________________
+ ________________________
+
5 62 8 0
3 3 6
2 7 04 5 0
7 2 0
0 07 6 0
7 6 0
1 8 06 0 0
7 8 0
1 6 08 0 0
9 6 0
1
1
3
1
1
Th H T U
1 1 6
9x____________
Th H T U
2 9 0
6x____________
Th H T U
2 2 2
5x____________
____________ ________________________
321
1 1 1 0 1 0 4 4 1 7 4 0
1 1 1 5 5
1
21
5.6 Multiplication with a Two-digit Multiplier
22
Find the product:
Use > , < or :=
2 x 10 = 9 x 10 = 1 220 90
9
1x
410
3x
3 10
5x
5 9
8x
6 5
9x
7
30 9 50 72 45
40 x 9 5+35 9 x 10 8x 96 > >
9 x 10 8x 81 5 – 65 15x 102< =
10 +50 50x 103 9 x 9 7x 74= =
Problem Solving
The teacher is hanging up his students' pictures.The display is 5 pictures wide and 6 pictures long.
How many pictures are in the display?
1
6x 5
3030 pictures
Solve these questions with a two-digit multiplier:
Th H T U
5 1 5
3x____________
____________
Th H T U
4 1 4
4x____________
____________
Th H T U
3 2 6
5x____________
____________
654
1 5 4 5 1 6 5 6 1 6 3 0
1 1 1 3
H T
45
____________
____________
U
____________
H T
44
____________
____________
U
____________
H T
77
____________
____________
U
____________
H T
____________
____________
U
____________
H T
6421x 31x 01x x61x____________
____________
U
____________
54321
1 0 8 1 3 2 0 0 2 7 6+ + + ++5 4 0 4 4 0 7 7 0 4 6 0
6 4 8 5 7 2 7 7 0 7 3 6
9891
8 0 18 9 0
9 11 6
1 3
1
3
5.7 Multiply by 10
Umer goes to karate class 2 times each week.
How many classes does he go to in 8 weeks?
3
8x 2
16 classes
Aqsa is setting the table for 9 guests. Every guestgets 2 forks, 1 knife and 1 spoon.
How many forks, knives and spoons will Aqsaput on the table in all?
4
Number of forksNumber of knivesNumber of spoons
===
2 x 91 x 91 x 9
===
18 forks9 knives9 spoons
Mohsin buys a for Rs. 350, a for Rs. 150 and a for
Rs. 225. How much does he spend in all?
2
1
3 5 01 5 0
+ 2 2 57 2 5350 + 150 + 225 = Rs.
How can you use multiplication to check ÷ =0 3 0 ?
6 ÷ 3 = 2 12 ÷ 3 = 4 10 ÷ 2 = 5
2 x 3 = 6 4 x 3 = 12 5 x 2 = 10
Write a pair of related multiplication and division sentences:
23
6
Unit Division Facts Through Division Facts Through 10x1010x10
Division Facts Through 10x10
6.1 Division Facts Through 5
24
Find the quotient:
= = = =2 ÷ 1 4 ÷ 4 6 ÷ 3 20 ÷ 51 4322 1 2 4
= = = =10 ÷ 2 15 ÷ 3 3 ÷ 1 10 ÷ 58765 5 5 3 2
6 ÷ 2 = 3 12 ÷ 4 = 3 10 ÷ 5 = 2
3 x 2 = 6 3 x 4 = 12 2 x 5 = 10
5 25250
3 12120
2 660
5 550
9 10 11 125 4 3 1
Find the missing factor and quotient:
÷ =30 6x = 3061 5 5
÷ =42 6x = 4262 7 7
÷ =63 7x = 6373 9 9
÷ =21 77 x = 214 3 3
÷ =49 7x = 4975 7 7
÷ =54 6x = 5466 9 9
Find the quotient:
÷ =421 6
÷ =73 7
÷ =215 7
÷ =562 7
÷ =244 6
÷ =06 7
7
1
3
8
4
0
÷
6
6 12 18 24 30
1 2 3 4 5
35 42 49 56 63
7
÷
5 6 7 8 9
Problem Solving
Javed has 56 marbles.
He puts an equal number of marbles in each of 7 bags.
How many marbles are in 2 bags?
1
(i) 56 7 = 8 marbles÷
(ii) 8 x 2 = 16
6.2 Divide 2-Digit Numbers by 6 and 7
2 Fatima bakes 16 .
She eats 2 and divides the rest equally among 7 friends.
What division sentence shows how many each friend gets?
14 7 = 2÷
Solve the following questions:
1 4
1 4
0
2
7
—
1
Quotient = 2Remainder = 0
2 0
2 0
0
5
4
—
2
Quotient = 5Remainder = 0
2 4
2 4
0
4
6
—
3
Quotient = 4Remainder = 0
3 2
3 2
0
8
4
—
4
Quotient = 8Remainder = 0
6 0
6 0
0
10
6
—
5
Quotient = 10Remainder = 0
3 6
3 6
0
6
6
—
6
Quotient = 6Remainder = 0
5 0
5 0
0
10
5
—
7
Quotient = 10Remainder = 0
4 5
4 5
0
5
9
—
8
Quotient = 5Remainder = 0
Solve the following questions:
Quotient = 19Remainder = 1
5 83
2 82 7
1
1 93
—
1
— Quotient = 12Remainder = 2
7 46
1 41 2
2
1 26
—
2
—
25
6.3 Vertical Division
8 27
1 275
1 1
7
—
3
Quotient = 11Remainder = 5
—
9 88
1 81 6
2
1 2
8
—
4
Quotient = 12Remainder = 2
—
1 0 09
1 091
1 1
9
—
5
Quotient = 11Remainder = 1
—
1 1 31 0
1 31 0
3
2 2
5
—
6
Quotient = 22Remainder = 3
—
3 4 22
1 41 4
0 220
1 7 1
2
—
7
Quotient = 171Remainder = 0
—
—
6 1 84
2 12 0
1 81 6
2
1 5 4
4
—
7
Quotient = 154Remainder = 2
—
—
Solve the following simple division questions:
1 6
1 5
1
5
3
—
1
Quotient = 5Remainder = 1
2 8
2 8
0
4
7
—
2
Quotient = 4Remainder = 0
4 2
4 2
0
7
6
—
3
Quotient = 7Remainder = 0
5 5
5 4
1
6
9
—
4
Quotient = 6Remainder = 1
4 7
4 2
5
6
7
—
5
Quotient = 6Remainder = 5
6 8
6 4
4
8
8
—
6
Quotient = 8Remainder = 4
26
7 5
7 2
3
9
8
—
7
Quotient = 9Remainder = 3
8 2
8 1
1
9
9
—
8
Quotient = 9Remainder = 1
Solve these questions of division into two or three steps.
4 44
0 440
1 1
4
—
1
Quotient = 4Remainder = 0
—
4 53
1 51 5
0
1 5
3
—
2
Quotient = 15Remainder = 0
—
6 05
1 01 0
0
1 2
5
—
3
Quotient = 12Remainder = 0
—
9 08
1 00 8
2
1 1
8
—
4
Quotient = 11Remainder = 2
—
6 24
2 22 0
2
1 5
4
—
5
Quotient = 15Remainder = 2
—
1 1 51 0
1 51 5
0
2 3
5
—
6
Quotient = 23Remainder = 0
—
4 2 24
2 22 0
2
105
4
—
7
Quotient = 105Remainder = 2
—
6 3 85
1 31 0
3 83 5
127
5
—
8
Quotient = 127Remainder = 3
—
3—
27
Problem Solving
There are 8 carrots in each bag. Noor needs48 carrots. How many bags should she buy?
1
=3 8 6 x 44=45 9 50 ÷ 103 ÷ x
=32 8 40 =13 6 70 ÷ 1021 + –
Write + , – , x , or ÷ to complete the number sentence:
48 ÷ 8 = 6
Find the Quotient:
÷ =16 8 ÷ =18 9 ÷ =10 10321 2 2 1
÷ =27 9 ÷ =48 8 ÷ =60 10654 3 6 6
Divide:
56 40 48 32 24
8
÷1
7 5 6 4 3
2 54 45 72 63 81
9
÷ 3 70 60 90 80 100
10
÷
6 5 8 7 9 7 6 9 8 10
7070
0
10 9090
0
9 6464
0
887 9
7
— —
10
—
8
28
6.4 Divide 2-Digit Numbers by 8,9 and 10
Problem Solving
Total PriceCost of 1 toy dogRemaining price
Cost of 5 toy dogsCost of 1 toy dog
=======
Rs 30Rs 1530 -15Rs 15Rs 1515 ÷ 5Rs 3
1 Amir buys 6 toy dogs for Rs. 30. One toy costs Rs. 15.The others all cost the same.How much does each one cost?
4 Naveed spent Rs. 16. at the store.This is twice as much as Zainab and Ayesha spent there.Ayesha spent Rs. 5.How much did Zainab spend?
Total rupees spentby Naveed
Rupees spent byZainab and Aysha
Zainab spent rupees
=
=
===
16
16 ÷ 2
Rs 88 – 5Rs 3
29
Circle the shapes that shows :12
Write under the shapes those show one half.12
Circle the shapes that shows halves:
4321
12
12
4321
2 31 4
30
7
Unit
FractionsFractionsFractions
7.1 Halves and One Half
Circle the shapes that shows thirds:
4321
7.2 Thirds and One Third
31
Circle the shapes that shows :13
4321
Circle the shapes that shows two thirds:
Write the fraction that shows the coloured part:
4321
4321
12
13
13
14
7.3 Two Thirds
Circle the fraction that shows the coloured part:
321
12
23
34
12
13
23
12
13
23
Write the fraction that shows the coloured part:
321
13
23
23
32
Write the fraction that shows the coloured parts.
4321
4321
Circle the fraction that shows the coloured part:
Circle the shapes that shows fourths:
12
14
12
14
12
14
12
14
14
14
14
14
1 2 3 4
7.4 Fourth and One Fourth
Circle the shapes that shows :34
Circle the fraction that shows the coloured part:
4321
12
14
34
12
14
34
12
14
34
12
14
34
4321
7.5 Three Fourths
33
Write the fraction that shows the coloured part:
4321
14
34
34
34
Problem Solving
12
13
14
They ate equal parts.What fraction did each eat?
cut into thirds.
12
12
14
321
Colour the shape that shows the fraction:
Write the fraction that shows the coloured part.
321
24
14
12
34
12
34
34
54 6
Write ‘open’ or ‘closed’ for the shapes given below.
1 2 3
open closed open
8
Unit
Primeter and AreaPrimeter and AreaPrimeter and Area
8.1 Perimeter
4 5 6
closed open closed
Write down the number of sides and find the perimeter for the followingshapes:
Number of sides = ___________________
Name of closed shape =_______________
Perimeter = _____+_____+_____+_____
= ________ cm
3 cm3 cm
3 cm
3 cm
1 4
Square
3 3 3 3
12
35
2 cm 2 cm
2 cm2 Number of sides = ___________________
Name of closed shape =_______________
Perimeter = _____+_____+_____+_____
_____+_____ = ________ cm
6
Hexagon
2 2 2 22 cm 2 cm
2 cm122 2
3 cm 3 cm
4 cm
3 Number of sides = ___________________
Name of closed shape =_______________
Perimeter = _____+_____+_____
= ________ cm
3
Triangle
3 3 4
10
1 cm
1 cm
1 cm 1 cm
1 cm 1 cm
1 cm 1 cm4
Number of sides = ___________________
Name of closed shape =_______________
Perimeter = _____+_____+_____+_____+
_____+_____+_____+_____ = _____ cm
8
Octagon
1
1
1 1 1
1 1 1 8
2 cm
2 cm
5 cm
5 cm
5 Number of sides = ___________________
Name of closed shape =_______________
Perimeter = _____+_____+_____+_____
= ________ cm
4
Rectangle
2 5 5 2
14
Perimeter = ____________
= ____________ cm
Perimeter = ____________
= ____________ cm
1 2
2 + 3 + 2 + 3
10
2 + 4 + 2 + 4
12
8.2 Perimeter on a Grid
Find the area of the following shapes given on the grids.2
For all pictures below, suppose the area of each square is 1 cm .
2Area = _____ x _____ = _____ cm
2Area = _____ x _____ = _____ cm4 2 8 5 1 5
2Area = _____ x _____ = _____ cm
2 Area = _____ x _____ = _____ cm8 2 16 3 2 6
36
8.3 Area
Perimeter = ____________
= ____________ cm
Perimeter = ____________
= ____________ cm
3 4
3 + 3 + 3 + 3
12
1 + 5 + 5 + 1
12
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