**Rd Sharma Solutions Class 7 Chapter 5 Operations on Rational Numbers**

Welcome to NCTB Solution. Here with this post we are going to help 7th class students for the Solutions of Rd Sharma Class 7 Mathematics, Chapter 5, Operations on Rational Numbers. Here students can easily find Exercise wise solution for chapter 5, Operations on Rational Numbers. Students will find proper solutions for Exercise 5.1, 5.2, 5.3, 5.4 and 5.5. 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.

**Operations on Rational Numbers Exercise 5.1 Solution**

**Question no – (1) **

**Solution : **

**(i) -5/7 and 3/7**

= -5/7 + 3/7

= 5 + 3/7

= -2/7

**(ii) -15/4 and 7/4**

= -15 + 7/4

= -8/4

**(iii) -8/11 and -4/11**

= -8 -4/11

= -12/11

**(iv) 6/13 and -9/13**

= 6 -9/13

= -13

**Question no – (2) **

**Solution : **

**(i) 3/4 and -3/5**

= 15 – 12/20

= 3/20

**(ii) -3 and 3/5**

= +15 + 3/5

= -12/5

**(iii) -7/27 and 11/18**

= -14 + 33/54

= 19/54

**(iv) 31/-4 and -5/8**

= -62 – 5/8

= -67/8

**(3) Simplify**

**Solution : **

**(i) 8/9 + -11/6**

= 16 – 33/18

= -17/18…(Simplified)

**(ii) -5/16 + 7/24**

= -15 + 14/48

= -1/48…(Simplified)

**(iii) 1/-12 + 2/-15**

= – 5 – 8/60

= – 13/60…(Simplified)

**(iv) -8/19 + -4/57**

= – 24 – 4/57

= – 28/57…(Simplified)

**Question no – (4)**

**Solution : **

**(i) 12/5 + 4 3/10**

**∴** -12/5 + 4 3/10

= – 24 + 43/10

= + 19/10

= 19/10

= 1 9/10

**(ii) Form question we get, 24/7 + -11/4**

**∴** 24/7 + -11/4

= 96 – 77/28

= 19/28

**(iii) -31/6 + – 27/8**

**∴** -31/6 + -27/8

= -124 – 81/24

= -205/24

= -8 13/24

**Operations on Rational Numbers Exercise 5.2 Solution**

**Question no – (1)**

**Solution : **

**(i) 3/8, 5/8**

= 5/8 – 3/8

= 5 – 3/8

= 2/8

= 1/4

**(ii) -7/9, 4/9**

= 4/9 + 7/9

= 4 + 7/9

= 11/9

**(iii) -2/11, -9/11**

= -9/11 + 2/11

= 9 + 2/11

= -7/11

**(iv) 11/13, -4/13**

= -4/13 – 11/13

= -4 – 11/13

= -15/13

**Question no – (2)**

**Solution : **

(i) In the given question, 2/3 – 3/5

∴ 2/3 – 3/5

= 10 – 9/15

= 1/15

(ii) From question we get, 4/7 – 2/-3

∴ 4/7 – 2/-3

= -4/7 + 2/3

= -12 + 14/21

= 2/21

(iii) In the question, (4/7) – (-5/- 7)

∴ (4/7) – (-5/- 7)

= 4/7 – 5/7

= 4 – 5/7

= – 1/7

(iv) In the given question, -2 – 5/9

∴ -2 – 5/9

= -18 – 5/9

= -23/9

**Question no – (3)**

**Solution : **

As per the question,

Sum of the two numbers = 5/9

One numbers = 1/3

Other number = ?

∴ Other number,

= 5/9 – 1/3

= 5 – 3/9

= 2/9

Therefore, the other number is 2/9.

**Question no – (4)**

**Solution :**

According to the question,

The sum of two numbers = -1/3

One numbers is = -12/3

Other number = ?

∴ Other number,

= -1/3 + 12/3

= -1 + 12/3

= 11/3

Hence, the other number is 11/3.

**Question no – (5)**

**Solution :**

As per the question,

The sum of two numbers = -4/3

One numbers is = -5

Other number = ?

∴ Other number,

= -4/3 – (-5)

= -4/3 + 5

= -4 + 15/3

= 11/3

Therefore, the other number is 11/3.

**Question no – (6)**

**Solution :**

According to the question,

The sum of two numbers = -8

One numbers is = -15/7

Other number = ?

**∴** Other number,

= -8 – (-15/7)

= -8 + 15/7

= -56 + 15/7

= -41/7

Therefore, the other number is -41/7.

**Question no – (7)**

**Solution :**

Required number,

= 5/7 – (- 7/8)

= 5/9 + 7/8

= 40 + 63/72

= 103/72

Hence, 103/72 should be added to get 5/9.

**Question no – (8)**

**Solution :**

Required number,

= 26/33 – (-5/11)

= 26/33 + 5/11

= 26 + 15/33

= 41/33

Therefore, 41/33 should be added to get 26/33.

**Question no – (9)**

**Solution :**

Required number,

= -2/3 – (-5/7)

= 2/3 + 5/7

= -14 + 15/21

= 1/21

Thus, 1/21 should be added to get -2/3.

**Question no – (10)**

**Solution :**

Required number,

= 5/6 – (-5/3)

= 5/6 + 5/3

= 5 + 10/6

= 15/6

= 5/2

Therefore, 5/2 should be subtracted to get 5/6.

**Question no – (11)**

**Solution :**

Required number,

= 3/7 – 5/4

= 12 – 35/28

= -23/28

Hence, -23/28 should be subtracted to get 5/4.

**Question no – (12)**

**Solution :**

Given in the question,

2/3 + 3/5

= 10 + 9/15

= 19/15

**∴** Required number,

= – 2/15 – 19/15

= – 2 – 19/15

= – 21/15

= -7/5

Therefore, -7/5 should be added to get -2/15.

**Question no – (13)**

**Solution :**

In the question, 3/4 – 2/3

= 9 – 8/12

= 1/12

**∴** Required number,

= 1/12 – (- 1/6)

= 1/12 + 1/6

= 1 + 2/12

= 3/12

= 1/4

Therefore, 1/4 should be subtracted to get 5/6.

**Question no – (14)**

**Solution :**

As per the question,

3/4 – 2/3

= 9 – 8/12

= 1/12

**∴** Required number,

= 1/12 – (- 1/6)

= 1/12 + 1/6

= 1 + 2/12

= 3/12

= 1/4

Hence, 1/4 should be subtracted to get 5/6.

**Question no – (15)**

**Solution :**

**(i) Given, -3/2 + 5/4 – 7/4**

= (-6 + 5 – 7)/4

= -8/4

= -2…(Simplified)

**(ii) In the given question, 5/3 – 7/6 + -2/3**

**∴** 5/3 – 7/6 + -2/3

= 5/3 – 7/6 – 2/3

= 10 – 7 – 4/6

= -1/6…(Simplified)

**(iii) Given in the question, 5/4 – 7/6 – -2/3**

**∴** 5/4 – 7/6 – (-2/3)

= 5/4 – 7/6 + 2/3

= 30 – 28 + 16/24

= 18/24

= 6/8

= 3/4 …(Simplified)

**(iv) From the given question, -2/5+ 3/10 + 4/7**

**∴** -2/5+ 3/10 + 4/7

= -28 + 21 + 40/70

= 33/70 …(Simplified)

**Question no – (16) **

**Solution : **

**(i) (-4/13) – (-3/26) = -5/26**

Explanation :

= -4/13 + 3/26

= -8 + 3/26

= -5/26

**(ii) -9/14 + (-5/14) = -1**

Explanation :

= -1 + 9/14

= 14 + 9/14

= -5/14

**(iii) -7/9 + 34/9 = 3**

Explanation :

= 3 -(-7/9)

= 23 + 7/9

= 34/9

**(iv) 77/23 + 15/23 = 4**

Explanation :

= 4 – 15/23

= 92 – 15/23

= 77/23

**Operations on Rational Numbers Exercise 5.3 Solution**

**Question no – (1) **

**Solution : **

**(i) Given, 7/11 by 5/4**

= 7/11 × 5/4

= 35/44

**(ii) Given, 5/7 by (-3/4)**

= 5/7 × (-3/4)

= – 15/28

**(iii) Given, (-2)/9 by 5/11**

= – 2/9 × 5/11

= – 10/99

**(iv) Given, -3/17 by -5/-4**

= – 3/17 × -5/-4

= – 15/68

**Question no – (2)**

**Solution :**

**(i) -5/17 by 51/- 60**

**∴** (- 5/17) × (51/- 60)

= 3/12

= 1/4

**(ii) -6/11 by -55/36**

=- 6/11 × – 55/36

= 6 × 55/11 × 36

= 5/6

**(iii) -825 by -5/16**

**∴** -8/25 × -5/16

= 8 × 5/25 × 16

= 1/10

**(iv) Given, 6/7 by -49/36**

= 6/7 × -49/36

= 6 × 49/7 × 36

= -7/6

**Question no – (3)**

**Solution :**

**(i) -16/21 × 14/5**

= -16 × 14/21 × 5

= -32/15…(Simplified)

**(ii) 7/6 × -3/28**

= – 7 × 3/6 × 2

= – 1/8…(Simplified)

**(iii) -19/36 × 16**

= = 19 × 16/36

= – 76/6…(Simplified)

**(iv) -13/9 × 37/-26**

= 13 × 27/9 × 26

= 3/2…(Simplified)

**Question no – (4) **

**Solution :**

**(i) (-5 × 2/15) – (-6 × 2/9)**

**∴** (-5 × 2/15) – (-6 × 2/9)

= -2/3 + 4/3

= -2 + 4/3

= 2/3…(Simplified)

**(ii) (-9/4 × 5/3) + (13/2 × 5/6)**

**∴** (-9/4 × 5/3) + (13/2 × 5/6)

= -15/4 + 65/12

= -45 + 65/12

= 20/12

= 5/3…(Simplified)

**Question no – (5) **

**Solution : **

**(i)** According to the question,

= (13/9 × -15/2) + (7/3 × 8/5) + (3/5 × 1/2)

**∴** [13/9 × (-15/2)] + (7/3 × 8/5) + 3/5 × 1/2

= -195/18 + 56/15 + 3/10

= -957 + 336 27/90

= -612/90

= -34/5…(Simplified)

**(ii)** As per the question,

= (3/11 × 5/6) – (9/12 × 4/3) + (5/13 × 6/15)

**∴** (3/11 × 5/6) – (9/12 × 4/3) + (5/13 × 6/15)

= 5/22 – 1 + 2/39

= 195 – 858 + 132/858

= -531/858

= -177/286…(Simplified)

**Operations on Rational Numbers Exercise 5.4 Solution**

**Question no – (1) **

**Solution :**

**(i) Given, 1 by 1/2**

= 1 ÷ 1/2

= 1 × 2/1

= 2

**(ii) Given, 5 by -5/7**

= 5 ÷ -5/7

= 5 × 7/-5

= -7

**(iii) Given, -3/4 by 9/-16**

= -3/4 ÷ 9/-16

= 3/4 × 16/33

= 4/3

**(iv) Given, -7/8 by -21/16**

= 7/8 ÷ -21/16

= -7/8 × 16/24

= 2/3

**(v) Given, 7/-4 by 63/64**

= -7/8 ÷ 63/64

= 7/4 × 64/63

= -16/9

**(vi) Given, 0 by -7/5**

= 0 ÷ -7/5

= 0 × -5/7n

= 0

**(vii) Given, -3/4 by -6**

= -3/4 ÷ -6

= -3/4 × -1/6

= -1/8

**Question no – (2)**

**Solution :**

**(i) 2/5 ÷ 26/15**

= 2/5 × 15/26

= 5/13

Thus, the value will be 5/13 in standard form.

**(ii) 10/3 ÷ -35/12**

= 10/3 × -12/35

= -8/7

Hence, the value will be -8/7 in standard form.

**(iii) -6 ÷ (-8/17)**

= -6 × + 17/8

= 51/4

Therefore, the value will be 51/4 in standard form.

**Question no – (3)**

**Solution :**

According to the question,

Product of two rational numbers = 15

One numbers is = -10

Other number = ?

**∴** Other number,

= 15/-10

= -3/2

Therefore, the other number will be -3/2.

**Question no – (4)**

**Solution : **

As per the given question,

Product of two rational numbers = -8/9

One numbers is = -4/15

Other number = ?

**∴** Other number,

= -8/9 ÷ -4/15

= -8/9 × -15/4

= 10/3

Hence, the other number will be 10/3.

**Question no – (5)**

**Solution : **

Required number,

= -23/9 ÷ -1/6

= -23/9 × -6

= 46/3

Therefore, 46/3 should be multiplied.

**Question no – (7)**

**Solution :**

Required number,

= 24 ÷ -8/13

= 24 × -13/8

= -39

Therefore, -39 should be multiplied.

**Question no – (8)**

**Solution :**

Required number,

= 2/3 ÷ -3/4

= 2/3 × -4/3

= -8/9

Therefore, -8/9 should be multiplied.

**Question no – (9) **

**Solution :**

**(i)** x = 2/3, y = 3/2

= (2/3 + 3/2) ÷ (2/3 -3/2)

= (4 + 9/6) ÷ 4 -9/6

= 13/6 × 6/-5

= -13/5

**(ii)** x = 2/5, y = 1/2

= (x + y) ÷ (x – y)

= (2/5 + 1/2) ÷ (2/5 – 1/2)

= (4 + 5/10) ÷ (4 – 5/10)

= 9/10 × 10/-1

= -9

**Question no – (10)**

**Solution : **

According to the give question,

Cost of 7 2/3 metres of rope = 12 3/4

Cost of per metre = ?

**∴** Cost per metre,

= 12 3/4 ÷ 7 2/3

= 51/4 ÷ 23/3

= 51/4 × 3/23

= 153/92

= 1 61/92 Rs.

Therefore, the cost of per metre is 1 61/92 Rs.

**Question no – (11)**

**Solution : **

As per the question,

Cost of 2 1/3 metres of cloth = 75 1/4

Cost of per metre = ?

**∴** Cost per metre,

= 75 1/4 ÷ 2 1/3

= 301/4 ÷ 7/3

= 301/4 × 3/7

= 129/4 Rs.

Hence, the cost of per metre is 129/4 Rs.

**Question no – (12)**

**Solution : **

Required number,

= -33/16 ÷ -11/4

= -33/16 × -4/11

= 3/4

Thus, 3/4 should be divided.

**Question no – (13)**

**Solution : **

As per the question,

= – 13/5 + 12/7

= -91 + 60/35

= -31/35

And, -31/7 × -1/2

= 31/14

Then, -31/35 ÷ 31/14

= -31/35 × 14/31

= -14/31

Therefore, the result will be -14/31

**Question no – (14)**

**Solution :**

First, the sum,

= 65/12 + 8/3

= 65 + 32/12

= 97/12

Now, the difference,

= 65/12 – 8/3

= 65 – 32/12

= 33/12

**∴** Required number,

= 97/12 ÷ 33/12

= 97/12 × 12/33

= 97/33

Hence, the answer will be 97/33.

**Question no – (15)**

**Solution :**

Length of the cloth required for each pair of trousers,

= 54 ÷ 24

= 54/24

= 9/4

= 2 1/4 m

Therefore, the 2 1/4 m cloth will be required.

**Operations on Rational Numbers Exercise 5.5 Solution**

**Question no – (1) **

**Solution : **

Six rational numbers between -4/8 and 3/8 are,

**(i)** -3/8,

**(ii)** -2/8,

**(iii)** -1/8,

**(iv)** 0,

**(v)** 1/8,

**(vi)** 2/8,

**(vii)** 3/8

**Question no – (2) **

**Solution : **

10 rational numbers between 7/13 and -4/13 are,

**(i)** 7/13,

**(ii)** 6/13,

**(iii)** 5/13,

**(iv)** 4/13,

**(v)** 3/13,

**(vi)** 2/13,

**(vii)** 1/13,

**(viii)** 0,

**(ix)** -1/13,

**(xi)** -2/13,

**(xii)** -3/13

**Question no – (3) **

**Solution : **

**(i)** Between any two distinct integers there is always an integer –

This statement is **False.**

**(ii)** Between any two distinct rational numbers there is always a rational number –

This statement is **True.**

**(iii)** Between any two distinct rational numbers there are infinitely many rational numbers –

This statement is **True.**

**Next Chapter Solution : **

👉 Chapter 6 👈