Vedanta C. Math - 4 Re-print Final (2078)

Fundamental Operations

14. a) In a school assembly, students are arranged in 16 rows with 25 students
in each row. How many students are there in the assembly?

b) In a hall, chairs are arranged in 15 columns with 18 chairs in each
column. How many chairs are there in the hall?

It's your time - Project work!

15. a) A 8-10 year old child needs to drink roughly 1500 ml of water each day.
Estimate, how many millilitres of water do you drink in 1 day and in 1
week?

b) How many grams (or kilograms) of vegetables do your family (or your
hostel) consume in 1 day? Discuss with your family members (or with
hostel incharge) and estimate the quantities of vegetables consumed
in 30 days.

C) How many grams (or kilograms) of rice do your family (or your hostel)
consume in 1 day? Discuss with your family members (or hostel
incharge) and estimate the quantities of rice consumed in 30 days.

16. a) Let's draw as many circles as the number of rows equally in each row
in a chart paper. Then find the number of circles by multiplication.

b) Let's draw as many circles as the number of columns equally in
each column in a chart paper. Then find the number of circles by
multiplication.

3.9 Division - Looking back

Let's investigate a few interesting ideas about division from these
illustrations.

When 6 pencils are shared between 2 children, how many pencils will each
share?

6 ÷ 2 = 3 Each will share 3 pencils.
How many twos are there in 6?
6 ÷ 2 = 3 There are 3 twos in 6.

Classwork - Exercise

1. Let's tell and write the correct numbers in the blank spaces.

a) If 3 children share 6 pencils, how many does each get?

Each gets ÷ = pencils.

How many twos are there in 6? ÷=
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vedanta Excel in Mathematics - Book 4

Fundamental Operations

b) If 2 boys share 8 apples, how many does each get?

Each gets ÷ = apples.

How many fours are there in 8?

÷ =

c) If 4 girls share 12 guavas, how many does each get?

Each gets ÷ = guavas.

How many threes are there in 12?

÷ =

2. Let's circle and group the marbles. Then complete the division.

a) 9 divided into 3 groups b) 10 divided into 2 groups



÷ = ÷=
d) 16 divided into 4 groups
c) 15 divided into 5 groups

÷ = ÷=

3.10 Dividend, divisor, quotient, and remainder

Classwork - Exercise

Let's tell and write the answer in the blank spaces.

1. a) 18 ÷ 3 = 6 dividend is 18 divisor is 3 quotient is 6

b) 36 ÷ 4 = dividend is divisor is quotient is

c) 56 ÷ 7 = dividend is divisor is quotient is

d) 70 ÷ 10 = dividend is divisor is quotient is

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2. a) 9 ÷ 2 = 4 quotient and 1 is remainder

b) 7 ÷ 2 = quotient and is remainder

c) 10 ÷ 3 = quotient and is remainder

d) 11 ÷ 3 = quotient and is remainder

e) 18 ÷ 4 = quotient and is remainder

f) 23 ÷ 5 = quotient and is remainder

3.11 Division as repeated subtraction

Let's investigate the relation between division and subtraction from the
following illustrations.

1. How many times 2 is subtracted from 6 to get 0?

6 – 2 = 4 4–2=2 2–2=0
1 time
2 times 3 times So, 6 ÷ 2 = 3

2. How many times 3 is subtracted from 12 to get 0?

12 – 3 = 9 9 – 3 = 6 6–3=3 3 – 3 = 0
4 times
1 time 2 times 3 times So, 12 ÷ 3 = 4

Did you investigate the fact of division and subtraction?
Division is a process of repeated subtraction.

Classwork - Exercise

1. Let's write the correct number in the blank spaces.

a) How many times 2 is subtracted from 8 to get 0?

8 – 2 = , 6 – 2 = , 4 – 2 = , 2 – 2 = So, 8 ÷ 2 =

b) How many times 3 is subtracted from 9 to get 0?

9 – 3 = , 6 – 3 = , 3 – 3 = So, 9 ÷ 3 =

c) How many times 4 is subtracted from 16 to get 0?

16 – 4 = , 12 – 4 = , 8 – 4 = , 4 – 4 = So, 16 ÷ 4 =

d) How many times 6 is subtracted from 12 to get 0?

12 – 6 = , 6 – 6 = So, 12 ÷ 6 =

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Fundamental Operations

3.12 Relation between multiplication and division

Classwork - Exercise

Let's investigate the relation between multiplication and division from
the given example. Then, tell and write the correct numbers in the blank
spaces.

1. a) It is 4 × 3 = 12 It also means 12 ÷ 4 = 3

4 times 3 dots 12 dots are divided into 4 groups.

b) × = and ÷ =

c) × = and ÷ =

d) × = and ÷ =

2. a) 5 × 3 = 15, So, 15 ÷ 5 = 3 and 15 ÷ 3 = 5

b) 2 × 4 = , So, 8 ÷ 2 = and 8 ÷ 4 =

c) 4 × 7 = , So, 28 ÷ 4 = and 28 ÷ 7 =

d) 8 × 6 = , So, ÷ 8 = 6 and ÷6 =8

e) 9 × 10 = , So, ÷ 9 = 10 and ÷ 10 = 9

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

a) × = So, ÷ = and ÷ =

b) × = So, ÷ = and ÷ =

c) × = So, ÷ = and ÷ =

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Quiz time!

4. Let's tell and write the numbers as quickly as possible.
a) The product of two numbers is 14 and one of them is 2.

The other number is ÷ =

b) The product of two numbers is 18 and one of them is 6.

The other number is ÷ =

c) The quotient of 30 divided by a number is 5.

The number is ÷ =

d) The quotient of 56 divided by a number is 8.

The number is ÷ =

e) Dividend is 13, divisor is 2, quotient = remainder =

f) Dividend is 27, divisor is 5, quotient = remainder =

Puzzle Time!

5. Let's fill in the missing numbers to complete the sums.

× 4 = 20 90 ÷ =9 ÷ 4=

× × ×÷ ÷ ÷× ××

×= ÷= ÷ =3

= == = == = ==
÷ 8 =9
15 × = 60 15 ÷ =3

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

a) 24 ÷ 4 = b) 30 ÷ 5 = 5 × 1 = 5, 5 × 2 = 10, 5 × 3 = 15,
c) 42 ÷ 7 = d) 54 ÷ 6 = 5 × 4 = 20, 5 × 5 = 25, 5 × 6 = 30
So, 30 ÷ 5 = 6

e) 72 ÷ 9 = f) 80 ÷ 8 =

g) 45 ÷ 5 = h) 56 ÷ 7 =

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3.13 Division by row and column
Let's investigate the fact that how dividing into rows is different from dividing

into columns.

Dividing into rows Dividing into column
6 ÷ 2 = 3 in each row 6 ÷ 3 = 2 in each column

Classwork - Exercise

1. Let's complete these rows and columns division.

a) b) c)

÷ = ÷ = ÷ =

d) e) f)

÷ = ÷ = ÷=

2. Let's draw dotted lines and divide into rows or in columns. Then find
the quotient.

a) b) c)

12 ÷ 3 = 10 ÷ 5 = 24 ÷ 4 =

3.14 Dividing tens, hundreds, thousands,... by 10, 20, 300, 4000, ...

Let's investigate the rule of division with these numbers and become
faster than a calculator!

1. Divide 60 by 20. Equal number of zeros from
60 ÷ 20 = 6 ÷ 2 = 3 60 and 20 are cancelled.
Then 6 ÷ 2 = 3!

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2. Divide 2800 by 400. Fundamental Operations
2800 ÷ 400 = 28 ÷ 4 = 7
Equal number of zeros from
2800 and 400 are cancelled.
Then 28 ÷ 4 = 7!

3. Divide 1200 by 30. Equal number of zeros from 1200 and
1200 ÷ 30 = 120 ÷ 3 = 40 30 are cancelled. Then divide 12 by 3
and add one zero to the quotient 4.

Classwork - Exercise

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

a) 80 ÷ 20 = b) 90 ÷ 30 = c) 80 ÷ 40 =

d) 100 ÷ 50 = e) 120 ÷ 40 = f) 140 ÷ 20 =

g) 1500 ÷ 300 = h) 1800 ÷ 600 = i) 2400 ÷ 400 =

j) 2700 ÷ 300 = k) 3200 ÷ 800 = l) 4500 ÷ 500 =

m) 800 ÷ 20 = n) 1600 ÷ 80 = o) 2800 ÷ 70 =

3.15 Division facts

Now, let's learn a few important facts about division.

(i) When a number is divided by 1, the quotient is the number itself.

4 ÷ 1 = 4, 7 ÷ 1 = 7, 12 ÷ 1 = 12, and so on.

(ii) When a number is divided by itself, the quotient is always 1.

5 ÷ 5 = 1, 8 ÷ 8 = 1, 15 ÷ 15 = 1, and so on.

(iii) When 0 is divided by any non-zero number, the quotient is always 0.

0 ÷ 6 = 0, 0 ÷ 9 = 0, 0 ÷ 18 = 0, and so on.

(iv) Dividend = Divisor × Quotient + Remainder

In 7 ÷ 2 = 3 is the quotient and 1 is remainder.

So, 7 = 2 × 3 + 1 = 6 + 1 = 7 = Divisor × Quotient + Remainder

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Fundamental Operations

3.16 Division of bigger numbers

1. Let's divide 54 by 4.

4 5 4 13 ← Quotient
54 ÷ 4 = = – 4 ↓

14
40 ÷ 4 12÷4 R 1 ten 3 ones Remainder – 1 2
2 ← Remainder

2. Let's divide 118 by 5.

118 ÷ 5 = = 5 1 1 8 23 ← Quotient
= – 10 ↓
100 ÷ 5 15 ÷ 5 R
18
–15

3 ← Remainder

3. Let's divide 7246 by 7. 4. Let's divide 9018 by 9.

7) 7246 )1035 Quotient 9) 9018 )1002 Quotient
–7 –9

02 00
–0 –0

24 01
– 21 –0

36 18
– 35 – 18

1 Remainder 0 Remainder



5. Let's divide 278 by 25.

25) 278 )11 Here, divisor 25 has two digits.
–25 So, at first try to divide two digits
27 of the dividend 278.
28 27 ÷ 25 = 1 time and 2 remainder.
– 25 Then continue the process.

3
Q = 11 and R = 3

6. Let's divide 5976 by 84. Here, we cannot divide 59 by 84.
So, let's divide 597 by 84.
84) 5976)71 Trick: Let's think 59 ÷ 8. It goes 7 times.
–588 Let's try 84 × 7 = 588.
So, 597 ÷ 84 = 7 times and remainder 9.
96 Then, continue the process.
– 84

12
Q = 71 and R = 12

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Exercise - 3.3
Section A - Classwork
1. Let's tell and write the dividend and divisor. Then, find the quotient.

a) b) c)

÷ = ÷ = ÷ =

2. Let's draw as many dots as to match the sums. Ten tell and write the
quotient as quickly as possible.

a) 15 ÷ 5 = =

b) 15 ÷ 3 = =

c) 24 ÷ 6 = =

d) 24 ÷ 4 = =

3. Let's write the total number of dots and divide by number of rows or
by number of columns. Then, find the number of dots in each row and
column.

a) b)

÷ = dots in each row ÷ = dots in each column

4. Let's tell and write the missing dividend, divisor or quotient.

a) 36 ÷ = 9 b) 42 ÷ = 6 c) 56 ÷ = 7

d) 63 ÷ 7 = e) ÷ 9 = 8 f) ÷ 8 = 10

5. Let's tell and write the answer as quickly as possible. = Rs
a) The cost of 4 pencils is Rs 32. The cost of 1 pencil = ÷ = Rs
b) The cost of 5 sweets is Rs 35. The cost of 1 sweet = ÷

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c) 40 cherries are shared between 8 children equally.

Each of them gets ÷= cherries.

d) 45 students are kept in 5 rows equally. The number of students in each row

=÷= students.

e) How many times are twos be subtracted from 10 to get 0?

÷ = times
f) How many times are fives be subtracted from 15 to get 0?

÷ = times

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

a) 100 cm = 1m So, 200 cm = 200 ÷ 100 = m

b) 1000 m = 1 km So, 4000 m = 4000 ÷ 1000 = km

c) 1000 g = 1 kg So, 5000 g = 5000 ÷ 1000 = kg

d) 1000 ml = 1 l So, 8000 ml = 8000 ÷ 1000 = l

e) 100 kg = 1 quintal So, 7000 kg = 7000 ÷ 100 = quintal

7. Let's tell and write the number of rupees notes.

a) How many Rs 5 notes are there in Rs 100? ÷=

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

c) How many Rs 10 notes are there in Rs 1000? ÷=

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

e) How many Rs 50 notes are there in Rs 1000? ÷=

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

8. Let's complete division by using number lines as shown.
a)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

12 ÷ 4 =

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b)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

÷=

c)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

÷=

Section B
9. Let's rewrite the sums and find the quotients in your exercise book.

a) 80 ÷ 20 b) 800 ÷ 20 c) 8000 ÷ 20 d) 8000 ÷ 200

e) 60 ÷ 30 f) 600 ÷ 30 g) 6000 ÷ 30 h) 6000 ÷ 300

i) 120 ÷ 40 j) 250 ÷ 50 k) 360 ÷ 90 l) 4200 ÷ 60

m) 5600 ÷ 70 n) 32000 ÷ 400 o) 45000 ÷ 500 p) 72000 ÷ 800

Let's divide and find the quotient and remainder.

10. a) 58 ÷ 70 b) 74 ÷ 6 c) 65 ÷ 4 d) 84 ÷ 7 e) 96 ÷ 8
f) 213 ÷ 2 g) 326 ÷ 3 h) 416 ÷ 4 i) 530 ÷ 5 j) 927 ÷ 9
k) 429 ÷ 2 l) 638 ÷ 3 m) 853 ÷ 4 n) 767 ÷ 5 o) 852 ÷ 6

11. a) 4602 ÷ 4 b) 5963 ÷ 5 c) 6792 ÷ 6 d) 7856 ÷ 7 e) 3276 ÷ 3

f) 7156 ÷ 7 g) 8024 ÷ 8 h) 1348 ÷ 3 i) 2352 ÷ 4 j) 5257 ÷ 7

12. a) 168 ÷ 14 b) 185 ÷ 15 c) 216 ÷ 21 d) 360 ÷ 24 e) 550 ÷ 32

f) 152 ÷ 16 g) 210 ÷ 26 h) 1470 ÷ 35 i) 3358 ÷ 54 j) 5699÷ 78

Let's read these problems carefully and solve them.

13. a) The cost of 5 kg of rice is Rs 425. Find the cost of 1 kg of rice.

b) If the cost of 1 kg of rice is Rs 85, how many kilograms of rice can be
bought for Rs 425?

c) The cost of 8 l of milk is Rs 768. Find the cost of 1 l of milk.

d) If the rate of cost of milk is Rs 96 per litre, how many litres of milk can
be purchased for Rs 768?

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14. a) In 1 dozen of pencils there are 12 pencils. How many dozens of pencils
are there in 180 pencils?

b) 1 crate eggs contains 30 eggs. How many crates of eggs are there in 750
eggs?

c) 5 dozens of cricket balls can be kept in a box. How many boxes are
needed to keep 1440 balls?

15. a) If 12 quintals of weight is equal to 1200 kg, how many kilograms are
there in 1 quintal?

b) If 9 metric tons weight is equal to 9000 kg, how many kilograms are
there in 1 metric ton?

c) 15 bottles of equal capacity can hold 7500 ml of liquid. Find the capacity
of each bottle in millilitres.

16. a) 154 children of 14 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. 154 children of different school
teams are playing football in an inter-school football match. How many
teams are playing the match?

17. a) 540 students are arranged in 18 rows with the equal number of students
in each row. How many students are there in 1 row?

b) 480 students are arranged in some columns with 32 students in each
column. How many columns of students are there?

18. a) There are 7 days in one week. How many weeks are there in 364 days?

b) There are 12 months in one year. How many years are there in 300
months?

c) There are 365 days in one year. How many years are there in 4380
days?

It's your time - Project work!

19. a) Let's write any three 2-digit numbers. Divide them separately by any
three 1-digit divisor. Then, show that

Dividend = Divisor × Quotient + Remainder

b) Let's write any three 3-digit numbers. Divide them separately by any
three 1-digit divisor. Then, show that

Dividend = Divisor × Quotient + Remainder
Let's stick your findings on the wall-magazine of your school!

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c) Let's draw 12 circles in 1 row, 2 rows, 3 rows, 4 rows, 6 rows and 12
rows with equal number of circles in each row in a chart paper. Find
the number of circles in each row by using division process. Stick your
findings on the school's wall-magazine!

3.17 Simplification - A single solution of a mixed operation

Classwork - Exercise

1. Let's listen to your teacher! Tell and write the answer as quickly as
possible.

a) Add 6 and 8. Then subtract 5. 6 + 8 – 5 = 14 – 5 = 9

b) Add 4 and 7. Then subtract 3. +–=–=

c) Subtract 7 from 15. Then add 9. –+=+=

d) Subtract 6 from 16. Then again subtract 4.

– – = – =

e) Multiply 5 and 4, then add 7. ×+=+=

f) Divide 27 by 3 and subtract 6. ÷–=–=

The problems given above are the mixed operations, because these problems
have more than one operations. To workout these mixed operations, we
should perform division, multiplication, addition, and subtraction in order
to get a single answer. The order of performing such mixed operation to get
a single and simple answer is called simplification.

2. First divide, then multiply, add, and subtract.

a) 8 ÷ 2 × 3 + 4 – 6 b) 10 + 7 – 15 ÷ 5 × 4

= × + – =+–×

= + – = + –

= – = –

= = vedanta Excel in Mathematics - Book 4
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3.18 Order of operations

Order of addition and subtraction

Example 1: Simplify a) 12 + 6 – 8 b) 12 – 8 + 6 c) 15 – 6 – 3

Solution

a) 12 + 6 – 8 = 18 – 8 b) 12 – 8 + 6 = 4 + 6 c) 15 – 6 – 3 = 9 – 3

= 10 = 10 =6

Order of multiplication, addition, and subtraction

Example 2: Simplify a) 4 × 7 + 2 b) 2 + 4 × 7 c) 20 – 5 × 3

Solution 4 × 7 + 2 = 4 × 9 = 36
Which is the wrong order!
a) 4 × 7 + 2 = 28 + 2
2 + 4 × 7 = 6 × 7 = 42
= 30 Which is the wrong order!

b) 2 + 4 × 7 = 2 + 28 20 – 5 × 3 = 15 × 3 = 45
Which is the wrong order!
= 30

c) 20 – 5 × 3 = 20 – 15

=5

Order of division and multiplication

Example 3: Simplify a) 24 ÷ 4 × 2 b) 2 × 24 ÷ 4

Solution 24 ÷ 4 × 2 = 24 ÷ 8 = 3
Which is the wrong order!
a) 24 ÷ 4 × 2 = 6 × 2
Another process
= 12 2 × 24 ÷ 4 = 48 ÷ 4 = 12

b) 2 × 24 ÷ 4 = 2 × 6

= 12

Example 4: Simplify 3 × 10 ÷ 5 + 12 – 4

Solution

3 × 10 ÷ 5 + 12 – 4 Another process Short process

= 3 × 2 + 12 – 4 3 × 10 ÷ 5 + 12 – 4 3 × 10 ÷ 5 + 12 – 4

= 6 + 12 – 4 = 30 ÷ 5 + 12 – 4 = 3 × 2 + 8

= 18 – 4 = 6 + 12 – 4 =6+8

= 14 = 18 – 4 = 14 = 14

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3.19 Use of brackets in simplification

Let's read these illustrations carefully and learn to use brackets in
simplifications.

Example 5: Multiply the sum of 5 and 4 by 7.
Solution

Here, the mathematical expression is (5 + 4) × 7 but not 5 + 4 × 7

(5 + 4) × 7 = 9 × 7 But 5 + 4 × 7 = 5 + 28 = 33 and it is the
wrong answer for the given problem
= 63

In this problem, at first, we need to find the sum of 5 and 4. Then, the sum
is multiplied by 7. Therefore, to find the sum at first, we enclose 5 + 4 in
the brackets ( ).

Example 6: Find 5 times the difference of 16 and 12.
Solution

Here, the difference of 16 and 12 = 16 – 12

So, 5 × (16 – 12) = 5 × 4

= 20

Example 7: Simplify a) 40 ÷ 5 × 2 + 12 – 7 b) 40 ÷ (5 × 2) + 12 – 7
Solution

a) 40 ÷ 5 × 2 + 12 – 7 b) 40 ÷ (5 × 2) + 12 – 7

= 8 × 2 + 12 – 7 = 40 ÷ 10 + 12 – 7

= 16 + 5 = 4 + 5

= 21 = 9

Exercise - 3.4
Section A - Classwork

1. Let's read the instructions and make mathematical expressions. Then
simplify.

a) Add 5 and 7, and then subtract 8. +–=–=

b) Subtract 6 from 18, and then add 4. – + = + =

c) Subtract 9 from 20, and then subtract 3. – – = – =

d) Multiply 6 and 7, and then add 10. × + = + =

e) Divide 72 by 9, and then multiply by 5. ÷ × = × =

63Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

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

a) 4 + 7 – 2 = – = b) 10 – 3 + 8 = + =

c) 16 – 5 – 6 = – = d) 4 × 6 + 3 = + =

e) 5 × 7 – 10 = – = f) 9 + 7 × 2 = + =

g) 30 – 4 × 3 = – = h) 27 ÷ 9 × 6 = × =

i) 4 × 10 ÷ 5 = × = j) 4 × 10 ÷ 5 = ÷ =

3. Let's insert the appropriate sign (+, – , ×, or ÷) in the blank spaces to
get the given answer.

a) 4 5 2 = 7 b) 4 5 2 = 18

c) 4 5 2 = 22 d) 4 5 2 = 14

e) 3 4 2 = 6 f) 3 4 2 = 5

g) 3 4 2 = 10 h) 3 4 2 = 24

i) 12 6 3 = 3 j) 12 6 3 = 5

k) 12 6 3 = 10 l) 12 6 3 = 9

Section B b) 5 × 7 – 20 + 10
Let's simplify these mixed operations.
d) 60 ÷ 6 + 3 × 4
4. a) 6 × 4 + 8 – 9 f) 10 × 4 ÷ 2 – 5 + 6
h) 54 ÷ 6 – 5 × 3 + 7
c) 30 ÷ 5 × 2 + 7 j) 4 × 18 ÷ 9 – 3 × 5 + 12
e) 9 × 8 ÷ 4 – 3
g) 56 ÷ 7 + 4 × 5 – 8
i) 30 + 2 × 10 ÷ 5 × 3 – 15

5. a) 9 + (8 – 3) b) 15 – (7 + 5)

c) 4 × (20 – 12) d) 36 ÷ (8 + 4)
e) (50 – 20) ÷ 6 f) (6 + 4) × 8 ÷ 2
g) (5 + 3) × (7 + 2) h) (12 + 16) ÷ (18 – 11)
i) 72 ÷ (15 – 6) × (12 – 8) j) 80 ÷ (14 – 9) × 2 + 7
k) (8 + 4 × 8) ÷ (6 × 3 – 10) l) (60 – 3 × 4) ÷ (7 × 5 – 29)

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6. Let's enclose the operation to perform it first by using brackets. Then,

simplify to get the given answer.

a) (3 + 2) × 5 = 25 b) 4 + 3 × 2 = 14 c) 4 × 10 – 8 = 8

d) 24 ÷ 4 × 2 = 3 e) 20 ÷ 7 + 3 = 2 f) 49 – 7 ÷ 7 = 6

g) 45 + 18 ÷ 9 = 7 h) 3 × 6 + 4 ÷ 2 = 15 i) 24 ÷ 6 – 2 × 5 = 30

7. Let's make mathematical expressions and simplify.

a) You have Rs 10 and mother gives you Rs 5 more. If you spend Rs 8, how
much money do you have now?

Solution

Rs10+Rs5–Rs8=

So, I have Rs now.

b) Bishwant had 9 sweets. He ate 4 sweets and again he bought 7 sweets.
How many sweets did he have now?

c) There are 25 students in a school bus. 6 students get down at one place
and 8 students get down at another place. How many students are left
in the bus?

d) There are 7 rows of 5 chairs in each row and 4 more chairs in a room.
How many chairs are there in the room?

Solution

7 × 5 + 4 =

So, there are chairs in the room.

e) Bina Magar had 7 color pencils. She bought a few more colour pencils
for Rs 40 at the rate of Rs 8 each. How many colour pencils does she
have now?

f) On Friday, there were 27 students in class four. 16 of them were girls
and the rest were boys. If only 3 boys were absent on that day, find the
number of boys in class four.

g) Ram, Hari and Laxmi were in a race. When Ram finished the race, Hari
was 5 metres behind Ram and Laxmi was 9 metres behind Hari. How
far away from the finish line was Laxmi?

h) After buying 5 chocolates at Rs 10 each, Kalpana Rai had Rs 25 left.
How much money did she have at first?

Let's make mathematical expressions using brackets. Then simplify.

8. a) The sum of 6 and 10 is subtracted from 25.

Solution

25 – (6 + 10) =

65Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

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b) The sum of 4 and 5 is multiplied by 6.
c) The difference of 20 and 8 is divided by 3.
d) The product of 6 and 4 is divided by 8.
e) 56 is divided by the sum of 3 and 4.

9. a) A sick person takes 20 ml of medicine twice a day. How much medicine
does she take in a week?

Solution

7 × (20 ml + 20 ml) =

So, she takes ml of medicine in a week.

b) The distance between your house and your school is 4 km. How many
kilometres do you travel in 6 days?

c) The highway distance between Birendra Bazar and Lahan is 55 km.
Mr. Mahato travelled 25 km by a taxi, 27 km by a bus and the remaining
distance he walked. How many kilometres did he walk?

d) You buy a pen for Rs 30 and a box for Rs 85. If you give Rs 150 to the
shopkeeper, what changes does the shopkeeper return you?

e) There are 4 girls and 3 boys in each group. How many students are
there in 5 groups?

f) Mrs. Shrestha earns Rs 3500 in a week. She spends Rs 200 everyday to
run her house. How much money does she save in a week?

g) Teacher divided 50 sweets equally between 12 boys and 13 girls of
class four. How many sweets does each student get?

It's your time - Project work!

10. a) Let's rewrite these simplifications and find the mistakes. Then,
complete the simplification in the correct way. You can display your
work on wall-magazine of your school.

20 – 10 – 5 5 + 4 × 3 14 – 5 × 2 30 ÷ 3 × 2

= 20 – 5 = 9 × 3 = 9 × 2 = 30 ÷ 6

= 15 = 27 = 18 =5

b) Let's make any four your own mixed expressions by using all 4 signs
(+, –, ×, ÷) in each expressions. Simplify them and get the correct answer.

?

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Unit Factors and Multiples

4

4.1 Divisibility Test
Let's discuss about the answer of these questions.
a) Are 2, 4, 6, 8 and 10 exactly divisible by 2?
b) Are 3, 5, 7 and 9 exactly divisible by 2?
c) Are 3, 6, 9, 12, 15 and 18 exactly divisible by 3?
d) Are 4, 5, 7, 8, 10 and 11 exactly divisible by 3?

When a dividend is divisible by a divisor with no remainder, the dividend
is called exactly divisible by the divisor.

10 ÷ 2 = 5 quotient with no remainder. 10 is exactly divisible by 2.

13 ÷ 2 = 6 quotient with 1 remainder. 13 is not exactly divisible by 2.

Now, let's learn a few rules of divisibility test.

Exactly Rules of divisibility test

divisible by

The digit at ones place of any number is 0 or even number

2 (2, 4, 6, 8). So, 90, 132, 754, 3616, 5978, ... are exactly

divisible by 2.

The sum of the digits of any number is exactly divisible by

3 3. In 225, 2 + 2 + 5 = 9 and 9 is exactly divisible by 3. So,

225 is exactly divisible by 3.

The number formed by last two digits of any number is

4 exactly divisible by 4. So, 92, 308, 924, 2564, ... are exactly

divisible by 4.

5 The digit at ones place is 0 or 5. So, 80, 170, 245, 4195, ...
are exactly divisible by 5.

6 Any even number exactly divisible by 3 are also exactly
divisible by 6. So, 84, 198, 2580, ... are exactly divisible by 6.

The sum of the digits of any number is exactly divisible by

9 9. In 486, 4 + 8 + 6 = 18 and 18 is exactly divisible by 9.

So, 486 is exactly divisible by 9.

10 The digit at ones place is 0. So, 70, 350, 830, 4120, ... are
exactly divisible by 10.

67Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Factors and Multiples

Classwork - Exercise

1. Let's circle the numbers which are exactly divisible by the given
numbers.

a) by 2 → 50 92 117 354 700 945 1681 4218

b) by 3 → 62 87 102 460 540 893 2154 5307

c) by 4 → 48 94 108 282 628 714 3236 8560

d) by 5 → 56 70 145 378 500 903 4785 7129

e) by 6 → 72 93 234 416 738 825 5160 9204

f) by 9 → 93 108 319 558 6300 7210 2457 6980

g) by 10 → 60 95 130 305 550 1002 3700 5670

2. Let's use the rule of divisibility test to find whether these numbers are
exactly divisible by 3 or 9.

a) Is 174 exactly divisible by 3? 1 + 7 + 4 = 12 Yes.
b) Is 289 exactly divisible by 9? 2 + 8 + 9 = 19 No.

c) Is 253 exactly divisible by 3? ++=

d) Is 414 exactly divisible by 3? ++=

e) Is 153 exactly divisible by 9? ++=

4.2 Factors and multiples

Let's investigate the ideas of factors and multiples from the following
examples.

In how many ways can you In how many ways can you
make 12 by multiplication? make 18 by multiplication?

1 × 12 2×6 1 × 18 2×9

12 18

3×4 3×6

So, 1, 2, 3, 4, 6 and 12 are the So, 1, 2, 3, 6, 9 and 18 are the
factors of 12. factors of 12.
18 is the multiple of 1, 2, 3, 6,
12 is the multiple of 1, 2, 3, 4, 9 and 18.
6 and 12.
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vedanta Excel in Mathematics - Book 4 68

Factors and Multiples

The factors of a number can exactly divide the number.
12 ÷ 1 = 12, 12 ÷ 2 = 6, 12 ÷ 3 = 4, 12 ÷ 4 = 3, 12 ÷ 6 = 2 and 12 ÷ 12 = 1

18 ÷ 1 = 18, 18 ÷ 2 = 9, 18 ÷ 3 = 6, 18 ÷ 6 = 3, 18 ÷ 9 = 2 and 18 ÷ 18 = 1

4.3 Prime Factors
All possible factors of 15 are 1, 3, 5 and 15. Among these factors 3 and 5 are

the prime factors because 3 and 5 are prime numbers.
Similarly, all possible factors of 20 are 1, 2, 4, 5, 10 and 20. Among these

factors, 2 and 5 are the prime factors.

Classwork - Exercise

1. Let's find the multiples. Tell and write the all possible factors of the
multiples. Then list the prime factors.

a) 1 × 4 = , 2 × 2 =

All possible factors of 4 are , and

The prime factors of 4 is

b) 1 × 6 = , 2 × 3 = ,, and
All possible factors of 6 are and
The prime factors of 6 are

c) 1 × 10 = , 2 × 5 =
All possible factors of 10 are , , and
The prime factors of 10 are and
2. Let's tell and write the all possible factors of these numbers. Then,

circle the prime factors.
a) All possible factors of 8 are , , and

b) All possible factors of 9 are , and

c) All possible factors of 15 are , , and

d) All possible factors of 20 are , , , , and

4.4 Process of finding prime factors

Let's study these examples and investigate the idea of finding prime factors
of the given numbers.

69Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Factors and Multiples

Let's find the prime factors of 12.

Here, 12 ÷ 2 = 6 and 6 ÷ 2 = 3 Factor tree

2 12 → 12 ÷ 2 = 6 12
2 2 → 6 ÷ 2 = 3 2×6

3 2× 2×3
So, 12 = 2 × 2 × 3

So, 12 = 2 × 2 × 3

Thus, to find the prime factors of a given number, we should start to divide

the number by the lowest prime number. We should continue division till

the quotient becomes a prime number. Factor tree
Again, let's find the prime factors of 24. 24

2 24 → 24 ÷ 2 = 12 2 × 12
2 12 → 12 ÷ 2 = 6

2 6 → 6 ÷ 2 = 3 2 × 2 ×6

3 2 × 2× 2 × 3
So, 24 = 2 × 2 × 2 × 3 So, 24 = 2 × 2 × 2 × 3

Classwork - Exercise

1. Let's divide the given numbers by the prime numbers till the quotient

becomes a prime numbers.

a) 2 18 b) 3 27 c) 2 30

3 3

18 = × × 27 = × × 30 = × ×

2. Let's tell and write the correct numbers in the empty circles. Then, write
the number as the product of its prime factors from the factor tree.

a) 18 b) 28 c) 36

×9 2× × 18

× ×3 × ×7 ××

2× × ×3

18 = × × 28= × × 36 = × × ×
70
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Factors and Multiples

4.5 Highest Common Factor (H. C. F.)

Classwork - Exercise
Let's tell and write the correct answer as quickly as possible.
1. a) What are the all possible factors of 8? , , ,
b) What are the all possible factors of 12? , , , , ,
c) What are the Common Factors of 8 and 12? , ,
d) Which one is the Highest Common Factor of 8 and 12?
So, the Highest Common Factor (H. C. F.) of 8 and 12 is 4.
2. a) What are the all possible factors of 10? , , ,
b) What are the all possible factors of 15? , , ,
c) What are the Common Factors of 10 and 15? , ,
d) Which one is the Highest Common Factor of 10 and 15?
So, the Highest Common Factor (H. C. F.) of 10 and 15 is 5.
4.6 Process of finding multiples of a given number
Let's study these examples and investigate the process of finding multiples

of a given number.

2 × 1 = 2 2 × 2 = 4 2 × 3 = 6 2 × 4 = 8 2 × 5 =10
So, 2, 4, 6, 8, 10, ... are the first five multiples of 2.

3 × 1 = 3 3 × 2 = 6 3 × 3 = 9 3 × 4 = 12 3 × 5 =15
So, 3, 6, 9, 12, 15, ... are the first five multiples of 3.

4.7 Lowest Common Multiple (L. C. M.)
Classwork - Exercise

Let's tell and write the first ten multiples of these pairs of numbers.

1. a) Multiples of 2 are , , , , , , , , ,

b) Multiples of 3 are , , , , , , , , ,

71Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Factors and Multiples

c) Common Multiples of 2 and 3 are , ,
d) The Lowest Common Multiple (L. C. M.) of 2 and 3 is
2. a) Multiples of 4 are , , , , , , , , ,
b) Multiples of 6 are , , , , , , , , ,
c) Common Multiples of 4 and 6 are? , ,
d) The Lowest Common Multiple (L. C. M.) of 4 and 6 is

Exercise - 4.1
Section A - Classwork
1. Let's tell and write the correct answer as quickly as possible.

a) Numbers between 59 and 71 which are exactly divisible by 2 are

, , , , ,

b) Numbers between 89 and 100 which are exactly divisible by 3.

, , ,

c) Any 5 three-digit numbers which are exactly divisible by 4.

, , , ,

d) Any 5 three-digit numbers between 100 and 150 which are exactly
divisible by 5.

, , , ,

e) Any 5 numbers between 10 and 50 which are exactly divisible by 6.

, , , ,

f) Any 5 three-digit numbers which are exactly divisible by 9.

, , , ,

g) Any 5 three-digit numbers less than 300 and exactly divisible by 10.

, , , ,

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Factors and Multiples

2. Let's tell and write these numbers as the product of their prime factors.

a) 4 = × b) 6 = × c) 8 = × ×

d) 9 = × e) 10 = × f) 12 = × ×

g) 14 = × h) 15 = × i) 20 = × ×

3. The common factors of each pair of numbers are given. Let's circle and
write the Highest Common Factor (H. C. F.).

a) Common factors of 2 and 4 are 1, 2. So, H. C. F. of 2 and 4 =

b) Common factors of 3 and 6 are 1, 3. So, H. C. F. of 3 and 6 =

c) Common factors of 4 and 8 are 1, 2, 4. So, H. C. F. of 4 and 8 =

d) Common factors of 8 and 12 are 1, 2, 4. So, H. C. F. of 8 and 12 =

4. A few common multiples of each pair of numbers are given. Let's circle
and write the Lowest Common Multiple (L. C. M.).

a) Common multiples of 2 and 4 are 4, 8, 12, ... So, L. C. M. of 2 and 4 =

b) Common multiples of 3 and 6 are 6, 12, 18, ... So, L. C. M. of 3 and 6 =

c) Common multiples of 4 and 8 are 8, 16, 24, ... So, L. C. M. of 4 and 8 =

d) Common multiples of 6 and 9 are 18, 36, 54, ... So, L. C. M. of 6 and 9 =

Section B

5. Let's use the rules of divisibility test. Then, identify which of the
following numbers are exactly divisible by 3, or 3 and 9 both.

a) 153 b) 276 c) 387 d) 489 e) 5967

6. Rewrite and complete these Factor Trees. Then, write the numbers as
the product of their prime factors.

a) 16 b) 24 c) 36
× 12 2×
2×

×× × 2× × ×
×
2× × ×3 2× ×

16 = 2 × 2 × 2 × 2 24 = 36 =

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Factors and Multiples

d) 30 e) 40 f) 54

2× 2× 2 × 27

×× ×× ××

×× ×5 ×× ×

30 = 40 = 54 =

7. Let's use the process of finding prime factors of these numbers. Then,
write the numbers as the product of their prime factors.

a) 2 16 b) 12 c) 15 d) 18 e) 20 f) 24
h) 28 i) 30 j) 32 k) 35
2 8 g) 27 m) 40 n) 42 o) 45 p) 48

2 4 l) 36

2

So, 16 = 2 × 2 × 2 × 2

8. Let's write the all possible factors of each of the following pairs of
numbers. Then, find their H. C. F.

a) 4, 8 b) 6, 9 c) 6, 8 d) 8, 12 e) 6, 12 f) 10, 15

g) 12, 16 h) 12, 18 i) 14, 21 j) 18, 24 k) 20, 30 l) 24, 30

9. Let's write the first ten multiples of each of the following pairs of
numbers. Then, find their L. C. M.

a) 2, 3 b) 3, 4 c) 4, 5 d) 4, 6 e) 2, 4 f) 3, 6

g) 5, 10 h) 4, 8 i) 6, 9 j) 6, 8 k) 4, 10 l) 8, 10

It's your time - Project Work

10. Let's play a game of finding H. C. F. of any two numbers.

H. C. F. of 4 and 6 2 is less than 4. So, Equal number
4 is less than 6. So, remove 2 circles of circles in both
remove 4 circles from 4. sides.
from 6.
46 46
46

H. C. F. is 2.
74 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur
vedanta Excel in Mathematics - Book 4

H. C. F. of 3 and 4 1 is less than 3. So, Factors and Multiples
3 is less than 4. So, remove 2 circles
remove 3 circles from 3. Equal number
from 4. of circles in both
34 sides.
34
34

H. C. F. is 1
Now, let's find the H. C. F. of these numbers by playing the games.

a) 2 and 4 b) 6 and 8 c) 6 and 9 d) 5 and 6 e) 8 and 12

11. Let's play a game of finding L. C. M. of any two numbers from 2 and 10. Make
number cards of the first ten multiples of the numbers 2 to 10. Arrange the
multiple cards of each number separately in order.

Now, let's play to find the L. C. M. of 2 and 3. 4 8 7 14
3 6 6 12
2At first, pull the multiple card of 2 2 4 5 10

3Then, pull the multiple card of 3

4Again, pull the multiple card of 2

6Then, pull the multiple card of 3

6Again, pull the multiple card of 2 is the L. C. M. of 2 and 3.

Similarly, you can find the L. C. M. of 3 and 4, 4 and 6, 5 and 7, and so on...
You can play the game with a friend also. Remember, you should pull the
multiple cards of the smaller number at first.

12. Rolling number cubes (or dice)

You can play this game with a friend. Take turns 22 1122 33 3300
rolling two number cubes (or two dice). Find the
L. C. M. of the two numbers rolled and circle in the 2300 55 1155 66

square with the answer. The first person to get 4 3300 1100 44 2200

circles in a row is the winner! 66 11 99 1122

?

75Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Fraction Fraction

Unit

5

5.1 Fraction - Looking back!

Classwork - Exercise

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

a) A pizza is divided into equal parts.

b) Fraction of 1 part is 1
4

c) Fraction of 2 parts is

d) Fraction of 3 parts is e) Fraction of 4 parts is

f) How many quarters make a whole?

2. Let's write the stories of these fractions.

a) 1 An object is divided into 2 equal parts and 1 part is taken.

2 parts are taken.
parts are taken.
b) 2 An object is divided into equal parts and parts are taken.
3

c) 3 An object is divided into equal parts and
5 An object is divided into equal parts and

d) 9
10

3. Let's read the stories and write the fractions.

a) Mother cuts an apple into 4 equal pieces and you eat 3 pieces.

What fraction of the whole apple do you eat?

b) Father cuts a bread into 6 equal slices and sister eats 4 slices.

What fraction of the whole bread does she eat?

c) Teacher divides a rectangle into 8 equal parts and she shades 5 parts.

What fraction of the whole rectangle does she shade?

vedanta Excel in Mathematics - Book 4 76 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Fraction

4. Let's tell and write the fractions of the shaded and the non-shaded parts.

Shaded Shaded Shaded Shaded

Non-shaded Non-shaded Non-shaded Non-shaded

5. What do numerator and denominator tell? Let's write the correct
answers in the blank spaces.

a) In 1 , numerator tells part is taken, denominator tells total parts.
3 parts are taken, denominator tells total parts.

b) In 3 , numerator tells
4

6. Let's write the fractions of these fraction names.

a) Two-third = b) One-quarter = c) Three-fifth =

d) Five-sixth = e) Four-seventh = f) Nine-tenth =

7. Let's estimate which one is exactly half, one-third, or one quarter. Write
1, 1, or 1 below the exact diagram.
23 4



8. Let's join the equal parts and make the whole shape. Then, 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

77Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Fraction

Let's tell and write the answers in the blank spaces. parts
9. Sunayana eats 3 parts of a whole bread.

8

a) In how many parts is the bread divided?

b) How many parts does Sunayana eat? parts.

c) What is the fraction of the parts not eaten?

5.2 Equivalent fractions

Let's take a rectangular sheet of paper and fold it into halves. Shade
one-half part. Again, fold it into halves two times.

First folding Second folding Third folding

Classwork - Exercise

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

a) What is the fraction of the shaded part in the first folding?

b) What is the fraction of the shaded parts in the second folding?

c) What is the fraction of the shaded parts in the third folding?

d) Are the shaded parts of the three folding equal?

Therefore, 1, 2, 4 are the equivalent fractions.
248

However, the numerators and the denominators of these equivalent fractions
are not equal, the shaded parts of these fractions cover the same region. So,
they are equivalent fractions.

2. Let's tell and write the fractions of the shaded parts. Also, write whether
they are equivalent fractions or not equivalent.

a) b)

and are and are
78 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur
vedanta Excel in Mathematics - Book 4

Fraction

c) d)

and are and are

5.3 Process of finding a fraction equivalent to the given fraction

Let's investigate the rule of finding fractions 1
equivalent to the given fraction. 2

1, 2 , and 3 are the equivalent fractions. 2
24 6 4

Can you tell how we would get 2 and 3 from 1? 3
46 2 6

1 = 1 × 2 = 2 and 1 = 1 × 3 = 3
2 2×2 4 2 2×3 6
Did you investigate the rule to find fractions equivalent to the given fraction?

Similarly, 2 = 2 × 2 = 4 , 2 = 2 × 3 = 6 , 2 = 2 × 5 = 10
3 3 × 2 6 3 3 × 3 9 3 3 × 5 15

Here, the fractions 4 , 6 , and 10 are equivalent to the given fraction 2.
6 9 15 3

Again, 4 = 4 ÷ 2 = 2 , 6 = 6 ÷ 3 = 2 , 10 = 10 ÷ 5 = 2
6 6÷2 3 9 9 ÷ 3 3 15 15 ÷ 5 3

Thus, when we multiply or divide the numerator and denominator of a

fraction by the same natural number, we get its equivalent fractions.

5.4 Test of equivalent fractions

Let's take any two fractions 2 and 4. Multiply the numerators and
36

denominators of these fractions in the direction of arrows.

2 4 However, in 2 6 , 2 × 10 is not equal to 5 × 6.
36 5 10

2 × 6 = 3 × 4 So, 2 and 6 are not equivalent fractions.
12 = 12 5 10

The products are equal. Therefore, 2 and 4 are equivalent fractions.
36

79Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Fraction

Classwork - Exercise

1. Let's complete the multiplication or division and find the fractions
equivalent to the given fraction.

a) 13 = 1 × = 2 , 1 = 1 × = 3 , 1 = 1 × = 4
3 × 6 3 3 × 9 3 3 × 12

So, , and are equivalent fractions to 31.

b) 28 = 2 ÷ = 1 , 3 = 3÷ = 1 , 4 = 4÷ = 1
8 ÷ 4 12 12 ÷ 4 16 16 ÷ 4

So, , and are equivalent fractions to 41.

2. Let's tell and write 'Yes' or 'No' whether these pairs of fractions are
equivalent or not.

a) 13 3 b) 2 6 c) 3 6
9 3 8 5 10

5.5 Reducing fractions to their lowest terms

Let's study the following examples and learn the process of reducing a
fraction to its lowest terms.

Example 1: Reduce the fractions a) 2 b) 6 c) 8 to their lowest terms.
4 9 10

Solution

a) 42 = 21 = 1 4Inis422t.hSeo,H42. C÷÷. F22. o=f212. and b) 6 = 62 = 2 In 6 the H. C. F. of 6 and
42 2 9 93 3 9

9 is 3. So, 6 ÷ 3 = 32.
9 ÷ 3

c) 8 = 84 = 4 In 8 the H. C. F. of 8 and 10 is 2. So, 8÷2 = 45.
10 10 5 5 10 10 ÷ 2

Example 2: Reduce the fractions a) 20 b) 800 to their lowest terms.
60 1200
Solution
Innu26m00e,rcaatnocrelatnhde
a) 20 = 20 = 2 1 = 1 equal number of zeros from
60 60 6 3 3 denominator. Then divide

the remaining number by their H. C. F.

800 800 82 2 Two zeros from 800 and 1200 are
1200 1200 12 3 3
b) = = = cancelled. Then 8 and 12 are divided by

their H. C. F. 8÷4 = 32.
12 ÷ 4

vedanta Excel in Mathematics - Book 4 80 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Fraction

Classwork - Exercise

1. Let's reduce these fractions to their lowest terms.

a) b) c)

2 = 3 = 2 =
4 6 6

d) e) f)
4 6 6
8 = 9 = 8 =

2. Let's think quickly the H. C. F. of numerator and denominator. Then
divide them by their H. C. F. and reduce the fractions to the lowest terms.

a) 4 = 4 ÷ = b) 6 = 6 ÷ = c) 4 = 4 ÷ =
6 6 ÷ 8 8 ÷ 8 8 ÷

d) 3 = 3 ÷ = e) 8 = 8÷ = f) 10 = 10 ÷ =
9 9 ÷ 12 12 ÷ 15 15 ÷

3. Let's cancel the equal number of zeros from numerator and
denominator. Then reduce the fraction to the lowest terms.

a) 10 = b) 20 = c) 30 = d) 10 =
30 30 40 = 50

e) 20 = = f) 20 = = g) 40 = h) 60 = =
60 80 60 90

Exercise - 5.1

Section A - Classwork

1. Let's match the shaded parts to the non-shaded parts of each pair of
diagrams. Then, tell and write the equivalent fractions.
a) b)

and are equivalent. and are equivalent.

2. Let's shade the parts of each pair of diagram to show the equivalent fractions.

a) 2 b) 4
5
4 6
10 8

12

81Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Fraction

3. Let's tell and write the lowest terms of these fractions.

a) 2 = b) 2 = c) 3 = d) 3 =
4 8 6 9

e) 10 = f) 30 = g) 70 = h) 800 =
50 70 100 900

Section B

4. Let's multiply the numerator and denominator of each fraction by 2, 3
and 4 respectively and find their equivalent fractions.

a) 21 b) 31 c) 41 d) 51 e) 32 f) 3
4

g) 25 h) 53 i) 45 j) 27 k) 83 l) 3
10

5. Let's divide the numerator and denominator by the same number and

find a fraction equivalent to each of these fractions.

a) 42 b) 26 c) 28 d) 120 e) 63 f) 3
9

g) 48 h) 142 i) 182 j) 10 k) 1182 l) 16
15 20

6. Let's use the rule of testing equivalent fractions. Then, find which of

the following pairs of fraction are equivalent.

a) 1 and 63 b) 2 and 96 c) 1 and 94 d) 3 and 12
2 3 3 5 20

7. Let's reduce these fractions to their lowest terms.

a) 42 b) 26 c) 36 d) 84 e) 4 f) 5
12 10

g) 93 h) 155 i) 120 j) 4 k) 360 l) 7
16 35

8. Let's cancel the equal number of zeros from numerator and

denominator of each fraction to reduce them to their lowest terms.

a) 10 b) 10 c) 20 d) 2500 e) 30 f) 30
20 40 30 40 50

g) 5400 h) 7400 i) 5600 j) 670000 k) 490000 l) 700
800

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Fraction

9. Let's divide the numerator and denominator of each fraction by their
H. C. F. and reduce them to the lowest terms.

a) 46 b) 86 c) 96 d) 140 e) 6 f) 8
10 10

g) 8 h) 9 i) 195 j) 1105 k) 1126 l) 12
12 12 18

m) 14 n) 12 o) 1250 p) 1206 q) 18 r) 21
21 20 24 28

10. Let's cancel the equal number of zeros from numerator and

denominator and reduce the fractions to their lowest terms.

a) 40 b) 60 c) 9600 d) 14000 e) 16000 f) 80
60 80 100

g) 18200 h) 112000 i) 110500 j) 125000 k) 1920000 l) 1200
1500

It's your time - Project work!

11. a) Let's write any three pairs of equivalent fractions. Draw three pairs
of rectangles of the same size and divide each pair into as many equal
parts as your fractions. Then shade the parts to show your each pair of

equivalent fractions.

b) Let's take three rectangular sheets of paper. Fold each of them to show
1 1 14.
an equivalent fraction of each of 2 , 3 and

5.6 Like and unlike fractions

Classwork - Exercise

Let's tell and write the answer as quickly as possible. A
1. a) In how many equal parts is the rectangle A divided?

b) In how many equal parts is the rectangle B divided? B

c) Are both the rectangles divided into the same number of
parts?

d) What is the fraction of the shaded parts in A?

e) What is the fraction of the shaded parts in B?

83Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Fraction

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

parts. So, 1 and 2 are like fractions. Like fractions always have the same
4 4

denominators. 51, 25, and 3 are also the like fractions. P
5

2. a) Are the rectangles P and Q divided into the same number

of parts?

b) What is the fraction of the shaded parts in P? Q

c) What is the fraction of the shaded parts in Q?

Here, the rectangles P and Q are divided into the different (unlike) number

dofepnaormtsi. nSoa,t32orasn. d1242,a34re,uannldik52e fractions. Unlike fractions have the different
are also the unlike fractions.

Classwork - Exercise

1. Let's tell 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.

2. Let's list the like and unlike fractions separately.

a) 2 , 3 , 1 , 2 Like fractions Unlike fractions
3 4 3 5 a)

b) 3 , 5 , 3 , 5 b)
8 6 10 8

5.7 Comparison of like fractions
Classwork - Exercise

1. Let's compare the shaded parts of each pair of like fractions. Then
compare the fractions using the symbols '<' or '>'.

a) b)

43 5 6
55 8 8

vedanta Excel in Mathematics - Book 4 84 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Fraction

Could you investigate the rule of comparing the like fractions?

Like fractions have the same denominators. So, the rule is 'just compare
the numerators' and compare the fractions.

2. Let's insert the appropriate symbols '<' or '>' between these like
fractions and compare them.

a) 1 2 b) 3 2 c) 5 4 d) 3 7
3 34 47 7 10 10

5.8 Conversion of unlike fractions into like fractions

Let's learn from the diagrams how 1→ 3
1 1 2 6
the unlike fractions 2 and 3 are
2
converted into the like fractions 3 and 1 → 6
6 3
2
6 respectively.

In 1 = 3 and 1 = 2 , 6 is the lowest common denominator of the like
2 6 3 6
3 26.
fractions 6 and Here, 6 is also the L. C. M. of the denominators 2 and 3

of the unlike fractions 1 and 1 .
2 3

Example 1: Convert a) 1 and 1 b) 1 and 1 into like fractions.
23 34
Solution

a) In 1 and 1 , the L. C. M. of the b) In 1 and 1 , the L. C. M. of the
2 3 3 4

denominators = 2 × 3 = 6. denominators = 3 × 4 = 12.

Now, 21 = 1 × 3 = 3 Now, 13 = 1 × 4 = 4
2 × 3 6 3 × 4 12

And, 31 = 1 × 2 = 2 And, 41 = 1 × 3 = 3
3 × 2 6 4 × 3 12

So, 3 and 2 are the like fractions. So, 4 and 3 are the like fractions.
6 6 12 12

5.9 Comparison of unlike fractions

Let's compare the shaded regions of these equal rectangle. Then, compare
the unlike fractions and also compare them by converting into the like

fractions.

85Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

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1 > 1 1×3 > 1×3 3 > 2
2 3 2×3 2×3 6 6



1 > 1 1×4 > 1×3 4 > 3
3 4 3×4 4×3 12 12

Could you investigate the rule of comparing unlike fractions?
Of course, we should convert unlike fractions into the like fractions. Then
just by comparing the numerators, we can compare the fractions.

Example 2: Compare 3 and 3 .
54
Solution

The L. C. M. of the denominators 5 and 4 = 5 × 4 = 20

Now, 53 = 3 × 4 = 12 I understood!
5 × 4 20
Numerator and denominator are
And, 43 = 3 × 5 = 15 multiplied by the same number to make
4 × 5 20 each denominator equal to the L. C. M.

Here, 1202 < 15 . So, 3 < 3
20 5 4

5.10 Proper and improper fractions

Let's investigate the ideas about proper and improper fractions from the
given illustrations.

Bishnu and Laxmi shared 1 bread Shiva and Parbati shared 2 breads
equally between them.
equally between them. Each got 2 ÷ 2 = 1 bread.
1
Each got 1 ÷ 2 = 2 of the bread.

Sita and Ram shared 3 breads equally

between them. 3 1
2 2
Each got 3 ÷ 2 = = 1 and bread.

Here, 1 of the bread has only a half part of the whole bread. So, 1 is a proper
2 2
3 1 3
fraction. But 2 of breads have 1 whole bread and 2 of a bread. So, 2 is an

improper fraction.

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Now, let's compare the numerators and denominators of these proper
and improper fractions. Then, investigate the rule to identify proper and
improper fractions.

2 is a proper fraction but 3 is an improper fraction.
3 2

3 is a proper fraction but 5 is an improper fraction.
5 3

170 is a proper fraction but 9 is an improper fraction and so on.
8

Thus, in a proper fraction, numerator is less than denominator.

In an improper fraction, numerator is greater than denominator.

5.11 Mixed numbers

Let's read the stories of a few improper fractions.

Story of 3 : A rectangle is divided into 2 equal parts and 3 parts are shaded!
2 Is it possible?

Story of 5 : A rectangle is divided into 2 equal parts and 5 parts are shaded!
2 Is it possible?

Story of 7 : A rectangle is divided into 3 equal parts and 7 parts are shaded!
3 Is it possible?

1 whole half

3 1 + 1 = 112 . So, 121 is a mixed number.
2 2

2 whole half

5 2 + 1 = 212 . So, 212 is a mixed number.
2 2

2 whole one-third

7 2 + 1 = 231 . So, 231 is a mixed number.
3 3

Thus, a fraction made up of a whole number and a proper fraction is called
mixed number (or mixed fraction).

Wanedrseoaodn1. 21 as 'one whole and half' , 213 as 'two whole and one-third',

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Classwork - Exercise

1. Let's select the correct answer and fill in the blanks.

a) 9 is a/an fraction. (proper/improper)
4 fraction. (proper/improper)

b) 4 is a/an
9

c) In a proper fraction denominator is than numerator.

(less/greater)

d) In an improper fraction denominator is than numerator.
(less/greater)

e) We get a mixed number only from a/an fraction.
(proper/improper)

2. Let's circle the proper fractions and tick the mixed numbers.

34, 43, 113, 27, 252, 72, 59, 321, 9
5

5.12 Process of changing improper fraction to mixed number

Let's study these illustrations and investigate the rule of changing an
improper fraction to a mixed number.

3 121 I got it!
2
= 3 ÷ 2 = 1Q 1R = 112 Mixed number is

Quotient Remainder
Divisor

8 = 8 ÷ 3 = 2Q 2R = 223 232
3

Could you investigate the rule? Discuss with your friends.

5.13 Process of changing mixed number to improper fraction

Let's study the stories of these mixed numbers. Then investigate the rule of
changing a mixed number to an improper fraction.

112 1 time 2 parts 1 × 2 + 1 = 2 + 1 = 3
and 1 more part 2 2 2

223 2 times 3 parts 2 × 3 + 2 = 6 + 2 = 8
and 2 more parts 3 3 3

Could you investigate the rule? Discuss with your friends.

vedanta Excel in Mathematics - Book 4 88 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

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Exercise - 5.2

Section A - Classwork

1. Which of the following pairs of diagrams represent 'like' or 'unlike'
fractions? Let's write 'like' or 'unlike' below the diagrams.

a) b) c)

fractions fractions fractions

2. Let's list the like and unlike fractions separately.

a) 54 , 47 , 3 , 5 Like fraction Unlike fraction
5 6 a)

b) 23 , 14 , 1 , 1 b)
8 3

3. Let's write the fractions of the shaded parts and compare the fractions
by using symbols '<' or '>'.

a) b)

c) d)

4. Let's compare these like fractions by using the symbol '<' or '>'.

a) 2 1 b) 3 4 c) 6 5 d) 4 7
3 35 57 7 10 10

5. Let's write the fractions of the shaded parts in these diagrams. Then,
tell and write whether they are proper or improper fractions.

a) b)

is fractions is fractions
c)
d)

is fractions is fractions

89 vedanta Excel in Mathematics - Book 4
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6. Let's tell and write the improper fractions and the mixed numbers.

a) b) c)

= = =

7. Let's list the proper, improper, and mixed fractions separately.

4 , 152 , 3 , 243 , Proper fractions Improper Fractions Mixed fractions
3 4

7 , 2 , 313 , 29, 5
5 9 7

Section B

8. Let's draw diagrams and show each pair of like fractions by shading
the parts.

a) 31 and 23 b) 1 and 34 c) 2 and 45 d) 3 and 5
4 5 6 6

9. Let's convert these unlike fractions into the like fractions.

a) 12 and 13 b) 1 and 41 c) 1 and 15 d) 2 and 2
3 2 3 5

e) 21 and 41 f) 1 and 61 g) 3 and 83 h) 1 and 5
3 4 4 6

10. Let's arrange these fractions in ascending and descending orders.

a) 73 , 2 , 5 , 74 b) 5 , 1 , 7 , 96 c) 4 , 7 , 3 , 9
7 7 9 9 9 10 10 10 10

11. Let's compare each pair of fractions by using '<' or '>' symbol.

a) 12 and 13 b) 2 and 43 c) 1 and 43 d) 1 and 1
3 2 4 5

e) 12 and 52 f) 2 and 65 g) 3 and 170 h) 1 and 2
3 5 6 9

12. Let's convert these improper fractions to mixed numbers.

a) 32 b) 5 c) 72 d) 9 e) 4 f) 5
2 2 3 3

g) 130 h) 54 i) 94 j) 56 k) 152 l) 15
4

13. Let's convert these mixed numbers to improper fractions.

a) 1 1 b) 113 c) 132 d) 221 e) 232
2 g) 314 h) 153 i) 253 j) 315

f) 134

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14. It's your time - Project work!

a) Let's draw each pair of these shaded rectangles in sheets of paper. Then,
draw dotted lines to convert unlike fractions into the like fractions. The
first one is done for you.

(i) (ii)

1 = 2 1 1 = 1 =
2 4 4 3 6

(iii) (iv)

1 = 1 = 1 = 1 =
2 3 3 4

b) Let's write three improper fractions of your own. Show them by shading
the parts in rectangles. Then, write improper fractions in the form of
mixed numbers.

5.14 Addition and subtraction of like fractions + =

Classwork - Exercise
1. Let's read carefully and answer the given questions.

Teacher folded a sheet of paper into 8 equal
parts. She cut 2 parts and gave to Pratik. Again,
she cut 3 parts and gave to Pinky.

a) How many parts did the teacher give them altogether?

b) What is the fraction of 5 parts of the whole sheet of paper?

c) What is the fraction of the parts did Pratik get?

d) What is the fraction of the parts did Pinky get?

So, 28 + 3 = 2 + 3 = 5 → Total of numerators
8 8 8 The same denominator

91Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

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

a) 3 b) 5
4 6

+ = 2 + 1 = += =
4

Could you investigate the rule of addition of like fractions?

Of course, the sum of like fractions = Total of numerators
The same denominator

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

a) b)
×××
××× ××× ×××
××× ××× ×××
××× ×××
××× ×××

– = 3 – 1 = –= =
4

Could you investigate the rule of subtraction of like fractions?

The difference of like fractions = difference of numerators
The same denominator

Exercise - 5.3

Section A - Classwork

1. Let's tell and write the sum or difference as quickly as possible.

a) 31 + 1 = b) 1 + 2 = c) 3 + 1 = d) 2 + 3 =
3 4 4 5 5 6 6

e) 32 – 31 = f) 4 – 2 = g) 6 – 2 = h) 5 – 3 =
5 5 9 9 7 7

2. Let's tell and write the missing fraction in the blank space.

a) 52 + = 3 b) 3 + = 5 c) 5 + = 8
5 8 8 9 9

d) 45 – = 2 e) 5 – = 1 f) 7 – = 4
5 7 7 10 10

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Section B

3. Let's write the fractions of the green and pink shaded parts. Then, find
the sum of the fractions.

a) b) c)

4. Let's write the fractions of the shaded parts and subtract the fractions
of the crossed parts.

a) b)×××××××× ××× ××× ××× c) ××× ×××
××××× ××× ××× ××× ××× ×××
××××× ××× ××× ××× ××× ×××
××××××× ××× ××× ××× ××× ×××

5. Let's add these like fractions.

a) 1 + 25 b) 2 + 36 c) 3 + 71 d) 5 + 28 e) 3 + 5
5 6 7 8 9 9

6. Let's subtract these like fractions.

a) 3 – 26 b) 6 – 47 c) 7 – 28 d) 8 – 5 e) 9 – 6
6 7 8 9 9 10 10

7. Let's simplify these like fractions.

a) 1 + 2 + 37 b) 3 + 4 + 120 c) 6 – 1 – 82 d) 7 – 3 – 1
7 7 10 10 8 8 9 9 9

8. Let's convert the mixed numbers into improper fractions. Then, add

or subtract.

Example: Add 131 + 231 = 3 × 1 + 1 + 3 × 2 + 1
3 3

= 3 + 1 + 6 + 1 = 4 + 7 = 4 + 7 = 11 = 332
3 3 3 3 3 3

a) 113 + 131 b) 114 + 141 c) 115 + 152 d) 231 + 313 e) 225 + 115

f) 231 – 113 g) 314 – 141 h) 421 – 321 i) 325 – 215 j) 434 – 341

Let's read these problems carefully and solve them.

9. a) You cut your birthday cake into 8 equal pieces. You gave 2 pieces to
your brother and 3 pieces to your friends. What fraction of the whole
cake did you give them altogether?

28 + 3 = = So, I gave of the whole cake.
8

93Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

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b) Mother cut a bread into 6 equal slices. You ate 2 slices and sister
ate 2 slices. What fraction of the whole bread did you and sister eat
altogether?

c) Teacher asked you to fold a rectangular sheet of paper into 4 equal
parts. Then, she asked you to colour 1 part with green and 2 parts with
blue. What fraction of the whole sheet of paper did you colour?

10. a) Father cut a bread into 7 equal slices and he gave you 5 slices. If you ate
3 slices, what fraction of the whole bread is left with you?

75 – 3 = = So, of the whole bread it left with me.
7
b) Sunayana cuts a pizza into 8 equal pieces. She gives 3 pieces to Bishwant.
What fraction of the whole pizza is left with her?

88 – 3 = = So, of the whole pizza is left.
8

c) Teacher divided a sheet of paper into 9 equal parts. She cut 4 parts and

gave to a student. What fraction of the whole sheet of paper was left

with her? 1 2
5 5
11. a) A painter mixed litre of red paint and litre of yellow paint to get an

orange paint. Find the amount of orange paint.

b) Harka Bahadur completed three-tenth of his maths homework and

four-tenth of his science homework. How much homework did he

complete altogether?

c) A pole 541 metre high is standing on the ground. The length of the pole
under the ground is 3 metre. Find the length of the pole above the
ground. 4

d) Maya Limbu ate four-seventh parts of a pizza. What fraction of the
whole pizza was left?

5.15 Addition and subtraction of unlike fractions

Let's study the given illustrations. Investigate the process of addition and

subtraction of unlike fractions.

Example 1: Add 21 + 31
Solution:
+=+

Here, the L. C. M. of 2 and 3 = 2 × 3 = 6

So, 1 = 1×3 = 3 and 1 = 1×2 = 2 1 + 13 = 3 + 2
2 2×3 6 3 3×2 6 2 6 6

Now, 1 + 1 = 3 + 2 = 3 + 2 = 5 = 3+2 = 5
2 3 6 6 6 6 6 6

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Example 2: Subtract 12 – 13
Solution
– ××××
××××
Here, the L. C. M. of 2 and 3 = 2 × 3 = 6

So, 1 = 1×3 = 3 and 1 = 1×2 = 2 1 – 13 = 3 – 2
2 2×3 6 3 3×2 6 2 6 6

Now, 1 – 1 = 3 – 2 = 3 – 2 = 1 = 3–2 = 1
2 3 6 6 6 6 6 6

Example 3: Add or Subtract a) 2 + 41 b) 45 – 1
Solution 3 2

a) Here, 2 + 41 = 2 × 4 + 1 × 3 I got it!
3 3 × 4 4 × 3
At first 2 and 1 are converted
3 4
8 3
= 12 + 12 into the like fractions.

= 8+3 = 11
12 12

4 21 = 4 × 2 1 × 5 I also understood! 4
5 5 × 2 2 × 5 5
b) Here, – – I should first convert and

= 8 – 5 1 into the like fractions.
10 10 2

= 8 –5 = 3
10 10

Exercise - 5.4

Section A - Classwork

1. Let's convert unlike fractions into the like fractions then add them.

a) 13 + 1 = 1 × 4 + 1 × 3 = + = =
4 3 × 4 ×

b) 12 + 1 = 1 × 5 + 1 × 2 = + = =
5 2 × 5 ×

c) 13 + 1 = 1 × 2 + 1 × 1 = + = =
6 3 × 6 ×

2. Let's convert unlike fractions into the like fractions then subtract them.

a) 21 – 1 = 1× + 1× = – ==
4 2×2 4×1 ==
–
b) 14 – 1 = 1× – 1× = 95 vedanta Excel in Mathematics - Book 4
8 4×2 8×1

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Fraction

c) 31 – 1 = 1× – 1× = – = =
4 3×4 4×3

Section B

3. Let's write fractions of the shaded parts. Then, add the unlike fractions
converting them into the like fractions.

a) + = + b) + = +

21 + 1 = 2 + 1
4 4 4

c) + = + d) + =+

4. Let's add these unlike fractions.

a) 12 + 13 b) 1 + 14 c) 1 + 15 d) 1 + 15 e) 1 + 1
3 2 3 4 5

f) 21 + 14 g) 1 + 16 h) 1 + 18 i) 1 + 110 j) 1 + 2
3 4 5 3 9

k) 14 + 38 l) 1 + 25 m) 3 + 130 n) 3 + 134 o) 5 + 1
2 5 7 6 12

5. Let's subtract these unlike fractions.

a) 12 – 31 b) 1 – 41 c) 1 – 15 d) 1 – 15 e) 1 – 1
3 2 3 2 4

f) 13 – 16 g) 5 – 14 h) 7 – 25 i) 3 – 35 j) 4 – 5
8 10 4 7 14

6. Let's read these problems carefully then solve them.

a) Sumnima spent 2 of her pocket money to buy a pencil and 3 of her
5 10

pocket money to buy an eraser. What fraction of her pocket money did

she spend altogether?

b) Mr. Yadav farms vegetables in 5 parts of his land and crops in 1 parts of
8 4

the land. What fraction of the land does he farm altogether?

c) Anita's water bottle can hold a total of 3 litre of water. Monoj's water
5
3
bottle can hold a total of 4 litre of water. By how much does Manoj's

water bottle hold more water than Anita's?

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d) Shova buys 5 kg of apples. Bijay buys 4 kg of oranges. By how much
6 9

does Shova buy more fruits than Bijaya?

7. It's your time - Project work?

a) Let's take a few rectangular sheets of paper. Fold them into halves,

thirds, quarters, and sixths. Then, colour 1 , 1 , 1 , and 16. Draw dotted
2 3 4

lines in each sheet of paper to show these sums.

(i) 1 + 41 (ii) 1 + 31 (iii) 1 + 61 (iv) 1 + 1
2 2 3 2 6
b) Let's write three pairs of proper like fractions of your own. Then, find

their sums and differences.

c) Let's write three pairs of proper unlike fractions of your own. Then, find
their sums and differences.

5.16 Multiplication of fractions

Classwork - Exercise

1. Let's tell and write how many times the fractions are. Then, find the
products.

a) 1 + 12 = 2 times 1 = 2 × 1 = 2×1 = 2 = 1 (whole)
2 2 2 2 2

b) 1 + 1 + 12 = times 1 = × = ==
2 2 2

c) 1 + 1 = times 1 = × = ==
3 3 3

Could you investigate the rule of multiplication of a fraction by a whole
number?

Whole number × fraction = whole number × numerator
denominator
2. Let's study the shaded parts of the diagrams. Then, complete the sums

to get the products.

a) → Half of a half = 1 × 1 = 1 × 1 = 1
2 2 2 × 2 4

b) → One-third of a half = × = =
97Approved by Curriculum Development Centre, Sanothimi, Bhaktapur
vedanta Excel in Mathematics - Book 4

Fraction

c) → Half of a one-third = × = =

Could you investigate the rule of multiplication of a fraction by a fraction?

Fraction × fraction = numerator × numerator
denominator × denominator

5.17 To find the value of fraction of a number in a collection

Classwork - Exercise

1. Let's study the given illustrations. Then, complete the sums and find

the correct answer. I got it!

a) Half of 4 apples Half of 4 = 1 × 4 and
2
= 211× 42= 2 apples
1 × 4 = 4 ÷ 2 = 2!!
2

b) Half of 6 apples c) One-third of 6 pencils

= × = apples = × = pencils

d) Two-third of 9 cherries e) Three-quarter of 12 dots

= × = cherries = × = dots

Could you investigate the rule of finding the value of fraction of a number in
a collection?

The value of the given fraction of a number = fraction × number

Exercise - 5.5

Section A - Classwork

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

a) 2 × 1 = b) 2 × 1 = c) 3 × 1 = d) 3 × 1 =
2 6 3 6

e) 1 × 1 = f) 1 × 1 = g) 1 × 1 = h) 1 × 1 =
2 2 2 3 2 4 3 4

2. Let's draw dotted lines to divide the beads into the given fractions of
the number of beads. Then, find the values of the fractions.

vedanta Excel in Mathematics - Book 4 98 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur