# Class 8 RD Sharma – Chapter 1 Rational Numbers – Exercise 1.3 | Set 2

• Last Updated : 06 Apr, 2021

### Question 11. What number should be subtracted from 3/7 to get 5/4?

Solution:

Let the number be x

Attention reader! All those who say programming isn't for kids, just haven't met the right mentors yet. Join the  Demo Class for First Step to Coding Coursespecifically designed for students of class 8 to 12.

The students will get to learn more about the world of programming in these free classes which will definitely help them in making a wise career choice in the future.

3/7 – x = 5/4

-x = 5/4 – 3/7 (Transposing 3/7)

LCM of 4 and 7 is 28

-x = (5 × 7 – 3 × 4)/28

-x = (35 – 12)/28

-x = (23)/28

x = -23/28

Therefore, -23/28 should be subtracted.

### Question 12. What should be added to (2/3 + 3/5) to get -2/15?

Solution:

Let the number be x

(2/3 + 3/5) + x = -2/15

LCM of 3 and 5 is 15

(2 × 5 + 3 × 3)/15 + x = -2/15

(10 + 9)/15 + x = -2/15

19/15 + x = -2/15

x = -2/15 – 19/15 (Transposing 19/15)

x = (-2 – 19)/15

x = (-21)/15

x = (-7)/5

### Question 13. What should be added to (1/2 + 1/3 + 1/5) to get 3?

Solution:

Let the number be x

(1/2 + 1/3 + 1/5) + x = 3

LCM of 2, 3 and 5 is 30

(1 × 15 + 1 × 10 + 1 × 6)/30 + x = 3

(15 + 10 + 6)/30 + x = 3

31/30 + x = 3

x = 3/1 – 31/30 (Transposing 31/30)

LCM of 1 and 30 is 30

x = (3 × 30 – 31)/30

x = (90 – 31)/30

x = (59)/30

### Question 14. What number should be subtracted from (3/4 – 2/3) to get -1/6?

Solution:

Let the number be x

(3/4 – 2/3) – x = -1/6

LCM of 4 and 3 is 12

(3 × 3 – 2 × 4)/12 – x = -1/6

(9 – 8)/12 – x = -1/6

1/12 – x = -1/6

-x = -1/6 – 1/12

LCM of 6 and 12 is 12

-x = (-1 × 2 – 1)/12

-x = (-2 – 1)/12

-x = -3/12

x = 1/4

Therefore, 1/4 should be subtracted.

### Question 15. Fill in the blanks:

(i) -4/13 – -3/26 = …….

Solution:

This can be written as

-4/13 + 3/26

LCM of 13 and 26 is 26

= (-4 × 2 + 3 × 1)/26

= (-8 + 3)/26

= -5/26

Therefore, -5/26 is the required number

(ii) -9/14 + ….. = -1

Solution:

Let the number to be added be x

-9/14 + x = -1

x = -1/1 + 9/14 (Transposing -9/14)

LCM of 1 and 14 is 14

x = (-1 × 14 + 9 × 1)/14

= (-14 + 9)/14

= -5/14

Therefore, the number to be added is -5/14

(iii) -7/9 + …. = 3

Solution:

Let the number to be added be x

-7/9 + x = 3

x = 3 – (-7/9)

x = 3/1 + 7/9

LCM of 1 and 9 is 9

x = (3 × 9 + 7 × 1)/9

x = (27 + 7)/9

x = 34/9

Therefore, the number to be added is 34/9

(iv) ….. + 15/23 = 4

Solution:

Let the number be x

x + 15/23 = 4

x = 4/1 – 15/23

LCM of 1 and 23 is 23

x = (4 × 23 – 15 × 1)/23

x = (92 – 15)/23

x = 77/23

Therefore, the number to be added is 77/23

My Personal Notes arrow_drop_up