Skip to content
Related Articles

Related Articles

Improve Article
Save Article
Like Article

Class 8 RD Sharma – Chapter 1 Rational Numbers – Exercise 1.7 | Set 1

  • Last Updated : 06 Apr, 2021

Problem 1. Divide:

(i) 1 by 1/2

Solution:

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 Course, specifically 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.

= 1 / (1 / 2)



= 1 × (2 / 1)

= 2

ii) 5 by -5/7

Solution:

= 5 / (-5 / 7)

= 5 × (-7 / 5)

5 is the common factor

= -7

(iii) -3/4 by 9/-16

Solution:

= (-3 / 4) / (-9 / 16)

= -3 / 4 × (-16 / 9)

3 and 4 are the common factor

= (-3 × -16) / (4 × 9)

= 4 / 3

iv) -7/8 by -21/16

Solution:

= (-7 / 8) / (-21 / 16)



= -7 / 8 × (-16 / 21)

= (-7 × -16) / (8 × 21)

7 and 8 are the common factor

= 2 / 3

v) 7/-4 by 63/64

Solution:

= 7 / -4 / (63 / 64)

= -7 / 4 × (64 / 63)

= (-7 × 64) / (4 × 63)

4 and 7 are common factor

= -16 / 9

vi) 0 by -7/5

Solution:

= 0 / (-7 / 5)

= 0 × (-5 / 7)

= 0

(vii) -3/4 by -6

Solution:

= -3 / 4 / (-6 / 1)

= -3 / 4 × (-1 / 6)

= (-3 × -1) / (4 × 6)

3 is the common factor

= 1 / 8

(viii) 2/3 by -7/12

Solution:

= 2 / 3 / (-7 / 12)

= 2 / 3 × (12 / -7)

= (2 × 12) / (3 × -7)

3 is the common factor

= 8 / -7



= -8 / 7

(ix) -4 by -3/5

Solution:

= -4 / (-3 / 5)

= -4 × (5 / -3)

= (-4 × -5) / 3

= 20 / 3

(x) -3/13 by -4/65

Solution:

= -3 / 13 / (-4 / 65)

= -3 / 13 × (65 / -4)

= (-3 × -65) / (13 × 4)

13 is the common factor

= (-3 × -5) / 4

= 15 / 4

Problem 2. Find the value and express as a rational number in standard form:

(i) 2/5 ÷ 26/15

Solution:

= 2 / 5 / (26 / 15)

= 2 / 5 × 15 / 26

= (2 × 15) / (5 × 26)

5 and 2 are the common factor

= 3 / 13

(ii) 10/3 ÷ -35/12

Solution:

= 10 / 3 / (-35 / 12)

= 10 / 3 × -12 / 35

= (10 × -12) / (3 × 35)

Common factor is 5 and 3

= (2 × -4) / (7)

= -8 / 7

(iii) -6 ÷ -8/17

Solution:

= -6 / (-8 / 17)

= -6 × (-17 / 8)

= (-6 × -17) / (8 × 1)

2 is the common factor

= (-3 × -17) / 4

= 51 / 4

(iv) -40/99 ÷ -20

Solution:



= -40 / 99 / (-20 / 1)

= -40 / 99 × (-1 / 20)

= (-40 × -1) / (99 × 20)

20 is the common factor

= 2 / 99

(v) -22/27 ÷ -110/18

Solution:

= (-22 / 27) / (-110 / 18)

= (-22 / 27) × (18 / -110)

= (-22 × 18) / (27 × -110)

9 and 22 are the common factor

= 2 / (3 × 5)

= 2 / 15

(vi) -36/125 ÷ -3/75

Solution:

= (-36 / 125) / (-3 / 75)

= (-36 / 125) × (75 / -3)

= (-12 / 25) × (15 / -1)

= (-12 × 15) / (25 × -1)

= (-12 × -3) / 5

= 36 / 5

Problem 3. The product of two rational numbers is 15. If one of the numbers is -10, find the other.

Solution:

We know that the product of two rational numbers = 15

One of the number = -10

Let the other number be x

-10x = 15

x = 15 / -10

5 is the common factor

= -3 / 2

The other number is -3 / 2

Problem 4. The product of two rational numbers is -8/9. If one of the numbers is -4/15, find the other.

Solution:

We know that the product of two rational numbers = -8 / 9

One of the number = -4 / 15

Let the other number be x

(-4 / 15) x = -8 / 9

x = (-8 / 9) / (-4 / 15)

   = (-8 / 9) × (15 / -4)

3 and 4 are the common factor

= (-2 / 3) × (5 / -1)

= (-2 × 5) / (3 × -1)

= -10 / -3

= 10 / 3

The other number is 10 / 3

Problem 5. By what number should we multiply -1/6 so that the product may be -23/9?

Solution:

Let the number be x

So, x (-1 / 6) = -23 / 9

x = (-23 / 9) / (-1 / 6)

x = (-23 / 9) × (6 / -1)

= (-23 / 3) × (2 × -1)

= (-23 × -2) / (3 × 1)



= 46 / 3

It should be multiplied by 46 / 3

Problem 6. By what number should we multiply -15/28 so that the product may be -5/7?

Solution:

Let the number be x

So, x (-15 / 28) = -5 / 7

x = (-5 / 7) / (-15 / 28)

x = (-5 / 7) × (28 / -15)

   = (-5 ×28) / (7 × -15)

5 and 7 are the common factor

= -4 / -3

= 4 / 3

Problem 7. By what number should we multiply -8/13 so that the product may be 24?

Solution:

Let the number be x

So, x (-8 / 13) = 24

x = (24) / (-8 / 13)

   = (24) × (13 / -8)

   = (24 × 13) / (-8)

8 is the common factor

= -3 × 13

= -39

It should be multiplied by -39

Problem 8. By what number should -3/4 be multiplied in order to produce 2/3?

Solution:

Let the number be x

x (-3 / 4) = 2 / 3

x = (2 / 3) / (-3 / 4)

   = (2 / 3) × (4 / -3)

   = -8 / 9

It should be multiplied by -8 / 9

Problem 9. Find (x+y) ÷ (x-y), if

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

Solution:

x + y = 2 / 3 + 3 / 2

LCM is 6

= (2 × 2 + 3 × 3) / 6

= (4 + 9) / 6

= 13 / 6

x – y = 2 / 3 – 3 / 2

LCM is 6

= (2 × 2 – 3 × 3) / 6

= (4 – 9) / 6

= -5 / 6

(x + y) ÷ (x – y) = (13 / 6) / (-5 / 6)

= (13 / 6) × (6 / -5)

= (13 × -6) / (6 × 5)

6 is the common factor

= -13 / 5

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

Solution:

x + y = 2 / 5 + 1 / 2

LCM is 10

= (2 × 2 + 1 × 5) / 10

= (4 + 5) / 10

= 9 / 10

x – y = 2 / 5 – 1 / 2

LCM is 10

(2 × 2 – 1 × 5) / 10

= (4 – 5) / 10

= -1 / 10

(x + y) ÷ (x – y) = (9 / 10) / (-1 / 10)

= (9 / 10) × (10 / -1)

= (9 × 10) / (10 × -1)



10 is the common factor

= -9

(iii) x = 5/4, y = -1/3

Solution:

x + y = 5 / 4 + -1 / 3

LCM is 12

= (5 × 3 – 1 × 4) / 12

= (15 – 4) / 12

= 11 / 12

x – y = 5 / 4 – (-1/3)

= 5 / 4 + 1 / 3

LCM is 12

= (5 × 3 + 1 × 4) / 12

= 19 / 12

(x + y) ÷ (x – y) = (11 / 12) / (19 / 12)

= (11 / 12) × (12 / 19)

= (11 × 12) / (12 × 19)

Common factor is 12

= 11 / 19

(iv) x = 2/7, y = 4/3

Solution:

x + y = 2 / 7 + 4 / 3

LCM is 21

= (2 × 3 + 4 × 7) / 21

= (6 + 28) / 21

= 34 / 21

x – y = 2 / 7 – 4 / 3

LCM is 21

= (2 × 3 – 4 × 7) / 21

= (6 – 28) / 21

= -22 / 21

(x + y) ÷ (x – y) = (34 / 21) / (-22 / 21)

= (34 / 21) × (21 / -22)

21 is the common factor

= -34 / 22

= -17 / 11

(v) x = 1/4, y = 3/2

Solution:

x + y = 1 / 4 + 3 / 2

LCM is 4

= (1 + 3 × 2) / 4

= 7 / 4

x – y = 1 / 4 – 3 / 2

LCM is 4

= (1 – 3 × 2) / 4

= -5 / 4

(x + y) ÷ (x – y) = (7 / 4) / (-5 / 4)

= (7 / 4) × (4 / -5)

4 is the common factor

= -7 / 5

Problem 10. The cost of 723 meters of rope is Rs 12 ¾. Find the cost per meter.

Solution:

23 / 3 meters of rope = Rs 51 / 4

Let us consider a number = x

So, x (23 / 3) = 51 / 4

x = (51 / 4) / (23 / 3)

   = (51 / 4) × (3 / 23)

   = (51 × 3) / (4 × 23)

   = 153 / 92

   = 1 61 / 92

Cost per meter is Rs 1 61 / 92

Chapter 1 Rational Numbers – Exercise 1.7 |  Set 2




My Personal Notes arrow_drop_up
Recommended Articles
Page :

Start Your Coding Journey Now!