Vedanta Excel in Mathematics Book 3 Final (2078)

Multiplication - How many times, how many altogether?

Multiplication by using number lines

Classwork – Exercise
1. Let's jump forwards as many steps and as many times as to match the sums.

Then, ind the products.

Multiply 5 × 3 (Jumping 3 steps 5 times)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

5 × 3 = 15
a)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

×=
b)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

×=
c)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

×=
d)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

× = (Jumping 2 steps 3 times)
e)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

× = (Jumping 3 steps 4 times)
f)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

× = (Jumping 5 steps 3 times)

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 101 vedanta Excel in Mathematics - Book 3

Multiplication - How many times, how many altogether?

Multiplication with 10, 20, 300, 400, ...
Let's be faster than a calculator!

4 times 10 is 40. 2 times 100 is 200.
4 × 10 = 40 2 × 100 = 200

2×3=6 It's tricky and easier!
In 6 × 3000, at ϔirst 6 × 3 = 18.
3 times 20 = 3 × 20 = 60 Then, I should write as many
zeros at the end of 18 as 3000
4×2=8 has.
So, 6 × 3000 = 18000.
4 times 200 = 4 × 200 = 800

5 times 1000 = 5 × 1000 = 5000

6 times 3000 = 6 × 3000 = 18000

30 times 40 = 30 × 40 = 1200

Classwork – Exercise
1. Now, let's say and write the product as quickly as possible.

a) 3 × 10 = 3 × 100 = 3 × 1000 =

b) 2 × 20 = 2 × 200 = 2 × 2000 =

c) 4 × 30 = 4 × 300 = 4 × 4000 =

d) 10 × 20 = 10 × 60 = 10 × 90 =

e) 20 × 20 = 20 × 30 = 20 × 40 =

f) 30 × 50 = 30 × 60 = 30 × 70 =

g) 10 × 100 = 20 × 100 = 30 × 100 =

h) 40 × 100 = 50 × 100 = 60 × 100 =

i) 10 × 200 = 20 × 300 = 20 × 400 =

vedanta Excel in Mathematics - Book 3 102 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Multiplication - How many times, how many altogether?

Multiplication with 2, 3 and 4-digit numbers

Multiply 12 by 4

1 ten 4 tens

12 1 ten + 2 ones 2 ones 8 ones
×4 ×4
× 4=
48 4 tens + 8 ones

Multiply 123 by 2 1 hundred 2 tens

123 1 hundred + 2 tens + 3 ones 3 ones
×2 ×2
× 2=
246 2 hundreds + 4 tens + 6 ones

Multiply 2312 by 3 I understood!
The digit at thousands,
2312 2 thousands + 3 hundreds + 1 ten + 2 ones hundreds, tens and ones
×3 places are multiplied
×3 separately.
6936 6 thousands + 9 hundreds + 3 tens + 6 ones

Classwork – Exercise f)

1. Let's multiply and ind the products as quickly as possible. 44
a) b) c) d) e) ×2

13 24 23 32 34
×3 ×2 ×3 ×3 ×2

g) h) i) j) k) l)

123 213 321 232 4231 332

×2 ×3 ×2 ×3 ×2 ×3

m) n) o) p) q)

1342 2313 4231 3132 2121
×2 ×3 ×2 ×3 ×3

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 103 vedanta Excel in Mathematics - Book 3

Multiplication - How many times, how many altogether?

Multiplication with carry over

Multiply 27 by 4

TO 2 27 20 + 7 27
27 ×4 ×4 ×4
×4 TO 80 + 28
8 28 27 108 108

×4

108

HT O 12 325 300 + 20 + 5 3 25
32 5 ×5 ×5
HT O ×5
×5 32 5 1625 1500 + 100 + 25 1625

15 10 25 ×5

1625

2. Let's multiply and ind the products as quickly as possible. e)
a) b) c) d)

25 24 16 17 27
×3 ×4 ×6 ×5 ×5

f) g) h) i) j)

32 43 36 134 275
×6 ×7 ×5 × 4× 2

k) l) m) n) o)

3 2 4 4 5 7 12 4 3 25 6 4 1 4 7 5
× 5× 4× 4× 3× 6

vedanta Excel in Mathematics - Book 3 104 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Multiplication - How many times, how many altogether?

Multiplication with 2-digit multiplier

Multiply 16 by 13. Multiply 234 by 25.

16 13 = 10 + 3 23 4 25 = 20 + 5
×1 3 3 × 16 = 48 ×2 5 5 × 234 = 1170
10 × 16 = 160 117 0 20 × 234 = 4680
48 160 + 48 = 208 4 680 1170 + 4680 = 5850
16 0 5850
20 8

3. Let's multiply and get the products as quickly as possible.

17 24 28 35 42
×1 4 ×1 5 ×2 3 ×2 2 ×3 6

13 4 16 5 17 3 18 6 19 2
×1 3 ×1 2 ×1 4 ×1 6 ×1 5

21 3 22 7 32 4 43 2 54 3
×2 4 ×2 5 ×2 3 ×1 6 ×1 7

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 105 vedanta Excel in Mathematics - Book 3

Multiplication - How many times, how many altogether?

Row and column multiplication
Let's learn about row and column multiplication from the examples given below.

4 columns of lowers 4

3 rows 3
of lowers

3 × 4 = 12 lowers

Classwork – Exercise
1. Now, let's tell and write the answer as quickly as possible.

How many balls? How many lowers? How many cats?

2 × 3 = balls × = lowers × = cats
How many butter lies? How many marbles?
How many girls?

× = girls × = butter lies × = marbles
How many lowers?
How many baskets?

× = lowers 106 × = baskets

vedanta Excel in Mathematics - Book 3 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Multiplication - How many times, how many altogether?

Let's use multiplication in our real life!

Classwork – Exercise

1. Let's read the problems carefully and answer them as quickly as possible.

a) 3 times 4 kg of vegetables = 3 — 4= kg of vegetables

b) 4 times the group of 5 children = — = children

c) 5 times Rs 20 = — = Rs

d) 6 times 5 kg of fruits = — = kg of fruits

e) 7 times the packets of 10 pencils = — = pencils

f) 8 times 6 packets of pencils = — = packets

g) 10 times 7 m length of cloths = — = m of cloths
2. Let's say and write the answers as quickly as possible.

a) The cost of 1 pencil is Rs 7. The cost of 6 pencils — = Rs

b) The cost of 1 biscuit is Rs 10. The cost of 8 biscuits — = Rs

c) 1 packet contains 6 pencils. 6 packets contain — = pencils

d) Cost of 1 kg tomatoes is Rs 40. Cost of 3 kg of tomatoes — = Rs
e) A jar can hold 8 l of oil. 7 jars can hold — = l of oil.

f) The weight of a box is 9 kg. The weight of 4 boxes × = kg

g) A man earns Rs 300 in a day. His earning in a week × = Rs

h) A woman earns Rs 500 in a day. Her earning in 30 days × = Rs

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 107 vedanta Excel in Mathematics - Book 3

Multiplication - How many times, how many altogether?

3. Let's read the problems carefully and answer them.

a) The cost of 1 kg of sugar is Rs 75. What is the cost of 5 kg of sugar? 75
×5
The cost of 1 kg of sugar = Rs 75
The cost of 5 kg of sugar = 5 — Rs 75= 375

b) There are 60 minutes in 1 hour. How many minutes are there in
9 hours?

1 hour = minutes

9 hours = — = minutes

c) In a school assembly students are arranged in 15 rows with
18 students in each row. How many students are there in the
assembly?

Number of students in 1 row =

Number of students in 15 rows = — =

d) We get roughly 72 calories from 1 boiled egg. How much calories
do we get from a dozen of boiled eggs?

1 boiled egg gives calories

1 dozen (12) boiled eggs give — =

e) The distance between place A and place B is 21 km. A bus carries
passengers from A to B and B to A 4/4 times everyday. How many
kilometres does the bus travel in 1 day?

The distance between A and B = 21 km

The bus travels this distance 4 + 4 = 8 times everyday

The distance travelled by bus = — = km everyday

vedanta Excel in Mathematics - Book 3 108 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Multiplication - How many times, how many altogether?

EXERCISE

Let's copy and solve these problems in your exercise book.
4. a) The cost of 1 exercise book is Rs 40. Find the cost of 6 exercise books.

b) Mother buys 3 kg of vegetables. If the cost of 1 kg of vegetables is Rs 50, how many
rupees does she pay?

c) Father drives his motorbike 30 km with 1 litre of petrol. How many kilometres
does he drive with 20 l of petrol?

d) A water tanker carries 7,000 litres of water in 1 trip. How much water does it
carry in 4 trips?

5. a) On your happy birthday, you and your family had 7 plates of Mo:Mo in a restaurant.
If the cost of 1 plate of Mo:Mo was Rs 125, how much money did you pay to the
restaurant?

b) Mrs Gurung is a part-time teacher. She earns Rs 940 in a day. How much money
does she earn in 6 days?

c) One way distance between your home and your school is 7 km. How many
kilometres do you travel in 15 days?

d) The distance between place A and place B is 27 km. A bus carries passengers from
A to B and B to A 6/6 times everyday. How many kilometers does the bus travel in
a day?

e) A packet of 500 ml of milk gives 17 g of protein. If you drink 15 packets of milk in
a month, how much protein do you get?

f) There are 32 students in class 3. They collected Rs 140 per head for helping the
earthquake victims. How much money did they help to the victims?

g) A milk lorry carries milk to a city 4 times everyday. Each time it carries 2,320 litres
of milk. How many litres of milk does it carry in one day?

h) Mr. Gupta earns Rs 1,250 in a day. How much money does he earn in a week?

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 109 vedanta Excel in Mathematics - Book 3

Division - Sharing

Sharing things equally
Let's share 4 sweets equally between your 2 friends.
How many sweets will each friend get?
Each friend gets 4 › 2 = 2 sweets.
Let's share 6 pencils equally between your 3 friends.
How many pencil will each friend get?

Each friend gets 6 › 3 = 2 pencils

When we divide things, we are sharing the things equally.

Classwork – Exercise
1. Let's draw circles to divide and share the things.

a) Divide 8 oranges between 2 children. oranges.
Each child shares › =

b) Divide 9 cherries between 3 friends. cherries.
Each friend shares › =

c) Divide 10 candies between 5 children.

Each child shares ›

= candies.

d) Divide 12 strawberries between 4 friends.

Each friend shares ›

= strawberries. 110 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

vedanta Excel in Mathematics - Book 3

Division - Sharing

Drawing dots!

Classwork – Exercise

1. Let's draw as many equal dots in each box and complete the division.

Divide 8 dots equally into 2 groups.
11 22 33 44
In 8 ÷ 2.
8›2=4 I should recall the
table of 2!
2×4=8

2 dots 4 dots 6 dots 8 dots

a) Divide 8 dots equally into 4 groups. In 8 ÷ 4.
I should recall the
›= table of 4!
4×2=8

b) Divide 12 dots equally into 2 groups. In 12 ÷ 2.
›= I should recall the
table of 2!
c) Divide 12 dots equally into 3 groups. 2 × 6 = 12
›=
In 12 ÷ 3.
d) Divide 15 dots equally into 5 groups. I should recall
›= the table of 3!
3 × 4 = 12
e) Divide 15 dots equally into 3 groups.
›= In 15 ÷ 5.
I should recall
Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 111 the table of 5!
5 × 3 = 15

In 15 ÷ 3.
I should recall
the table of 3!
3 × 5 = 15

vedanta Excel in Mathematics - Book 3

Division - Sharing

Fun of multiplication and division
Classwork – Exercise

1. Let's investigate the fact, how multiplication and division go together.

It means 2 — 4 It also means 8 › 2

2 times 4 dots 8 dots are divided into 2 groups

a) 4— 2= and 8 › 4=

b) —= and › =

c) —= and › =

2. Now, let's say and write the answers as quickly as possible.

a) 2 — 9 = So, 18 › 2 = and 18 ÷ 9 =

b) 3 — 8 = So, 24 › 3 = and 24 ÷ 8 =

c) 4 — 7 = So, 28 › 4 = and 28 ÷ 7 =

d) 8 — 5 = So, 40 › 8 = and 40 ÷ 5 =

e) 9 — 6 = So, 54 › 9 = and 54 ÷ 6 =

3. It's your time! Let's write your numbers and have fun of multiplication and
division.

a) — = So, › = I got it!
b) — = So, › = 5 × 6 = 30
So, 30 ÷ 5 = 6
and 30 ÷ 6 = 5

c) — = So, › =

d) — = So, ›=

vedanta Excel in Mathematics - Book 3 112 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Division - Sharing

Classwork – Exercise

1. Let's recall the tables of 1, 2, 3, ... 10. Say and write the answers as quickly as
possible.

a) Recall the table of 2 and get 20 20 ÷ 2 = 20 ÷ 2 2 × 1 = 2, ...
b) Recall the table of 3 and get 21 21 ÷ 3 = 2 × 9 = 18
2 × 10 = 20

So, 20 ÷ 2 = 10

c) Recall the table of 4 and get 32 32 ÷ 4 =

d) Recall the table of 5 and get 45 45 ÷ 5 = 21 ÷ 3 3 × 1 = 3, ...
e) Recall the table of 6 and get 36 36 ÷ 6 = 3 × 6 = 18
f) Recall the table of 7 and get 35 35 ÷ 7 = 3 × 7 = 21

So, 21 ÷ 3 = 7

g) Recall the table of 8 and get 16 16 ÷ 8 =

h) Recall the table of 9 and get 54 54 ÷ 9 =

i) Recall the table of 10 and get 100 100 ÷ 10 =
2. Now, let's divide. Say and write the answers as quickly as possible.

a) 16 ÷ 2 = b) 18 ÷ 3 = c) 36 ÷ 4 = d) 40 ÷ 5 =

e) 24 ÷ 6 = f) 42 ÷ 7 = g) 56 ÷ 8 = h) 72 ÷ 9 =

i) 70 ÷ 10 = j) 45 ÷ 9 = k) 80 ÷ 8 = l) 49 ÷ 7 =

3. Let's tell and write the answer as quickly as possible. Very simple!
15 ÷ 5 = 3
a) The product of two numbers is 15 and one of them is 5. and 5 × 3 = 15
So, another
Another number is 15 › 5 = number is 3.

b) The product of two numbers is 24 and one of them is 4.

Another number is ›=

c) The product of two numbers is 56 and one of them is 8.

Another number is › =

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 113 vedanta Excel in Mathematics - Book 3

Division - Sharing

Dividend, Divisor, Quotient and Remainder

Let's divide 27 by 9. 36 ÷ 4 = 9
27 ÷ 9 = 3

27 is the Dividend. Dividend Divisor Quotient
9 is the Divisor.
3 is the Quotient.

Classwork – Exercise
1. Let's do these division. Say and write the dividend, divisor and the quotient.

a) 12 ÷ 4 = dividend is divisor is quotient is

b) 25 ÷ 5 = dividend is divisor is quotient is

c) 63 ÷ 7 = dividend is divisor is quotient is

2. It's your time! Let's write your dividend and divisor to get the given quotient.

a) › = 2 b) › = 3 c) › =4
d) › = 5
e) › = 6 f) › = 7

Again, let's divide 7 pencils equally between your 2 friends.
Each of your friends gets 3 pencils and 1 pencil is remained
to divide. 1 pencil is the remainder.

3. a) 3 is divided by 2. The remainder is

b) 8 is divided by 3. The remainder is

c) 13 is divided by 5. The remainder is

d) 18 is divided by 4. The remainder is

vedanta Excel in Mathematics - Book 3 114 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Division - Sharing

4. Let's say and write the missing dividend or divisor for the given quotient as
quickly as possible.

6÷ =3 ›3 =2 8› =2 8› =4

÷ =2 10 › =5 ÷4 =3 12 › =2

16 ÷ =4 ÷8 =2 20 ÷ = 4 ÷4 =5

÷4 =7 42 ÷ =6 ÷5 =9 90 ÷ = 10

Quiz Time!
5. Let's ind the dividend, divisor, quotient or remainder as quickly as possible.

a) dividend is 3, divisor is 2, quotient = remainder =

b) divisor is 3, quotient is 2, remainder is 1, dividend is

c) divisor is 4, quotient is 3, remainder is 2, dividend is

d) dividend is 9, quotient is 4, divisor is , remainder is

e) dividend is 10, quotient is 3, divisor is , remainder is

Puzzle Time!

6. Let's ill in the missing numbers to complete the sums.

18 › =9 › 4 =6 ›=

› ›› › ›› › ››
› =3
3› = 6› =2
= ==
= == = ==

6› =3 8› = 6› =2

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 115 vedanta Excel in Mathematics - Book 3

Division - Sharing

1-digit divisor

1. Let's divide 36 by 3.

36 ÷ 3 3 36 12
–3 ’
30 › 3 6›3 12 06

–6

0

36 ÷ 3 = 12 quotient and 0 is remainder.

2. Let's divide 42 by 2. 2 42 21
–4 ’
42 ÷ 2 02

40 › 2 2 › 2 –2

42 ÷ 2 = 21 quotient and 0 is remainder. 0
3. Let's divide 53 by 4.
21
53 ÷ 4
4 53 13
–4 ’
13

–1 2

1

40 › 4 12 › 4 R 13 R

53 › 4 = 13 quotient and 1 is remainder.

4. Let's divide 117 by 5. 5 117 23
–10’
117 ÷ 5 17

–15

2

100 › 5 15 › 5 R 23 R

117 ÷ 5 = 23 quotient and 2 is remainder.

vedanta Excel in Mathematics - Book 3 116 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Division - Sharing

Classwork – Exercise
1. Lets divide. Tell and write the quotient and remainder.

a) 2 24 b) 3 39 c) 4 44 d) 5 52

Q= R= Q= R= Q= R= Q= R=
e) f) g) h)

6 61 7 73 8 84 9 95

Q= R= Q= R= Q= R= Q= R=

2. Lets divide. Tell and write the quotient and remainder. d)
5 75
a) b) c)
2 34 3 45 4 56

Q= R= Q= R= Q= R= Q= R=

e) f) g) h)
2 106 3 102 4 208 5 307

Q= R= Q= R= Q= R= Q= R=

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 117 vedanta Excel in Mathematics - Book 3

Division - Sharing

EXERCISE

1. Lets divide in your exercise book. Then write the quotient and reminder.

a) 2 28 b) 3 33 c) 4 48 d) 5 50 e) 6 60

f) 7 70 g) 2 36 h) 3 52 i) 4 64 j) 5 65
k) 6 84 l) 7 91 m) 8 96 n) 9 93 o) 8 82

p) 7 71 q) 6 73 r) 5 86 s) 4 99 t) 3 97

2. Lets divide in your exercise book. Then write the quotient and reminder.

a) 2 246 b) 2 128 c) 3 363 d) 3 249 e) 6 480

f) 4 336 g) 5 525 h) 5 450 i) 6 672 j) 6 498

k) 7 785 l) 7 647 m) 8 890 n) 8 513 o) 8 945

p) 9 387 q) 2 2456 r) 3 1248 s) 4 4653 t) 3 3667

3. Lets divide in your exercise book. Then write the quotient and reminder.

a) 2 354 b) 3 438 c) 4 575 d) 5 607 e) 6 723
f) 7 982 g) 8 974 h) 5 7255 i) 6 9852 j) 7 8695

4. Let's read the problems carefully and answer them.

a) Divide Rs. 80 equally between 3 children. How many rupees will each get? How
many rupees are remained to divide?

b) Divide 98 sweets and put into 4 boxes equally. How many sweets are there in each
box? How many sweets are remained to put into the boxes?

c) Divide 124 students equally into 5 houses. How many students are there in each
house? How many students are left to divide into houses?

vedanta Excel in Mathematics - Book 3 118 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Division - Sharing

2-digit divisor

Let's divide 16 Let's divide 28 Let's divide 46 Let's divide 50
by 12. by 13. by 15. by 24.

12 1 6 1 13 2 8 2 15 4 6 3 24 5 0 2
–1 2 –2 6 –4 5 –4 8
4 2 1 2

Q=1 R=4 Q=2 R=2 Q=3 R=1 Q=2 R=2

Classwork – Exercise

1. Let's divide. Say and write the quotient and remainder.

a) b) c) d)
10 12 11 1 5 15 2 0 14 2 8

Q= R= Q= R= Q= R= Q= R=

e) f) g) h)
12 2 5 16 3 3 20 4 0 20 4 3

Q= R= Q= R= Q= R= Q= R=

i) 21 5 0 j) 25 6 0 k) 30 6 2 l) 15 8 0

Q= R= Q= R= Q= R= Q= R=

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 119 vedanta Excel in Mathematics - Book 3

Division - Sharing

Let's divide Let's divide Let's divide
105 by 10. 146 by 12. 325 by 25.

10 1 0 5 10 12 1 4 6 12 25 3 2 5 13
–1 0 ’ –1 2 ’ –2 5 ’
05 26 75
–0 –24 –75
5 2 0

Q = 10 R = 5 Q = 12 R = 2 Q = 13 R = 0

EXERCISE

1. Let's divide in your exercise book. Write the quotient and remainder.

a)10 107 b) 11 121 c) 12 124 d) 12 134 e) 13 135

f) 15 180 g) 16 192 h) 14 210 i) 12 300 j) 18 234

k)20 203 l) 24 288 m)25 400 n) 15 347 o) 30 605

p)10 1124 q) 12 1452 r) 15 2010 s) 16 3393 t) 18 3834

Let's divide 102 Let's divide 105 Let's divide
by 11. by 12. 1162 by 14.

11 1 0 2 9 12 1 0 5 8 14 1 1 6 2 83
– 99 – 96 –1 1 2’
03 09 42

Q=9 R=3 Q=8 R=9 –42

0

Q = 83 R = 0

2. Let's divide in your exercise book. Write the quotient and remainder.

a) 11 103 b) 12 102 c) 13 110 d)14 113 e)15 124

f) 16 115 g) 17 122 h)18 111 i) 20 140 j) 25 205

k) 11 1012 l) 12 1128 m)14 1135 n)15 1080 o)16 1168

vedanta Excel in Mathematics - Book 3 120 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Division - Sharing

Let's use division in our real life!
Classwork – Exercise

1. Let's read the problems carefully and answer them as quickly as possible.

14a) The cost of 2 pencils is Rs 14. The cost of 1 pencil ÷ 2 = Rs

b) The cost of 3 sweets is Rs 30. The cost of 1 sweet ÷ = Rs

c) In 4 groups, there are 20 students. In 1 group ÷ = students

d) 5 spiders have 40 legs. 1 spider has ÷= legs

e) 24 eggs are in 6 equal rows. 1 row has ÷= eggs.

f) 9 cockroaches have 54 legs. 1 cockroach has ÷ = legs

g) 4 times a sum of money is Rs 40. The sum is ÷ = Rs

h) 48 pencils are in 8 equal packets. 1 packet has ÷ = pencils.

2. Let's read the problems carefully and answer them. 6)96(

a) The cost of 6 exercise books is Rs 96. What is the cost of 1 exercise
book?

Cost of 6 exercise books = Rs 96

Cost of 1 exercise book = Rs 96 ÷ 6 = Rs

b) The cost of 1 exercise book is Rs 16. How many exercise books can you buy for Rs 96?

Total cost of a few number of exercise books = Rs 96

Cost of 1 exercise book = Rs 16

Number of exercise books = Rs 96 ÷ Rs 16 =

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 121 vedanta Excel in Mathematics - Book 3

Division - Sharing

EXERCISE

Let's read the problems carefully. Solve them in your exercise book.

1. a) The cost of 7 chocolates is Rs 98. Find the cost of 1 chocolate.

b) A chocolates costs Rs 14. How many chocolates can you buy for
Rs 98?

2. a) 72 students are equally divided into 6 groups. How many students are there in
each group?

b) 72 students are equally divided into some groups with 12 students in each group.
How many groups of students are there?

3. a) 110 children of 10 football teams of different schools are playing football in an
'Inter-School' football match. How many players are there in each team?

b) There are 11 players in a football team. 110 children of different school teams are
playing football in an 'Inter-School' football match. How many teams are playing
the match?

4. a) A man divides Rs 936 equally among 9 workers. How much money does a worker
get?

b) A man divides Rs 936 equally to a few number of workers and each worker gets
Rs 104. Find the number of workers?

c) A bag can hold 15 kg of rice. How many bags are needed to put 1815 kg of rice?

5. a) The product of two numbers is 24. If one of the numbers is 6, ind the other
number.

b) The product of two numbers is 35 and one of the number is 7. Find the other
number.

c) When a number is multiplied by 9, the product is 72. Find the number.

vedanta Excel in Mathematics - Book 3 122 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Division - Sharing

Dividing tens, hundreds, ... by 10, 20, ..., 100, 200...

1. Let's divide 20 by 10. 10 twos are 20. So, 20 ÷ 10 = 2.
20 ÷ 10 Equal number of zeros from
=2 dividend and divisor are cancelled.

2. Let's divide 80 by 20. Equal number of zeros from 80 and
80 ÷ 20 20 are cancelled.
=8÷2=4 80 ÷ 20 . Then 8 ÷ 2 = 4

3. Let's divide 1000 by 100. Equal number of zeros from 1000
1000 ÷ 100 and 100 are cancelled.
= 10 1000 ÷ 100 = 10

Classwork – Exercise
1. Let's tell and write the quotient as quickly as possible.

a) 10 ÷ 10 = b) 100 ÷ 10 = c) 1000 ÷ 10 =

d) 50 ÷ 10 = e) 500 ÷ 10 = f) 5000 ÷ 10 =

g) 20 ÷ 20 = h) 200 ÷ 20 = i) 2000 ÷ 20 =

j) 60 ÷ 20 = k) 600 ÷ 20 = l) 6000 ÷ 20 =

m) 3000 ÷ 3 = n) 3000 ÷ 30 = o) 3000 ÷ 300 =

p) 4000 ÷ 2 = q) 4000 ÷ 20 = r) 4000 ÷ 200 =
2. a) 8000 ÷ 400 = b) 9000 ÷ 300 = c) 9000 ÷ 90 =

d) 5000 ÷ 500 = e) 6000 ÷ 20 = f) 7000 ÷ 70 =

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 123 vedanta Excel in Mathematics - Book 3

Division - Sharing

Let's read the problems carefully. Say and write the answer as quickly as possible.

3. a) How many Rs 5 notes are there in Rs 10? 10 ÷ 5 = 2

b) How many Rs 5 notes are there in Rs 50? ÷=

c) How many Rs 10 notes are there in Rs 100? ÷=

d) How many Rs 10 notes are there in Rs 500? ÷=
e) How many Rs 10 notes are there in Rs 1000?
1000 ÷ 10 = 100

f) How many Rs 100 notes are there in Rs 500? ÷=

g) How many Rs 100 notes are there in Rs 1000? ÷=

h) How many Rs 20 notes are there in Rs 100 ? ÷=

i) How many Rs 20 notes are there in Rs 500 ? ÷=

j) How many Rs 20 notes are there in Rs 1000 ? ÷=

k) How many Rs 50 notes are there in Rs 100 ? ÷=

l) How many Rs 50 notes are there in Rs 500 ? ÷=

m) How many Rs 50 notes are there in Rs 1000 ? ÷=
4. a) How many 100 grams are there in 1 Kilogram ? ÷=

b) How many 100 millilitres are there in 1 litre ? ÷=

c) How many 10 centimetres are there in 1 metre ? ÷=

d) How many 100 meters are there in 1 Kilometre ? ÷=

vedanta Excel in Mathematics - Book 3 124 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Simplification

Mixed Problems - Addition, Subtraction, Multiplication, Division

Classwork – Exercise

Lets listen to your teacher! Say and write the answer as quickly as possible.

1. a) Add 4 and 5, then again add 7.

4 + 5 + 7 = 9 + 7 = 16 I should perform addition
b) Add 5 and 6, then subtract 4. and subtraction in the order
it appears, from left to right !

+– =–=

c) Subtract 9 from 10, then add 5. + = I got it!
–+= 10 – 9 + 5
=1+5=6

d) Add 5 and 8, then subtract 6. Now, it's a rule!
+–=-= Let's multiply at ϔirst,
then add or subtract!!
e) Subtract 3 from 10, then again subtract 4.

10 – 3 – 4 = 7 – 4 = 3 I know!
f) Subtract 5 from 15, then again subtract 7. 15 – 5 – 7
= 10 – 7
––=–= =3

g) Subtract 8 from 17, then again subtract 5.

––= – = It's easy!
h) Add 9 and 4, then subtract 3. – = 18 – 6 + 4
= 12 + 4 = 16
+–=

i) Subtract 6 from 18, then add 4.

–+=+=

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 125 vedanta Excel in Mathematics - Book 3

Simplification - Mixed Problems

2. a) Multiply 3 and 4, then add 6. 6= But what to do
with 6 + 3 × 4?
3 × 4 + 6 = 12+

b) Multiply 5 and 6, then add 2.

×+ =+=

c) Multiply 8 and 7, then subtract 6.

×– =–=

d) Multiply 9 and 5, then subtract 7.

×– =–=

3. a) Divide 15 by 3, then add 5.

15 ÷ 3 + 5 = 5 + 5 =

b) Divide 36 by 4, then subtract 3.

÷–=–= I should perform
c) Divide 80 by 8, then multiply by 10. multiplication and
division in the order
÷×=×= it appears from left
d) Divide 45 by 9, then multiply by 4. to right!

I understood!
4 × 10 ÷ 2 = 40 ÷ 2 = 20
15 ÷ 3 × 6 = 5 × 6 = 30

÷×=×=

4. a) First add, then subtract. 9 + 6 – 4 = – =

b) First multiply, then add. 5 × 7 + 8 = + =

c) First divide, then add. 63 ÷ 9 + 9 = + =

d) First divide, then multiply. 54 ÷ 6 × 5 = ×=

vedanta Excel in Mathematics - Book 3 126 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Simplification - Mixed Problems

My name is Calculator Machine. Let's input numbers inside me. I will simplify and
give you outputs!

a) 2 3 b) 4 7

1 2

+7 – 4 +5 – 3

45 6

c) 8 9 d) 5 6

7 3

–3 –2 ×4 + 1

e) 12 15 f)

9 16 24 28
÷4×5
÷3+2

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 127 vedanta Excel in Mathematics - Book 3

Simplification - Mixed Problems

Process of simpli ication
Now, let's learn the process of simpli ication.

1. Simplify. Another Process I got it!
7–4+6 7–4+6 In the case of addition and
=3+6 = 13 – 4 subtraction, I can add or I can
=9 =9 subtract at ϔirst!

2. Simplify Another Process
15 + 9 – 7 15 + 9 – 7
= 24 – 7 = 15 + 2
= 17 = 17

3. Simplify. But it is wrong But, in the case of addition
6+5×3 process. and multiplication, we must
= 6 + 15 multiply at ϔirst, then we
= 21 6+5×3 should add.
= 11 × 3
= 33 which is
wrong answer

4. Simplify. Another Process Oh!
2×8÷4 2×8÷4 3 × 6 ÷ 2 = 18 ÷ 2 = 9
=2×2 = 16 ÷ 4 3×6÷2=3×3=9
=4 =4 But, 6 ÷ 2 × 3 = 6 ÷ 6 = 1 is wrong

5. Simplify. But it is wrong It must be
8÷4×2 process. 6 ÷ 2 × 3 = 3 × 3 = 9 is the right
= 2× 2 answer.
=4 8÷4×2
=8÷8
= 1 which is
wrong answer

vedanta Excel in Mathematics - Book 3 128 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Simplification

EXERCISE

1. Let's tell and write the answer as quickly as possible.

a) 1 + 2 + 3 = b) 4 + 2 + 1 = c) 6 + 4 – 3 =

d) 2 + 7 – 4 = e) 5 – 3 + 2 = f) 10 – 7 – 2 =

g) 3 × 2 + 5 = h) 4 + 5 × 4 = i) 12 ÷ 6 × 3 =

j) 5 × 8 ÷ 4 = k) 7 + 12 ÷ 3 = l) 24 ÷ 8 – 1 =
2. Let's simplify.
a) 12 + 8 – 7 b) 14 – 4 – 2 c) 17 – 5 + 3
=– =+
=– = =
=

d) 5 + 2 × 4 – 1 e) 27 ÷ 9 × 4 + 3 f) 5 × 16 ÷ 2 – 10

=+– =×+ =×–

=– =+ =–

= ==
3. Let's rewrite the sums and simplify in your exercise book.

a) 8 + 5 – 7 b) 13 – 4 + 2 c) 16 – 6 – 3
f) 20 – 7 × 2
d) 4 × 2 + 5 e) 6 + 3 × 5 i) 2 × 18 ÷ 6
l) 3 × 5 + 6 – 10
g) 15 ÷ 3 – 1 h) 7 + 30 ÷ 5 o) 8 + 6 × 4 ÷ 2
r) 40 ÷ 5 × 2 – 6
j) 8 – 2 – 5 + 7 k) 10 – 4 + 8 – 6
vedanta Excel in Mathematics - Book 3
m) 9 + 7 × 4 – 8 n) 21 ÷ 3 × 2 + 5

p) 30 – 10 × 9 ÷ 3 q) 7 × 8 ÷ 4 + 6

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 129

7Unit Fraction

Fraction - Part of a whole

Classwork – Exercise
Let's say and write the answer as quickly as possible.

1. a) In how many equal parts is the avocado divided?

b) What is each part called?

Each part is of the whole avocado.

c) How do we write half in fraction?

d) How do we write two-halves in fraction?

e) How many halves make a whole? halves

2. a) In how many equal parts is the pizza divided? equal parts.

b) What is each part called?

Each part is of the whole pizza.

c) How do we write one-third in fraction?

d) How do we write two-thirds in fraction?

e) How do we write three-thirds in fraction?

f) How many thirds make a whole? thirds

3. a) In how many equal parts is the sheet of paper folded? equal part.

b) What is each part called?

Each part is of the whole sheet of paper.

c) How do we write one-quarter in fraction?

d) How do we write two-quarters in fraction?

e) How do we write three-quarters in fraction?

f) How do we write four-quarters in fraction?

g) How many quarters make a whole? quarters

vedanta Excel in Mathematics - Book 3 130 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Fraction - Part of a whole

Let's divide a rectangle into 2 equal parts. One-half
Each part is half of the whole rectangle. Two-halves

Now, let's shade half of the whole rectangle.

We write half as 1 .
2

We write two-halves as 2 .
2

Two-halves make a whole.

Let's divide a circle into 3 equal parts.

One-third Each part is one-third of the whole circle.
Two-thirds
Three-thirds Now, let's shade one-third of the whole circle.

We write one-third as 1 .
3

We write two-thirds as 2 .
3

We write three-thirds as 3 .
3

Three-thirds make a whole.

Let's divide a square into 4 equal parts.
Each part is one-quarter (or one-fourth) part of the whole square.

Let's shade one-quarter of the whole square.

We write one-quarter as 1 .
4

We write two-quarters as 2 .
4
One-quarters Two-quarters Three-quarters
3 vedanta Excel in Mathematics - Book 3
We write three-quarters as 4 .

We write four-quarters as 4 .
4

Four-quarters make a whole.

Four-quarters

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 131

Fraction - Part of a whole

Story of fraction

Dear students, let's learn what do the parts of the given fractions show?

a) What are 1 and 2 in 1 ? 1 1
2 2 3
2 1
b) What are 1 and 3 in 1 ? 3 4
3
3
c) What are 2 and 3 in 2 ? 4
3

d) What are 1 and 4 in 1 ?
4

e) What are 3 and 4 in 3 ?
4

In 1 , a whole object is divided into 2 equal parts and 1 part is taken.
2

In 1 , a whole object is divided into 3 equal parts and 1 part is taken.
3

In 2 , a whole object is divided into 3 equal parts and 2 parts are taken.
3

In 1 , a whole object is divided into 4 equal parts and 1 part is taken.
4

In 3 , a whole object is divided into 4 equal parts and 3 parts are taken.
4

Classwork – Exercise

1. Let's say and write the number of parts taken and the total number of parts in
the following fractions.

a) In 2 , the number of parts taken = , total number of parts =
2

b) In 2 , the number of parts taken = , total number of parts =
4

c) In 1 , the number of part taken = , total number of parts =
5

d) In 3 , the number of parts taken = , total number of parts =
5

e) In 7 , the number of parts taken = , total number of parts =
10

vedanta Excel in Mathematics - Book 3 132 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Fraction - Part of a whole

Classwork – Exercise
2. In the following diagrams, the parts which are taken are shaded. Let's say and

write the correct answers.

a) How many parts are taken?

How many total number of parts?

What is the fraction of the shaded parts?

b) How many parts are taken?

How many total number of parts?

What is the fraction of the shaded parts?

c) How many parts are taken?

How many total number of parts?

What is the fraction of the shaded parts?

d) How many parts are taken?

How many total number of parts?

What is the fraction of the shaded parts?

e) How many parts are taken?

How many total number of parts?

What is the fraction of the shaded parts?

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 133 vedanta Excel in Mathematics - Book 3

Fraction - Part of a whole

Classwork – Exercise
1. Let's circle the fraction that represents the shaded parts.
a) b) c) d)

433 584 226 10 3 6
343 858 562 6 10 10

2. Let's estimate which one is exactly half, one-third or one-quarter. Write 1 , 1 or
1 2 3
4 below the exact diagram.

3. Let's say and write the fractions of the shaded parts.

4. Let's shade the parts to show the given fractions.

23 1 43
35 6 10 4

vedanta Excel in Mathematics - Book 3 134 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Fraction - Part of a whole

5. Let's draw dotted lines to divide these shapes into equal parts. Shade the parts
to show the given fractions.

21 2 4
42 4 10

6. Let's count the equal parts of the whole. Say and write the answer as quickly as
possible.

There are equal parts in the whole shape.

The green triangle is 3 of the whole shape.
4

There are equal parts in the whole shape.

The green triangle is of the whole shape.

There are equal parts in the whole shape.

The yellow triangle is of the whole shape.

7. Let's tell and write the answer as quickly as possible.

a) How many halves make a whole? halves

b) How many thirds make a whole? thirds

c) How many quarters make a whole? quarters

d) How many ifths make a whole? ifths

e) How many eighths make a whole? eighths

f) How many tenths make a whole? tenths

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 135 vedanta Excel in Mathematics - Book 3

Fraction - Part of a whole

Game Time!
8. These are the equal parts of circles, rectangles and squares. Let's join these parts

and make two wholes of each of the shapes.

12

34 1
5 67 4

8 6
14 15
9 10
3
11
12 13

14 15

16 136 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

vedanta Excel in Mathematics - Book 3

Fraction - Part of a whole

9. Let's rewrite the fractions by using numerals.

a) One-half b) Two-thirds c) Three-quarters

d) Two- ifth e) Five-eighths f) Seven-tenths

10. Let's say and write the names of these fractions in words.

a) 2 b) 1 c) 3
2 3 4

d) 3 e) 2 f) 4
5 8 10

11. Let's say and write the answer as quickly as possible.

a) Mother cuts a bread into 3 equal pieces. She gives you 2 pieces. What fraction of
the bread do you get?

b) Teacher folded a paper into 4 equal parts and asked you to colour 3 parts. What
fraction of the paper did you colour?

c) You cut a pizza into 6 equal pieces. You ate 2 pieces and you gave the rest pieces
to your friends.

What fraction of the pizza did you eat?

What fraction of the pizza did you give to your friends?
It's your time!

12. Let's draw different shapes of diagram in your exercise book. Divide each diagram
into different equal parts. Shade as many parts as you wish. Write the fractions of the
shaded parts.

13. Let's take a rectangular sheet of a paper. Fold it into halves.
How many halves are there?

Shade one-half folded part.

Again, fold it into halves. Now, how many folded parts did you
make?

What is the new fraction of the previously shaded part?

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 137 vedanta Excel in Mathematics - Book 3

Fraction - Part of a whole

Numerator and denominator of a fraction

Classwork – Exercise
Let's say and write the answers as quickly as possible.

1. How many equal parts are there in the circle?

How many parts are taken to shade?

What is the fraction of the shaded part?

1In ← 1 is the numerator.
4 ← 4 is the denominator.

2. How many equal parts are there in the triangle?

How many parts are taken to shade?

What is the fraction of the shaded parts?

In this fraction, the numerator is

The denominator is

3. Again, let's say and write the total number of parts, number of parts taken,
numerators and denominators in the given fractions.

Fractions Total number Number of Numerators Denominators

of parts parts taken

1
2

3
4

4
10

4. It's your time! Let's write your fractions. Then write the numerators and
denominators.

a) Fraction is 138 b) Fraction is
numerator is numerator is
denominator is denominator is

vedanta Excel in Mathematics - Book 3 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Fraction - Part of a whole

Like and Unlike fractions

Classwork – Exercise
1. Let's tell and write the answer as quickly as possible.

Number of equal parts in rectangle A are A

Number of equal parts in rectangle B are B
The fraction of the shaded part in A is

The fraction of the shaded parts in B is

Here, both the rectangles are divided into the same (like) number of parts.

So, 1 and 2 are the like fractions.
3 3

P Number of equal parts in rectangle P are

Number of equal parts in rectangle Q are

Q
The fraction of the shaded part in P is

The fraction of the shaded part in Q is

Here, the rectangles are divided into different (unlike) number of parts.

Therefore, 1 and 1 are unlike fractions.
3 4

3. Let's say and write whether the fractions of the shaded parts in these pairs of
diagrams are like or unlike fractions.

a) and are fractions.

b) and are fractions.

c) and are fractions.

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 139 vedanta Excel in Mathematics - Book 3

Fraction - Part of a whole

4. Now, let's say the answer as quickly as possible.

a) What are the denominators of the fractions 14, 2 and 43?
4

Are the denominators of these fractions same (or like)?

So, 1 , 2 and 3 are the like fractions. Like fractions have the same denominators.
4 4 4
3 4 2
b) What are the denominators of the fractions 4 , 6 and 3 ?

Are the denominators of these fractions same or different?

So, 3 , 4 and 2 are the unlike fractions. Unlike fractions have different denominators.
46 3

5. Let's tick (√) and say the like fractions. Then write the like and unlike
fractions separately.

a) 41, 1 , 42, 2 Like fractions Unlike fractions
5 3

b) 25, 3 , 35, 1 Like fractions Unlike fractions
4 2

c) 130, 2 , 110, 3 Like fractions Unlike fractions
7 5

6. Let's tell and write the answers as quickly as possible.

a) Write any two fractions like to 15. , ,
b) Write any two fractions unlike to 38. ,
c) Write any three like fractions. ,

d) Write any three unlike fractions. , ,

vedanta Excel in Mathematics - Book 3 140 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Fraction - Part of a whole

Comparison of fractions

Let's divide three pizza of the same size into halves, thirds and quarter pieces. Now,
compare the size of each piece.

Classwork – Exercise

1. Let's answer the following questions as quickly as possible.

a) Which one is the biggest piece of pizza between one-half, one-third and

one-quarter ?

b) Which one is the smallest piece of pizza between one-half, one-third and

one-quarter ?

So, 1 is greater than 1 and 1 1 > 1 and 1 > 1
2 3 4 2 3 2 4

Also, 1 is less than 1 and 1 1 < 1 and 1 < 1
4 2 3 4 2 4 3

Now, which one is bigger between 1 and 1 ?
3 4

2. Again, Let's divide rectangles of same size into different equal parts. Write
the fractions of the shaded parts. Then compare the fractions by using < , >
or = in the blanks.

2 >2 1 and 1 2
3 2 2 3
3
Approved by Curriculum Development Centre, Sanothimi, Bhaktapur
1 2 and 2 1
2 4 4 2

2 2 and 2 2
3 4 4 3

3 2 and 1 3
4 4 2 4

141 vedanta Excel in Mathematics - Book 3

Fraction - Part of a whole

ClassrColoamss–wEoxrekrc–isEexercise

1. Let's say and write the fractions of the shaded parts. Then compare the like
fractions.

a) b) c)

3 > 2 or 2 < 3 e) f)
44 44

d)

2. Let's write the fractions of the shaded parts and compare them.

a) b) c)

>< =

Comparison of like fractions

Mother helped me to cut my birthday pizza into 8 equal
pieces. I ate 2 pieces and my sister ate 3 pieces.

What fraction of whole pizza did I eat?

What fraction of whole pizza did my sister eat?

Who ate more pieces of pizza?

So, 3 > 2 or 2 < 3
8 8 8 8

In this way, to compare like fractions, we should compare numerators. Like fraction with
greater numerator is greater fraction and smaller numerator is smaller fraction.

vedanta Excel in Mathematics - Book 3 142 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Fraction - Part of a whole

Classwork – Exercise

1. Let's tell the correct answer. Then compare the fractions using < or > signs.

a) Which fraction is greater between 1 and 23? 2 > 1
3 3 3

b) Which fraction is greater between 3 and 42?
4

c) Which fraction is smaller between 3 and 54?
5

d) Which fraction is smaller between 7 and 150?
10

2. Let's put the correct sign '<' or '>' between these fractions and compare them.

a) 2 1 b) 2 3 c) 3 2 d) 3 4
3 3 4 4 5 5 5 5

e) 4 5 f) 5 3 g) 6 7 h) 9 8
6 6 7 7 8 8 10 10

3. Let's arrange these fractions in increasing order.

a) 5 , 7 , 4 ,, b) 9 , 6 , 8 ,,
9 9 9 11 11 11

4. Let's arrange these fractions in decreasing order.

a) 6 , 7 , 5 ,, b) 3 , 8 , 4 ,,
8 8 8 10 10 10

It's your time!
5. Let's write any three like fractions in increasing order and in decreasing order.

a) Increasing order: , ,

b) Decreasing order: , ,

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 143 vedanta Excel in Mathematics - Book 3

Fraction - Part of a whole

Addition of like fractions

Classwork – Exercise

There are 8 equal slices of a whole bread.
You eat 3 slices and your friends eat 2 slices.
You and your friend eat 3 + 2 = 5 slices altogether.

1. Now, let's say and write the answer as quickly as possible.

a) What is the fraction of 3 slices of the whole bread?

b) What is the fraction of 2 slices of the whole bread?

c) What is the fraction of 5 slices of the whole bread?

So, 3 + 2 = 3 + 2 = 5 ‘ Total of numerators
8 8 8 8 The same denominator

In this way, when we add the like fractions, we simply add the numerators and we write
the same denominator as it is.

2. Let's write the fractions of the yellow and green shaded parts. Then, ind the
total of the shaded parts.

3 4

a) 4 b) 5

+ = 1 + 2 = += =
c) 4
6
5 10
7
d)

+= = += =

vedanta Excel in Mathematics - Book 3 144 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Fraction - Part of a whole

Subtraction of like fractions

Classwork – Exercise

Mother cut a pizza into 4 equal pieces.
She gave you 3 pieces.
From your 3 pieces, you gave 1 piece to your friend.

1. Now, let's answer these questions as quickly as possible.

a) What fraction of whole pizza did you get?

b) What fraction of whole pizza did you give to your friend?

c) How many pieces of pizza are left with you?

So, 3 – 1 = 3–1 = 2 ‘ Difference of numerators
4 4 4 4 The same denominator

In this way, when we subtract the like fractions, we simply ind the difference of the
numerators and write the same denominator as it is.

2. Let's write the fractions of the shaded parts. Then subtract the fraction of the
crossed parts.

a) b)

×××× ×× ××
×××× ×× ××
×××× ×× ××

– = 2–1 = –= =
3
c) d)

×× ×× ×××
×× ×× ×××
×× ×× ×××

–= = –= =

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 145 vedanta Excel in Mathematics - Book 3

Fraction - Part of a whole

EXERCISE

1. Let's say and write the totals or the difference of these like fractions.

a) 1 + 1 = b) 1 + 2 = c) 1 + 2 = 1 + 1 = 1 + 1
3 3 3 3 4 4 3 3 3

d) 3 + 1 = e) 3 + 2 = f) 3 – 1 = = 2
5 5 8 8 4 4 3

1 + 2 = 1 + 2
3 3 3
3
g) 4 – 3 = h) 5 – 2 = i) 7 – 4 = = 3 = 1
6 6 7 7 10 10

2. Let's add these like fractions in your exercise book.

a) 2 + 1 b) 3 + 2 c) 4 + 3 d) 5 + 2
5 5 7 7 9 9 10 10

e) 1 + 2 + 3 f) 2 + 2 + 4 g) 3 + 4 + 2 h) 1 + 1 + 1
8 8 8 9 9 9 10 10 10 6 6 6

3. Let's subtract these like fractions in your exercise book.

a) 3 – 1 b) 4 – 2 c) 3 – 2 d) 5 – 3
4 4 5 5 6 6 7 7

e) 7 – 4 f) 6 – 5 g) 6 – 1 h) 8 – 6
8 8 9 9 7 7 10 10

It's your time!
4. Let's write like fractions. Then add or subtract them.

a) + = b) + = c) + =

d) – = e) – = f) – =

5. Let's listen to your teacher! Say and write the totals or differences of like
fractions.

a) b) c)

d) e) f)

vedanta Excel in Mathematics - Book 3 146 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Fraction - Part of a whole

6. Let's write like fractions in the blanks. Then ind the total or difference of like
fractions.

a) + = 1 + 1 = b) + = 1 + 2=
3 4

c) + = 3 + 2 = d) + = 4 + 3=
6 8

e) – = 2 – 1 = f) – = 3 – 2 =
3 5

g) – = 5 – 3 = h) – = 7–4 =
8 10

Let's read the problems carefully and solve them.

7. a) Mother cut an apple into 4 equal pieces. You ate 1 piece and brother ate 2 pieces.
What fraction of the whole apple did you and your brother eat altogether?

You and brother ate + = 1 + 2= of whole apple.
4

b) You cut your birthday cake into 7 equal pieces. You gave 2 pieces to your sister
and 3 pieces to your friends. What fraction of the whole cake did you give them in
total?

I gave + = = of the whole cake.

c) Your teacher asked you to divide a rectangular chart paper into 8 equal parts. She
then asked you to shade 4 parts with green and 3 parts with red colour. What
fraction of the whole chart paper did you colour?

I coloured + = = of the whole chart paper.

8. a) Father cut a bread into 10 equal slices and gave you 7 slices. If you ate 4 slices,
what fraction of the whole bread is left with you?

– = 7–4 = of the whole bread is left.
10

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 147 vedanta Excel in Mathematics - Book 3

Fraction - Part of a whole

b) Teacher folded a chart paper into 10 equal foldings. She/he then took 7 foldings
and shaded 4 foldings with green and the rest foldings with blue colour. What
fraction of the chart paper did teacher shade with blue colour?

+= = of the chart paper is shaded with blue.

9. Let's read the problems carefully and solve them in your exercise book.

a) A pizza is divided into a few number of equal pieces. Sunayana eats 2 parts and
the whole pizza. 8
3
Bishwant eats 8 parts of

(i) In how many pieces is the pizza divided?

(ii) What fraction of the whole pizza did Sunayana and Bishwant eat in total?

b) A rectangular chart paper is divided into a few number of equal parts. Deejina

coloured 4 parts and Shreyasha coloured 2 parts of the whole chart paper.
7 7

(i) In how many parts is the chart paper divided?

(ii) What fraction of the chart paper is coloured by Deejina and Shreyasha in total?

c) A restaurant chef cut a cheese into a few number of e14q0upaal prtisectoesmaankdetoaopkiz1z80a.parts
of the whole cheese. From these parts she/he used

(i) In how many pieces was the cheese cut into?

(ii) What fraction of the whole cheese was left with the chef?

d) Out of 10 equal pieces of an apple you take 7 pieces. From these 7 pieces you give
3 pieces to your brother.

(i) What fraction of the whole apple do you take?

(ii) What fraction of the whole apple do you given to your brother?

(iii) What fraction of the apple is left with you?

e) Out of 8 equal slices of a bread, mother took 5 slices and gave 2 slices to her
daughter. What fraction of the whole bread was left with mother?

vedanta Excel in Mathematics - Book 3 148 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Fraction - Part of a whole

Fractions of number of things in a group or collection

Classwork – Exercise

1. Let's tell and write the answer as quickly as possible.

a) How many pencils are there in picture?

b) How many pencils are of green colour?

c) How many pencils are of red colour?

d) Are green and red coloured pencils equal?

Here, half of 6 pencils = 1 of 6 = 6 › 2 = 3 pencils are green
2

half of 6 pencils = 1 of 6 = 6 › 2 = 3 pencils are red
2

2. Let's write the correct numbers in the blanks spaces.

a) 1 of 8 fruits = 8 › 2 = are apples
2

1 of fruits = › = are bananas
2

b) 1 of fruits = › = are apples
3

1 of fruits = › = are bananas
3

1 of fruits = › = are persimmons.
3

c) 1 of crayons = › = are pink
4

1 of crayons = › = are green
4

1 of crayons = › = are yellow
4

1 of crayons = › = are blue
4

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 149 vedanta Excel in Mathematics - Book 3

Fraction - Part of a whole

3. Let's draw lines to divide each group of balls into halves, thirds or quarters.
Then tell and write the numbers.

a) b) c)

1 of = 1 of = 1 of =
2 2 2

d) e) f)

1 of = 1 of = 1 of =
3 3 3

g) h) i)

1 of = 1 of = 1 of =
4 4 4

4. Let's ind the value of the fractions of numbers.

a) 1 of 12 = ÷ = b) 1 of 20 = ÷ =
2 2

c) 1 of 24 = ÷ = d) 1 of 30 = ÷ =
3 3

e) 1 of 28 = ÷ = f) 1 of 36 = ÷ =
4 4

g) 1 of 40 = ÷ = h) 1 of 55 = ÷ =
5 5

i) 1 of 50 = ÷ = j) 1 of 100 = ÷ =
10 10

k) 1 of 24 = ÷ = l) 1 of 24 = ÷ =
6 8

vedanta Excel in Mathematics - Book 3 150 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur