# Rd Sharma Solutions Class 6 Chapter 6

## Rd Sharma Solutions Class 6 Chapter 6 Fractions

Welcome to NCTB Solution. Here with this post we are going to help 6th class students for the Solutions of Rd Sharma Class 6 Mathematics, Chapter 6, Fractions. Here students can easily find Exercise wise solution for chapter 6, Fractions. Students will find proper solutions for Exercise 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8 and 6.9. Our teachers solved every problem with easily understandable methods so that every students can understand easily. Here all solutions are based on the CBSE latest curriculum.

Fractions Exercise 6.1 Solution

Question no – (5)

Solution :

20 minutes of an hour

= 20/60 …(60 min = 1 hour)

= 1/3

Therefore, 20 minutes will be 1/3 fraction of an hour.

Question no – (6)

Solution :

Natural numbers from 2 to 12 are,

= 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

Here, Prime numbers is are,

= 2, 3, 5, 7, 11,

Therefore, 5/11 fraction of them will be prime number.

Question no – (7)

Solution :

From 102 to 113, natural numbers are,

= 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113,

Here, Prime numbers are,

= 103, 107, 109, 113

Now, lets find Fraction,

= 4/12

= 1/3

Therefore, 1/3 fraction of them will be prime numbers.

Question no – (8)

Solution :

According to question,

Mukesh has 24 pencils

He gave half of them to Sunita,

= (24 – 12)

= 12

Now, After giving Sunita, Mukesh still has,

= 24 – 24/2

= 24 – 12

= 12 Pencils

Therefore, Mukesh still have 12 pencils.

Question no – (9)

Solution :

According to question,

Kavita has cassettes = 44

She gives Sonia = 3/4

Sonia has,

= 44 × 3/4

= 33

Now, number of cassettes Kavita keeps,

= (44 – 33)

= 11 cassettes,

Hence, Kavita keeps 11 cassettes.

Question no – (10)

Solution :

Shikha has frocks = 3

Her mother dyed number of frocks = 2

Fraction of dyed frocks will be = 2/3

Fractions Exercise 6.2 Solution

Question no – (1)

Solution :

2/5 on a number line : Question no – (2)

Solution :

2/7, 5/7, and 6/7 on a number line.

Question no – (3)

Solution :

2/7, 5/7, and 6/7 on a number line : Question no – (4)

Solution :

Infinite number of fractions lie between 0 and 1.

Question no – (5)

Solution :

0/8 and 8/8 on a number line : Fractions Exercise 6.3 Solution

Question no – (1)

Solution :

(i) 6 ÷ 3

As fraction = 6/3

(ii) 25 ÷ 5

As fraction = 25/5

(iii) 125 ÷ 50

As fraction = 125/50

(iv) 55 ÷ 11

∴ As fraction = 55/11

Question no – (2)

Solution :

(i) 9/7

= 9 ÷ 7

As division = 9 ÷ 7

(ii) 3/11

= 3 ÷ 11

As division = 3 ÷ 11

(iii) 90/63

= 90 ÷ 63

As division = 90 ÷ 63

(iv) 1/5

= 1 ÷ 5

As division = 1 ÷ 5

Fractions Exercise 6.4 Solution

Question no – (1)

Solution :

(i) 28/9

= 9 ÷ 28

= 3 1/9

(ii) 226/15

= 15 ÷ 226

= 15 1/15

(iii) 145/9

= 9 ÷ 145

= 16 1/9

(iv) 128/5

= 5 ÷ 128

= 25 3/5

For more better understanding : Question no – (2)

Solution :

(i) 7 1/4

= 29/4

(ii) 8 5/7

= 61/7

(iii) 5 3/10

= 53/10

(iv) 12 7/15

= 187/15

Fractions Exercise 6.5 Solution

Question no – (3)

Solution :

(i) 2/7 = 6/21

(ii) 5/8 = 10/16

(iii) 4/5 = 16/20

(iv) 45/60 = 15/20

(v) 18/24 = 3/4

Question no – (4)

Solution :

(i) Equivalent fraction of 3/5 having numerator 9 is

= 9/15

(ii) Equivalent fraction of 3/5 having denominator 30 is

= 18/30

(iii) Equivalent fraction of 3/5 having numerator 21 is

= 21/35

(iv) Equivalent fraction of 3/5 having denominator 40 is

= 24/40

Question no – (5)

Solution :

(i) Equivalent fraction to 45/60 having 15 is

= 45 ÷ 3/60 ÷ 3

= 15/20

(ii) Equivalent fraction to 45/60 having denominator 4 is

= 3/4

(iii) Equivalent fraction to 45/60 having denominator 240 is,

= 180/240

(iv) Equivalent fraction to 45/60 having numerator 135 is,

= 135/180

Question no – (6)

Solution :

(i) Faction is 35/42 Equivalent fraction having Numerator 15,

= 35 ÷ 7/42 ÷ 7

= 5/6

= 15/18

(ii) Equivalent of 35/42, having denominator 18,

= 5/6

= 15/18

(iii) Equivalent of 35/42, having denominator 30

= 5/6

= 25/30

(iv) Equivalent of 35/42, having Numerator 30

= 5/6

= 30/36

Question no – (7)

Solution :

(i) 5/9, 30/54

= 5/9 = 5 × 6/9 × 6

= 30/54

These are equivalent

(ii) 2/7, 16/42

= 2/7 = 2/7 × 8/8

= 16/56 = 15/42

These are not equivalent

(iii) 7/13, 5/11

= 7/13 × 5/5

= 35/65

Now, 5/11 × 7/7

= 35/77

These are not equivalent

(iv) 4/11, 32/88

4/11 = 4 × 8/11 × 8

= 32/88

These are equivalent

(v) 3/10, 12/50

3/10

= 3 × 4/10 × 43

= -19/40

These are not equivalent

(vi) 9/27, 25/75

9/27

= 3/9

= 1/3

Now, 25/75

= 1/3

These are equivalent.

Question no – (8)

Solution :

(i) 250/400

= 250/400

= 25/40

= 5/8 (c)

(ii) 180/200

= 180/200

= 18/20

= 9/10 (d)

(iii) 660/990

= 660/990

= 66/99

= 6/9

= 2/3 (a)

(iv) 180/360

= 180/360

= 18/36

= 1/2 (b)

(v) 220/550

= 220/550

= 22/55

= 2/5 (b)

Matching :

(i) → (c)

(ii) → (d)

(iii) → (a)

(iv) → (b)

(v) → (b)

Question no – (9)

Solution :

The equivalent fractions which enation all digits from 1 to 9 once only are,

2/6 = 3/9

2/4 = 3/6

Question no – (10)

Solution :

Ravish = 10/20

= 1/2

Shikha = 25/50

= 1/2

Priya = 40/80

= 1/2

Each has used up an equal fraction of think pencils.

Fractions Exercise 6.6 Solution

Question no – (1)

Solution :

(i) 40/75

= 8/15

(ii) 42/28

= 6/4

= 3/2

(iii) 12/52

= 6/26

= 3/13

(iv) 40/72

= 20/36

= 5/9

(v) 80/24

= 80/24

= 10/3

(vi) 84/56

= 72/8

= 6/9

= 3/2

Question no – (2)

Solution :

(i) Given, 75/80

75/80

= 15/16

(ii) Given, 52/76

52/76

= 26/38

= 13/19

(iii) Given, 84/98

84/98

= 42/49

= 6/7

(iv) Given, 68/17

68/17

= 4/1

= 4

(v) Given,150/50

150/50

= 3/1

= 3

(vi) Given, 162/108

162/108

= 18/12

= 3/2

Fractions Exercise 6.7 Solution

Question no – (2)

Solution :

2/6, 4/6, 8/6 and 6/6 on the number line : Appropriate signs between fractions.

(i) 5/6 > 2/6

(ii) 3/6 > 0/6

(iii) 1/6 < 6/0

(iv) 8/6 > 5/6

Question no – (3)

Solution :

Appropriate sings for the given fractions,

(i) 3/6 < 5/6

(ii) 4/5 > 0/5

(iii) 3/20 < 4/20

(iv) 1/7 < 1/4

Question no – (4)

Solution :

(i) 6/7 ….. 6/11

= 6/7 > 6/11

(ii) 3/7 ….. 5/7

= 3/7 < 5/7

(iii) 2/3 ….. 8/12

= 8/12 = 2/3

= 2/3 = 2/3

(iv) 1/5 ….. 4/15

= 1/5 < 4/5

(v) 8/3 ….. 8/13

= 8/3 > 8/13

(vi) 4/9 ….. 15/8

= 4/9 < 15/8

Question no – (5)

Solution :

(i) 2/12

= 1/6

(ii) 3/15

= 1/5

(iii) 8/50

= 4/25

(iv) 16/100

= 4/25

(v) 10/60

= 1/6

(vi) 15/75

= 1/5

(vii) 12/60

= 1/5

(viii) 16/96

= 1/6

(ix) 12/75

= 4/25

(x) 12/72

= 1/6

(ix) 3/18

= 3/18

= 1/6

(xii) 4/25

= 4/25

Question no – (6)

Solution :

= 2/100 < 50/100

Question no – (7)

Solution :

(i) In ascending order

= 1/9 < 2/9 < 3/9 < 4/9 < 5/9 < 6/9 < 7/9

(ii) In ascending order,

7/25 < 7/18 < 7/11 < 7/10 < 7/8

(iii) In ascending order,

= 37/1000 < 37/100 < 37/85 < 37/50 < 37/47 < 37/41

(iv) In an ascending order,

= 1/5 < 2/5 < 3/5 < 4/5

(v) In ascending order,

= 2/5 < 1/2 < 3/5 < 3/4

(vi) In ascending order,

= 3/12, 3/8, 3/6, 3/4

(vii) In ascending order,

= 5/16, 3/8, 6/12, 4/6

Question no – (8)

Solution :

(i) In descending order,

= 8/5 > 8/9 > 8/13 > 8/17

(ii) In an descending order,

= 5/9 > 1/3 > 4/15 > 3/12

(iii) In descending order,

= 5/9 > 1/3 > 4/15 > 3/12

Question no – (9)

Solution :

(i) Given, 5/9 = 4/5

5 × 5 = 4 × 9

= 25 ≠ 36

(ii) Given, 9/16 = 5/9

9 × 9 = 16 × 5

= 81 ≠ 80

(iii) Given, 4/5 = 16/20

4 × 20 = 5 × 16

80 = 80

(iv) Given, 1/15  = 4/30

1/15 = 1*2/15*2 = 2/30

Since, 2/30 < 4/40 that is 1/15 < 4/30.

Fractions Exercise 6.8 Solution

Question no – (2)

Solution :

(i) 5/12 + 1/12

= 6/12

(ii) 3/15 + 7/15

= 10/15

= 2/3

(iii) 3/22 + 7/22

= 10/22

= 5/11

(iv) 1/4 + 0/4

= 1/4

(v) 4/13 + 2/13 + 1/13

= 7/13

(vi) 0/15 + 2/15 + 1/15

= 3/15

= 1/5

(vii) 7/13 + 4/31 + 9/31

= 7 – 4 + 69/31

= 12/31

(viii) 3 2/7 + 1/7 + – 2 3/7

= 23/7 + 1/7 – 17/7

= 23 + 1 – 17//7

= 7/7

= 1

(ix) 2 1/3 – 1 2/3 + 4 1/3

= 7/3 – 5/3 + 13/3

= 7 -5 + 13/3

= 15/3

= 5

(x) 1 – 2/3 + 7/3

= 3 – 2 + 7/3

= 8/3

(xi) 16/7 – 5/7 + 9/7

= 16 – 5 + 9/7

= 20/7

= 2 6/7

Question no – (3)

Solution :

They paint together,

= (1/5 + 3/5)

= 1 + 3/5

= 4/5

Now, total unpainted part,

= (1 – 4/5)

= 5 – 4/5

= 1/5

Therefore, 1/5 room is left unpainted.

Question no – (4)

Solution :

In the question,

Ramesh bought = 2 1/2 kg sugar

Rohit bought = 3 1/2 kg of sugar

Total amount of sugar bought

= (2 1/2 + 3 1/2) kg

= (5/2 + 7/2) kg

= 12/2

= 6 kg

Therefore, total 6 kg of sugar bought by both of them.

Question no – (5)

Solution :

From the question we get,

Teacher taught of the book = 3/5

Vivek revised more on his own = 1/5

Vivek still have to revise,

= (3/5 – 1/5)

= 3 – 1/5

= 2/5

Therefore, 2/5 still have to revise.

Question no – (6)

Solution :

In the given question,

Amit was given 5/7 of a bucket of oranges

Fraction of oranges left in the basket,

= (1 – 5/7)

= 7 – 5/7

= 2/7

Therefore, 2/7 fraction of oranges was left in the basket.

Question no – (7)

Solution :

(i) 7/10 – _ = 3/10

= 7/10 – 3/10

= 7 – 3/10

= 4/10

= 2/5

(ii) _ – 3/21 = 5/21

= 5/21 + 3/21 = 5 + 3/21

= 8/21

(iii) 1 – 3/6 = 3/6

(iv) _ – 5/7 = 12/27

= 12/27 + 5/27 = 12 + 5/27

= 17/27

Fractions Exercise 6.9 Solution

Question no – (1)

Solution :

(i) In the question,

3/4 and 5/6

3/4 + 5/6

= 9 + 10/12

= 19/12

(ii) Given,

7/10 and 2/15

7/10 + 2/15

= 21 + 4/30

= 25/30

= 5/6

(iii) In the question,

= 8/13 and 2/3

8/13 + 2/3

= 24 + 26/39

= 50/39

(iv) Given,

= 4/5 and 7/15

4/5 + 7/15

= 12 +/7/15

= 19/12

Question no – (2)

Solution :

(i) In the given question,

7/16 from 2

∴ 2 – 7/16

= 32 – 7/16

= 25/16

(ii) In the given question,

= 2/7 from 19/21

19/21 – 2/7

= 19 – 2/21

= 17/21

(iii) In the question,

= 4/15 from 2 1/5

2 1/15 – 4/15

= 31/15 – 4/15

= 31/- 4/15

= 27/15

(iv) Given,

21/25 from 18/20

18/20 – 21/25

= 90 – 84/100

= 6/100

= 3/50

Question no – (3)

Solution :

(i) In the given question,

13/24 and 7/16

13/14 – 7/16

= 26 – 231/48

= 5/48

Therefore, the difference will be 5/48.

(ii) In the question,

5/18 and 4/15

5/18 – 4/15

= – 25 – 24//90

= 1/90

So, the difference is 1/90.

(iii) In the question,

1/12 and 3/4

1/12 – 3/4

= 1 – 9/12

= – 8/12

= – 2/3

Therefore, the difference is -2/3

(iv) In the question,

2/3 and 6/7

2/3 – 6/7

= 6/7 – 2/3

= 18 – 74/21

= 4/21

Hence, the difference is 4/21.

Question no – (4)

Solution :

(i) Given, 8/3 – 5/9

= 24 – 5/9

= 19/9

(ii) 4 2/5 – 2 1/5

= 4 2/5 – 2 1/5

= 22 – 11/5

= 11/5

(iii) 5 6/7 – 2 2/3

= 41/7 – 8/3

= 12 3 /56/21

= 67/21

(iv) 4 3/4 – 2 1/6

= 19/4 – 13/6

= 57 – 126/12

= 31/12

Question no – (5)

Solution :

(i) Given, 2/3 + 3/4 + 1/2

= 8 + 9 + 6/12

= 23/12

(ii) Given, 5/8 + 2/5 + 3/4

= 5/8 + 2/5 + 3/4

= 25 + 16 + 30/40

= 71/40

(iii) Given, 3/10 + 7/15 + 3/5

= 9 + 14 + 18/30

= 41/30

(iv) Given, 3/4 + 7/16 + 5/8

= 12 + 7 + 10/16

= 29/16

(v) Given, 4 2/3 + 3 1/4 + 7 1/2

= 14/3 + 13/4 + 15/2

= 56 + 39 + 90/12

= 185/12

(vi) Given, 7 1/3 + + 2/3 + 5 1/6

= 22/3 + 11/3 + 31/6

= 44 + 22 + 31/6

= 97/6

(ix) Given, 7/18 + 5/6 + 1 1/12

= 7/18 + 5/6 + 13/12

= 14 30 + 39/36

= 83/36

Question no – (6)

Solution :

(i) _ – 5/8 = 1/4

= 1/4 + 5/8

= 2 + 5/8

= 7/8

(ii) _ – 1/5 = 1/2

= – 1/5 = 1/2

= 5 + 2/10

= 7/10

(iii) 1/2 – _ = 1/6

= 1/2 – 1/6

= 3 – 1/6

= 2/6

= 1/3

Question no – (7)

Solution :

From the question we get,

Savita bought = 2/5 m of ribbon

Kavita bought = 3/4 m of ribbon

Total length of Ribbon

= (2/5+3/4)

= 8 + 15/20

= 23/20

Therefore, the total length of the ribbon they bought is 23/20 m.

Question no – (8)

Solution :

Ravish takes,

= 2 1/5 minutes

= 11/5 min

Rahul takes,

= 7/4 min

L,C,M of 4, 5 = 20

11/5 × 20 = 44 minutes (Ravish)

7/4 × 20 = 35 minute (Rahul)

Ravish take less time.

Question no – (9)

Solution :

In the question,

A wire 7/8 metres long broke into two pieces.

One piece was 1/4 meter long

Length of the other piece,

= (9/8 – 1/4)

= 7 -2/8

= 5/8 meter

Hence, the length of the other piece 5/8 metre.

Question no – (10)

Solution :

Shikhas shelf is 5/6 full of book

Priya’s shelf is 2/5 full of book

5/6 and 2/5

L.C.M of 5,6 30

= 5/6 × 30 = 25

= 2/5 × 30 = 12

Shikha’s shelf is more full

Now, (5/6-2/5) = 25 – 12/30

By 13/30

Question no – (11)

Solution :

Ravish walk,

= (9/10 – 1/2) km

= 9 – 5/10

= 4/10

= 2/5 km

Therefore, he walk 2/5 km.

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Updated: June 7, 2023 — 3:22 pm