RD SHARMA SOLUTION CHAPTER – 1 Rational Numbers | CLASS 8TH MATHEMATICS-EDUGROWN

Exercise 1.1

Question 1.
Add the following rational numbers:

Solution:

Question 2.
Add the following rational numbers:

Solution:

Question 3.
Simplify:

Solution:

Question 4.
Add and Express the sum as mixed fraction:

Solution:

Exercise 1.2

Question 1.
Verify commutativity of addition of rational numbers for each of the following pairs of rational numbers :

Solution:

Question 2.
Verify associativity of addition of rational numbers i.e., (A: + y) + z = x + (y + z), when :

Solution:

Question 3.
Write the additive inverse of each of the following rational numbers :

Solution:

Question 4.
Write the negative (additive inverse) of each of the following :

Solution:

Question 5.
Using commutativity and associativity of addition of rational numbers, express ‘iach of the following as a rational number :

Solution:

Question 6.
Re-arrange suitably and find the sum in each of the following :


Solution:

Exercise 1.3

Question 1.
Subtract the first rational number from the second in each of the following :



Solution:

Question 2.
Evaluate each of the following :

Solution:

Question 3.
The sum of two numbers is 59. If one of the numbers is 13, find the other.
Solution:

Question 4.
The sum of two numbers is −13. If one of the numbers is −123, find the other.
Solution:

Question 5.
The sum of two numbers is −43. If one of the number is -5, find the
Solution:

Question 6.
The sum of two rational numbers is -8. If one of the numbers is −157 find the other.
Solution:

Question 7.
What should be added to so as to −78 get 59 ?
Solution:

Question 8.
What number should be added to −511 so as to get 263 ?
Solution:

Question 9.
What number should be added to −57 to get −23 ?
Solution:

Question 10.
What number should be subtracted from −53 to get 56 ?
Solution:

Question 11.
What number should be subtracted from 37 to get 54 ?
Solution:

Question 12.
What should be added to (23+35) to get −1215 ?
Solution:

Question 13.
What should be added to (12+13+15) to get 3 ?
Solution:

Question 14.
What should be subtracted from (34−23) to get −16 ?
Solution:

Question 15.
Fill in the blanks :

Solution:

Exercise 1.4

Question 1.
Subtract the first rational number from the second in each of the following :



Solution:

Question 2.
Evaluate each of the following :

Solution:

Question 3.
The sum of two numbers is 59. If one of the numbers is 13, find the other.
Solution:

Question 4.
The sum of two numbers is −13. If one of the numbers is −123, find the other.
Solution:

Question 5.
The sum of two numbers is −43. If one of the number is -5, find the
Solution:

Question 6.
The sum of two rational numbers is -8. If one of the numbers is −157 find the other.
Solution:

Question 7.
What should be added to so as to −78 get 59 ?
Solution:

Question 8.
What number should be added to −511 so as to get 263 ?
Solution:

Question 9.
What number should be added to −57 to get −23 ?
Solution:

Question 10.
What number should be subtracted from −53 to get 56 ?
Solution:

Question 11.
What number should be subtracted from 37 to get 54 ?
Solution:

Question 12.
What should be added to (23+35) to get −1215 ?
Solution:

Question 13.
What should be added to (12+13+15) to get 3 ?
Solution:

Question 14.
What should be subtracted from (34−23) to get −16 ?
Solution:

Question 15.
Fill in the blanks :

Solution:

Exercise 1.5

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 1.6

Question 1.
Verify the property : x x y = y x x by taking :

Solution:

Question 2.
Verify the property : x x (y x z) = (x x y) x z by taking :

Solution:

Question 3.
Verify the property :xx(y + 2) = xxy + x x z by taking :

Solution:

Question 4.
Use the distributivity of multiplication of rational numbers over their addition to simplify :

Solution:

Question 5.
Find the multiplicative inverse (reciprocal) of each of the following rational numbers :


Solution:

Question 6.
Name the property of multiplication of rational numbers illustrated by the following statements :

Solution:

Exercise 1.7

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 is15. If one of the numbers is -10, find the other.
Solution:

Question 4.
The product of two rational numbers is−98 if one of the numbers is −415, find other.
Solution:

Question 5.
By what number should we multiply −16 so that the product may be −239 ?
Solution:

Question 6.
By what number should we multiply −1528 so that the product may be −57 ?
Solution:

Question 7.
By what number should we multiply −813 so that the product may be 24 ?
Solution:

Question 8.
Bv what number should −34 multiplied in order to produce 23 ?
Solution:

Question 9.
Find (x +y) + (x – y), if

Solution:

Question 10.
The cost of 7 23 metres of rope is Rs 12 34.Find its cost per metre.
Solution:

Question 11.
The cost of 2 13 metres of cloth is Rs. 75 14Find the cost of cloth per metre.
Solution:

Question 12.
By what number should −3316 be divided to get −114 ?
Solution:

Question 13.
Divide the sum of −135 and 127 by the product of −317 and −12.
Solution:

Question 14.
Divide the sum of 6512 and 127 bv 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:

Exercise 1.8

Question 1.
Find a rational number between -3 and 1.
Solution:

Question 2.
Find any five rational number less than 1.
Solution:

Question 3.
Find four rational numbers between −29 and 59 .
Solution:

Question 4.
Find two rational numbers between 15 and 12 .
Solution:

Question 5.
Find ten rational numbers between 14 and 12 .
Solution:

Question 6.
Find ten rational numbers between −25 and 12 .
Solution:

Question 7.
Find ten rational numbers between 35 and 34 .
Solution: