Class 5 Mathematics - Chapter – 7 Fractions

D.T.E.A. Senior Secondary Schools, New Delhi.

Class 5 Mathematics

Chapter – 7 Fractions

Exercise 7 A

1.Tick the fraction that is equal to the fraction shown by the shaded figure.

2. Fill in the blanks.

(a) 𝟏

𝟐 of 36 =

𝟏

𝟐 of 36 =

𝟏

𝟐 X 36

= 18

(b) 𝟏

𝟑 of 45 =

𝟏

𝟑 of 45 =

𝟏

𝟑 X 45

= 15

3.Choose and write the like fractions:

a) 𝟑

𝟕 ,

𝟖

𝟗 ,

𝟒

𝟕 ,

𝟑

𝟏𝟏

Like Fractions: 𝟑

𝟕 ,

𝟒

𝟕

b) 𝟒

𝟗 ,

𝟒

𝟏𝟑 ,

𝟒

𝟏𝟓 ,

𝟔

𝟏𝟑

Like Fractions: 𝟒

𝟏𝟑 ,

𝟔

𝟏𝟑

4. Choose the proper and improper fractions and fill in.

𝟕

𝟗 ,

𝟕

𝟔 ,

𝟕

𝟕 ,

𝟏𝟐

𝟏𝟏 ,

𝟏𝟐

𝟐𝟏 ,

𝟑𝟓

𝟓𝟑

Proper Fractions: 𝟕

𝟗 ,

𝟏𝟐

𝟐𝟏 ,

𝟑𝟓

𝟓𝟑

Improper Fractions: 𝟕

𝟔 ,

𝟕

𝟕 ,

𝟏𝟐

𝟏𝟏

5. Choose and write the mixed fractions.

a) 𝟑𝟒

𝟗 ,

𝟓

𝟗 , 𝟔

𝟐

𝟓 , 7

𝟏𝟏

𝟏𝟐

Mixed Fractions: 𝟑𝟒

𝟗 , 𝟔

𝟐

𝟓 , 7

𝟏𝟏

𝟏𝟐

2

5

1

3

2

7

18

15

1

2

6

7

3

4

b) 𝟗

𝟏𝟏 ,

𝟏𝟕

𝟏𝟗 , 𝟏𝟐

𝟗

𝟏𝟑 ,

𝟏𝟓

𝟏𝟗

Mixed Fraction: 𝟏𝟐𝟗

𝟏𝟑

6. Change into mixed fractions:

a) 𝟗

𝟒

Solution:

2

4 9

-8

1

Mixed Fraction = 2𝟏

𝟒

b) 𝟕

𝟓

Solution:

1

5 7

-5

2

Mixed Fraction = 1𝟐

𝟓

7. Change into improper fraction:

a) 𝟑𝟐

𝟑

Solution:

Improper Fraction = (𝑾𝒉𝒐𝒍𝒆 𝑵𝒖𝒎𝒃𝒆𝒓 𝑿 𝑫𝒆𝒏𝒐𝒎𝒊𝒏𝒂𝒕𝒐𝒓)+𝑵𝒖𝒎𝒆𝒓𝒂𝒕𝒐𝒓

𝑫𝒆𝒏𝒐𝒎𝒊𝒏𝒂𝒕𝒐𝒓

= (𝟑 𝑿 𝟑) + 𝟐

𝟑

= 𝟏𝟏

𝟑

b) 𝟒𝟖

𝟗

Solution:

Improper Fraction = (𝑾𝒉𝒐𝒍𝒆 𝑵𝒖𝒎𝒃𝒆𝒓 𝑿 𝑫𝒆𝒏𝒐𝒎𝒊𝒏𝒂𝒕𝒐𝒓)+𝑵𝒖𝒎𝒆𝒓𝒂𝒕𝒐𝒓

𝑫𝒆𝒏𝒐𝒎𝒊𝒏𝒂𝒕𝒐𝒓

= (𝟒 𝑿 𝟗) + 𝟖

𝟗

= 𝟒𝟒

𝟗


Class 5 Mathematics

Chapter – 7 Fractions

Exercise 7 B

1. Fill in the blanks.

a) 𝟑

𝟒 =

𝟐𝟒

Solution:

As 4 x 6 = 24, the numerator should be multiplied by 6 to get equivalent fraction

𝟑 𝑿 𝟔

𝟒 𝑿 𝟔 =

𝟏𝟖

𝟐𝟒

b) 𝟓

𝟗 =

𝟑𝟔

Solution:

As 9 x 4 = 36, the numerator should be multiplied by 4 to get equivalent fraction

𝟓 𝑿 𝟒

𝟗 𝑿 𝟒 =

𝟏𝟖

𝟑𝟔

2. Use multiplication to write two equivalent fractions of:

a) 𝟐

𝟓

Solution:

𝟐 𝑿 𝟐

𝟓 𝑿 𝟐 =

𝟒

𝟏𝟎

𝟐 𝑿 𝟑

𝟓 𝑿 𝟑 =

𝟔

𝟏𝟓

Ans: 𝟐

𝟓 ,

𝟒

𝟏𝟎 ,

𝟔

𝟏𝟓

b) 𝟑

𝟖

Solution:

𝟑 𝑿 𝟐

𝟖 𝑿 𝟐 =

𝟔

𝟏𝟔

𝟑 𝑿 𝟑

𝟖 𝑿 𝟑 =

𝟗

𝟐𝟒

Ans: 𝟑

𝟖 ,

𝟔

𝟏𝟔 ,

𝟗

𝟐𝟒

3.Write two equivalent fractions using division:

a) 𝟏𝟖

𝟐𝟕

Solution:

𝟏𝟖÷𝟑

𝟐𝟕÷𝟑 =

𝟔

𝟗

𝟏𝟖÷𝟗

𝟐𝟕÷𝟗 =

𝟐

𝟑

Ans: 𝟐

𝟑 ,

𝟔

𝟗,

𝟏𝟖

𝟐𝟕

4.Change to like fractions

(a) 𝟐

𝟑 𝒂𝒏𝒅

𝟑

𝟓

Solution:

Step: 1

Find the LCM denominators

3 3 5

5 1 5

1 1

The LCM of 3 and 5 = 3 x 5 =15

Step: 2

Find the equivalent fraction of 2

3 𝑎𝑛𝑑

3

5 with common denominator 15

𝟐

𝟑=

𝟐 𝑿 𝟓

𝟑 𝑿 𝟓 =

𝟏𝟎

𝟏𝟓

𝟑

𝟓=

𝟑 𝑿 𝟑

𝟓 𝑿 𝟑 =

𝟗

𝟏𝟓

The like fractions of 𝟐

𝟑 𝒂𝒏𝒅

𝟑

𝟓 are

𝟏𝟎

𝟏𝟓 and

𝟗

𝟏𝟓

5. Are the fractions equivalent?

a) 𝟓

𝟔

𝟏𝟓

𝟏𝟐

Solution:

𝟓

𝟔

𝟏𝟓

𝟏𝟐

5X 12=60

15 X 6=90

As the products are not equal, 𝟓

𝟔 and

𝟏𝟓

𝟏𝟐 are not equal.

b) 𝟑

𝟒

𝟏𝟐

𝟏𝟔

Solution:

𝟑

𝟒

𝟏𝟐

𝟏𝟔

3 X 16 = 48

12 X 4 = 48

As the products are equal, 𝟑

𝟒 and

𝟏𝟐

𝟏𝟔 are equal.

6. Fill in with <, > or =

a) 𝟕

𝟗

𝟔

𝟗

b) 𝟏𝟑

𝟏𝟓

𝟏𝟒

𝟏𝟓

7. a) 𝟏

𝟐

𝟐

𝟓

Solution:

𝟏

𝟐

𝟐

𝟓

1 X 5= 5

2 X 2 =4

AS 5 > 4, 𝟏

𝟐

𝟐

𝟓

8. a) 𝟒𝟏𝟏

𝟐𝟏 𝟓

𝟐

𝟑

Solution:

Among mixed fraction, as 4<5

𝟒𝟏𝟏

𝟐𝟏 𝟓

𝟐

𝟑

b) 𝟓𝟏

𝟐 𝟓

𝟏

𝟑

Solution:

𝟏

𝟐

𝟏

𝟑

1 X 3 = 3 1 X 2= 2

5 𝟏

𝟐 5

𝟏

𝟑

9. Write in descending order:

a) 𝟐

𝟗 ,

𝟖

𝟗 ,

𝟔

𝟗 ,

𝟕

𝟗, 𝟏

𝟒

𝟗

Descending order = 𝟏𝟒

𝟗,

𝟖

,𝟗,

𝟕

𝟗,

𝟔

𝟗 ,

𝟐

𝟗

b) 𝟏𝟓

𝟏𝟑 ,

𝟏𝟓

𝟏𝟕 ,

𝟏𝟓

𝟏𝟗 ,

𝟏𝟓

𝟐𝟏,

𝟏𝟓

𝟏𝟔

Descending order: 𝟏𝟓

𝟏𝟑,

𝟏𝟓

𝟏𝟔,

𝟏𝟓

𝟏𝟕,

𝟏𝟓

𝟏𝟗,

𝟏𝟓

𝟐𝟏

10. Write in ascending order:

a) 𝟔

𝟕 ,

𝟓

𝟕 ,

𝟒

𝟕 ,

𝟏𝟓

𝟕, 𝟐

𝟑

𝟕

Ascending order: 𝟒

𝟕,

𝟓

𝟕 ,

𝟔

𝟕 ,

𝟏𝟓

𝟕, 𝟐

𝟑

𝟕

b) 𝟏𝟒

𝟐𝟏,

𝟏𝟕

𝟐𝟏,

𝟏𝟐

𝟐𝟏,

𝟐𝟐

𝟐𝟏, 𝟏

𝟐

𝟐𝟏

Ascending order: 𝟏𝟐

𝟐𝟏 ,

𝟏𝟒

𝟐𝟏 ,

𝟏𝟕

𝟐𝟏 ,

𝟐𝟐

𝟐𝟏, 𝟏

𝟐

𝟐𝟏

>

<

>

<

<

>

11. Arrange in ascending order.

𝟐

𝟑 ,

𝟓

𝟔 ,

𝟕

𝟗

Solution:

Step: 1

Take LCM of 3,6 and 9

2 3, 6, 9

3 3, 3, 9

3 1, 1, 3

1, 1, 1

LCM = 2 x 3 x 3 = 18

Step: 2

Find the equivalent fraction of 𝟐

𝟑 ,

𝟓

𝟔 and

𝟕

𝟗 with denominator 18

𝟐

𝟑 =

𝟐 𝑿 𝟔

𝟑 𝑿 𝟔 =

𝟏𝟐

𝟏𝟖

𝟓

𝟔 =

𝟓 𝑿 𝟑

𝟔 𝑿 𝟑 =

𝟏𝟓

𝟏𝟖

𝟕

𝟗 =

𝟕 𝑿 𝟐

𝟗 𝑿 𝟐 =

𝟏𝟒

𝟏𝟖

Ascending order = 𝟏𝟐

𝟏𝟖 ,

𝟏𝟒

𝟏𝟖 ,

𝟏𝟓

𝟏𝟖

= 𝟐

𝟑 ,

𝟕

𝟗 ,

𝟓

𝟔

12. Arrange in descending order:

𝟐

𝟒 ,

𝟕

𝟖,

𝟑

𝟖

Take LCM of 4, 8 and 8

2 4, 8, 8

2 2, 4, 4

2 1, 2, 2

1, 1, 1

LCM = 2 x 2 x 2 = 8

𝟐

𝟒 =

𝟐 𝑿 𝟐

𝟒 𝑿 𝟐 =

𝟒

𝟖

𝟕

𝟖 =

𝟕 𝑿 𝟏

𝟖 𝑿 𝟏 =

𝟕

𝟖

𝟑

𝟖 =

𝟑 𝑿 𝟏

𝟖 𝑿 𝟏 =

𝟑

𝟖

Descending order = 𝟕

𝟖 ,

𝟒

𝟖 ,

𝟑

𝟖

= 𝟕

𝟖 ,

𝟏

𝟐 ,

𝟑

𝟖

13. Reduce the fractions to lowest terms:

a) 𝟑

𝟗

Solution:

HCF of 3 and 9 = 3

Lowest term of 𝟑

𝟗 =

𝟑 ÷𝟑

𝟗÷𝟑 =

𝟏

𝟑

b) 𝟖

𝟏𝟖

Solution:

HCF of 8 and 18 = 2

Lowest term of 𝟖

𝟏𝟖 =

𝟖 ÷𝟐

𝟏𝟖 ÷𝟐 =

𝟒

𝟗


Class 5 Mathema<cs

Chapter - 7 Frac<ons

Exercise 7 C

I. Add:

a) +

Solu4on:

Sum of Like Frac4ons =

+ =

=

b)

Solu4on:

Sum of Like Frac4ons =

=

=

c) + 2

Solu4on:

= =

2 = =

+ 2 = +

= = =

27

37

Sum of Numerators Common Denominator

27

37

2 + 37

57

415

+815

Sum of Numerators Common Denominator

415

+815

=4 + 8

15121545

138

18

138

1 X 8 + 38

118

18

2 X 8 + 18

178

138

18

118

178

288

348

312

d) +

Solu<on:

= =

+ = + = = 4

2. Subtract:

a) -

Solu<on:

Difference of Like Frac<ons =

- =

=

c) -

Solu4on:

= =

- -

=

=1 = 1

56

316

316

3 X 6 + 16

196

56

316

56

196

246

815

215

Dif ference of NumeratorsCommon Denominator

815

215

615

35

249

79

249

2 X 9 + 49

229

249

79

=229

79

159

69

23


Class 5 Mathematics

Chapter - 7 Fractions

Exercise 7 D

1. Convert into like fractions and add.

a) 𝟐

𝟑 +

𝟏

𝟔

Solution:

Step: 1

Find the LCM of denominators

2 3, 6

3 3, 3

1, 1

LCM = 2 x 3 = 6

Step: 2


3 and

1


2

3 =

2 𝑋 2

3 𝑋 2 =

4

6

1

6=

1 𝑋 1

6 𝑋 1 =

1

6

2

3 +

1

6 =

4

6 +

1

6 =

5

6

b) 𝟑

𝟏𝟎 +

𝟕

𝟑𝟎

Solution:

Step: 1

Find the LCM of the denominators 10 and 30

2 10, 30

3 5, 15

5 5, 5

1, 1

Step:2


10 and

7


3 𝑋 3

10 𝑋 3 =

9

30 ;

7 𝑋 1

30 𝑋 1 =

7

30

3

10 +

7

30 =

9

30 +

7

30 =

16

30 =

8

15

c) 𝟏𝟓

𝟏𝟔 -

𝟑

𝟖

Solution:

Step:1


2 16, 8

2 8, 4

2 4, 2

2 2, 1

1, 1

LCM of 16 and 8 = 2 x 2 x 2 x 2 =16

Step: 2

Find the equivalent fraction of 𝟏𝟓

𝟏𝟔 and

𝟑

𝟖 with common denominator 16

𝟏𝟓

𝟏𝟔 =

15 𝑋 1

16 𝑋 1 =

15

16 ;

𝟑

𝟖 =

3 𝑋 2

8 𝑋 2 =

6

16

𝟏𝟓

𝟏𝟔 -

𝟑

𝟖 =

15

16 -

6

16 =

9

16

d) 𝟏𝟏

𝟏𝟐 -

𝟕

𝟏𝟓

Solution:

Step: 1


2 12, 15

2 6, 15

3 3, 15

5 1, 5

1, 1

LCM of 12 and 15 = 2 x 2 x 3 x 5 = 60


12 and

7


11

12 =

11 𝑋 5

12 𝑋 5 =

55

60 ;

7

15 =

7 𝑋 4

15 𝑋 4 =

28

60

55

60 -

28

60 =

27

60 =

9

20

2. Simplify:

𝒂) 𝟑

𝟕 +

𝟓

𝟕 -

𝟒

𝟕

Solution:

3

7 +

5

7 -

4

7 =

3+5−4

7 =

4

7

b) 5 - 𝟏

𝟔 + 2

𝟏

𝟑

Solution:

Step: 1

5

1 -

1

6 =

30−1

6 =

29

6

2 1

3 =

2 𝑋 3+1

3 =

7

3

5 - 1

6 + 2

1

3=

29

6 +

7

3

Step: 2


2 6, 3

3 3, 3

1, 1

LCM of 6 and 3 = 2 x 3 = 6

29

6 =

29 𝑋 1

6 𝑋 1=

29

6 ;

7

3=

7 𝑋 2

3 𝑋 2=

14

6

29

6+

14

6 =

43

6 = 7

1

6

3. Word Problems:

a) Sunny cuts off 3

8 of a paper strip. What portion of the strip is left?

Solution:

The portion of paper Sunny cuts off = 3

8

The portion of strip left = 1 −3

8 =

8−3

8 =

5

8

b) Mrs. Seth filled 10 litres of petrol in her car on Monday. That day her car used 31

3 litres of petrol, and on

Tuesday it used 41

2 litres of petrol.

i) How much petrol did the car use on these two days?

ii) Out of the petrol bought on Monday, how much petrol was left at the end of Tuesday?

Solution:

i) Petrol used on Monday = 31

3 litres

Petrol used on Tuesday = 41

2 litres

Total Petrol used on both days = 31

3 + 4

1

2

31

3=

(3 𝑋 3)+1

3 =

10

3

41

2=

(4 𝑋 2)+1

2 =

9

2

31

3 + 4

1

2=

10

3+

9

2

LCM 3 and 2 = 6

31

3 + 4

1

2=

10

3+

9

2 =

10 𝑋 2

3 𝑋2+

9 𝑋 3

2 𝑋 3 =

20

6+

27

6=

47

6

Total Petrol used on both days = 47

6 = 7

5

6 litres

ii) Petrol bought on Monday =10 litres

Petrol left at the end of Tuesday = 10 - 47

6

= 10 𝑋 6

1 𝑋 6−

47

6 2

= 60

6 -

47

6 6 1 3

= 13

6 - 1 2

= 21

6 litres 1

D.T.E.A. SENIOR SECONDARY SCHOOLS, NEW DELHI.

CLASS V MATHEMATICS

CHAPTER- 8 MORE ON FRACTIONS

Exercise 8A

I. Fill in the blanks.

a) 1

7 +

1

7 +

1

7 +

1

7 +

1

7 =

𝟓

7

b) 8 times 1

11 =

11

8 X 1

11=

𝟖

11

II. Multiply:

a) 3 by 𝟐

𝟏𝟑

Solution: 3 X 2

13 =

3 𝑋 2

13 =

𝟔

𝟏𝟑

b) 10 by 𝟒

𝟏𝟓

Solution: 10X 4

15 =

102𝑋 4

153 =

8

3 = 𝟐

𝟐

𝟑

c) 18 by 𝟓

𝟐𝟒

Solution: 18 X5

24 =

183𝑋 5

244 =

15

4 = 𝟑

𝟑

𝟒

d) 𝟒

𝟑𝟑 by 11

Solution:𝟒

𝟑𝟑X 11 =

4 𝑋 111

333 =

4

3 = 𝟏

𝟏

𝟑

e) 91X𝟓

𝟏𝟑

Solution: 91X 5

13 =

917𝑋 5

131 = 𝟑𝟓

f) 𝟐

𝟐𝟕 X 14

Solution:2 𝑋 14

27 =

28

27= 𝟏

𝟏

𝟐𝟕

g) 𝟖

𝟏𝟓 X 10

Solution: 8 𝑋 102

153 =

16

3= 𝟓

𝟏

𝟑

h) 𝟏𝟗

𝟑𝟓 X 1

Solution: 19 𝑋 1

35 =

𝟏𝟗

𝟑𝟓

i) 𝟏𝟎

𝟐𝟏 X 105

Solution: 10 𝑋 105155

2131

= 50

j) 𝟐𝟏

𝟏𝟎𝟎 X 0 = 0

Exercise 8B

I. Multiply:

a) 𝟏𝟐

𝟐𝟓 by

𝟓

𝟔

Solution: 12

25 X

5

6 =

122 𝑋 51

255 𝑋 61 =

𝟐

𝟓

b) 𝟑

𝟕 by

𝟐𝟖

𝟒𝟓

Solution: 3

7 X

28

45 =

31 𝑋 284

71 𝑋 4515 =

𝟒

𝟏𝟓

c) 𝟗

𝟐𝟓 X

𝟑

𝟒

Solution: 9

25 X

3

4 =

9 𝑋 3

25 𝑋 4 =

𝟐𝟕

𝟏𝟎𝟎

d) 𝟑𝟏

𝟔 X

𝟏𝟖

𝟏𝟗

Solution: 31

6 X

18

19 =

19

6 X

18

19

= 19 𝑋 183

6 𝑋 19 =3

e) 𝟐𝟏

𝟑by 6

Solution: 21

3 X 6 =

7

3X 6

= 7 𝑋 62

31 = 14

f) 3𝟑

𝟕 by 21

Solution: 33

7 X 21 =

24

7X 21

= 24 𝑋 213

71 =72

g) 6𝟑

𝟖 X 12

Solution: 63

8 X 12 =

51

8 X 12

=51 𝑋 123

82 =

153

2=76

𝟏

𝟐

h) 𝟔𝟎 X 𝟕𝟓

𝟐𝟒

Solution: 60 X 75

24 = 60X

173

24

= 605 𝑋 173

242 =

865

2= 432

𝟏

𝟐

i) 𝟗

𝟓𝟎 X 𝟖

𝟏

𝟑

Solution: 9

50 X 8

1

3 =

9

50 X

25

3

= 93 X 251

502 X 31 =

3

2 = 𝟏

𝟏

𝟐

j) 10𝟏

𝟐 X 2

𝟑

𝟕

Solution: 101

2 X 2

3

7 =

21

2 X

17

7

= 213𝑋 17

2 𝑋 71 =

51

2 = 25

𝟏

𝟐

Class 5 Mathematics - Chapter – 7 Fractions

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