RD SHARMA SOLUTION CHAPTER – 5 Operations on Rational Numbers| CLASS 7TH MATHEMATICS-EDUGROWN

Exercise 5.1

Question: 1

Add the following rational numbers:

Solution:

We have,

We have,

We have,

We have,

Question: 2

Add the following rational numbers:

Solution:

If p/q and r/s are two rational numbers such that q and s do not have a common factor

If p/q and r/s are two rational numbers such that q and s do not have a common factor

LCM of 27 and 18 is 54

LCM of 4 and 8 is 4

Question: 3

Simplify

Solution:

LCM of 5 and 10 is 10

LCM of 16 and 24 is 48

LCM of 12 and 15 is 60

LCM of 19 and 57 is 57

Question: 4

Add and express the sum as a mixed fraction:

Solution:

LCM of 5 and 10 is 10

LCM of 7 and 4 is 28

Exercise 5.2

Question: 1

Subtract the first rational number from the second in each of the following:

Solution:

Question: 2

Evaluate each of the following:

Solution:

LCM of 3 and 5 is 15

LCM of 3 and 7 is 21

Question: 3

The sum of the two numbers is 5/9. If one of the numbers is 1/3, find the other.

Solution:

LCM of 3 and 9 is 9

Question: 4

The sum of two numbers is -1/3. If one of the numbers is -12/3, find the other.

Solution:

Let the required number be x

The required number is 11/3

Question: 5

The sum of two numbers is – 4/3. If one of the numbers is -5, find the other.

Solution:

Let the required number be x

The required number is 11/3

Question: 6

 The sum of two rational numbers is – 8. If one of the numbers is – (15/7), find the other.

Solution:

Let the required number be x

The required number is – (41/7)

Question: 7

What should be added to – (7/8) so as to get 5/9?

Solution:

Let the required number be x

The required number is 103/72

Question: 8

What number should be added to (-5)/11 so as to get 26/33?

Solution:

Let the required number be x

The required number is 41/33

Question: 9

What number should be added to (-5)/7 to get (-2)/3?

Solution:

Let the required number be x

The required number is 1/21

Question: 10

What number should be subtracted from -5/3 to get 5/6?

Solution:

Let the required number be x

The required number is 15/6

Question: 11

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

Solution:

Let the required number be x

The required number is 23/28

Question: 12

Solution:

Let the required number be x

The required number is (-7)/5

Question: 13

Solution:

Let the required number be x

The required number is 59/30

Question: 14

Solution:

Let the required number be x

x = 1/4

The required number is ¼

Question: 15

Simplify:

Solution:

Question: 16

Fill in the blanks:

Solution:

Exercise 5.3

Question: 1

Multiply:

Solution:

Question: 2

Multiply:

Solution:

Question: 3

Simplify each of the following and express the result as a rational number in standard form:

Solution:

Question: 4

Simplify:

Solution:

Question: 5

Simplify:

Solution:

Exercise 5.4

Question: 1

Divide:

Solution:

Question: 2

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

Solution:

Question: 3

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

Solution:

Let the number to be found be x

x ×- 10 = 15

x = 15/(-10)

x = 3/(-2)

x = (-3)/2

Hence the number is x = (-3)/2

Question: 4

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

Solution:

Let the number to be found be x

Hence the number is x = 10/3

Question: 5

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

Solution:

Let the number to be found be x

Hence the number is x = 46/3

Question: 6

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

Solution:

Let the number to be found be x

Hence the number is x = 4/3

Question: 7

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

Solution:

Let the number to be found be x

x = – 39

Hence the number is x = – 39

Question: 8

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

Solution:

Let the number to be found be x

x = 8/9

Hence the number is x = 8/9

Question: 9

 Find (x + y) ÷ (x —y), if

Solution:

Question: 10

The cost of 7(2/3) metres of rope is Rs. 12(3/4). Find its cost per metre. 7(2/3) metres of rope cost = Rs. 12(3/4).

Solution:

Question: 11

The cost of 2(1/3) metres of cloth is Rs.75 1/4. Find the cost of cloth per metre. 2(1/3) metres of rope cost = Rs. 75(1/4)

Solution:

Question: 12

By what number should (-33)/16 be divided to get (-11)/4?

Solution:

x = 3/4

The number is x = 3/4

Question: 13

Divide the sum of (-13)/5 and 12/7 by the product of (-31)/7 and (-1)/2

Solution:

Question: 14

Divide the sum of 65/12 and 8/3 by their difference. 

Solution:

Question: 15

If 24 trousers of equal size can be prepared in 54 metres of cloth, what length of cloth is required for each trouser?

Solution:

= 54/24

= 9/4 metres

9/4 metres of cloth is required to make each trouser

Exercise 5.5

Question: 1

Find six rational numbers between (-4)/8 and 3/8

Solution:

We know that

– 4, -3, -2, -1, 0, 1, 2, 3

Question: 2

Find 10 rational numbers between 7/13 and (- 4)/13

Solution:

We know that

76543210 -1 -2 -3 –4

Question: 3

State true or false:

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

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

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

Solution:

(i) False
(ii) True
(iii) True