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

Chapter 1 Rational Numbers – Exercise 1.3 | Set 1

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

Solution:

Let the number be x

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

Therefore, -7/5 should be added.

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

Therefore, 59/30 should be added.

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

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