Class 8 RD Sharma Solutions Chapter 1 Rational Numbers Exercise 1.3 | Set 1 (original) (raw)
Last Updated : 23 Jul, 2025
Chapter 1 of RD Sharma's Class 8 Mathematics textbook focuses on Rational Numbers a fundamental concept in mathematics. This chapter lays the groundwork for understanding how to work with the numbers that can be expressed as the fraction of the two integers. Exercise 1.3 | Set 1 specifically deals with the problems designed to enhance students' skills in performing the operations with rational numbers.
Rational Numbers
The Rational numbers are numbers that can be expressed in the form p\q where p and q are integers and 𝑞≠0. These numbers include integers, fractions, and repeating or terminating decimals. The concept of rational numbers is essential because it extends the number system to include values that are not whole numbers thus providing a more comprehensive way to describe and solve mathematical problems.
**Question 1. Subtract the first rational number from the second in each of the following:
****(i) 3/8 and 5/8**
**Solution:
= 5/8 - 3/8
As denominators are same
= (5 - 3) / 8
= 2/8
= 1/4
****(ii) -7/9 and 4/9**
**Solution:
= 4/9 - (-7/9)
= 4/9 + 7/9
As denominators are same
= (4 + 7) / 9
= 11/9
****(iii) -2/11 and -9/11**
**Solution:
= -9/11 - (-2/11)
= -9/11 + 2/11
As denominators are same
= (-9 + 2) / 11
= -7/11
****(iv)11/13 and -4/13**
**Solution:
=-4/13-11/13
As denominators are same
=(-4-11) / 13
=(-15) / 13
****(v)1/4 and -3/8**
**Solution:
=-3/8-1/4
LCM of 4 and 8 is 8
=(-3-1×2) / 8
=(-3-2) / 8
=(-5) / 8
=(-5) / 8
****(vi)-2/3 and 5/6**
**Solution:
=5/6- (-2/3)
=5/6+2/3
LCM of 2 and 3 is 6
=(5+(2×2)) / 6
=(5+4) / 6
=9/6
=3/2
****(vii)-6/7 and -13/14**
**Solution:
=-13/14- (-6/7)
=-13/14+6/7
LCM of 14 and 7 is 14
=(-13+6×2) / 14
=(-13+12) / 14
=-1/14
****(viii)-8/33 and -7/22**
**Solution:
=-7/22- (-8/33)
=-7/22+8/33
LCM of 22 and 33
22=11×2
33=11×3
LCM is 66
=(-7×3+8×2) / 66
=(-21+16) / 66
=(-5) / 66
**Question 2.Evaluate each of the following:
****(i) 2/3-3/5**
**Solution:
LCM of 3 and 5 is 15
=(2×5-3×3) / 15
=(10-9) / 15
=1/15
****(ii) -4/7-2/-3**
**Solution:
This can be written as
=-4/7- (-2)/3
=-4/7+2/3
LCM of 7 and 3 is 21
=(-4×3+2×7) / 21
=(-12+14) / 21
=2/21
****(iii) 4/7 - (-5/-7)**
**Solution:
This can be written as
=4/7-(5)/7
As denominators are same
=(4-5) / 7
=(-1) / 7
****(iv) -2 - (5/9)**
**Solution:
=-2/1-5/9
LCM of 1 and 9 is 9
=(-2×9-5×1) / 9
=(-18-5) / 9
=(-23) / 9
****(v) -3/-8 - (-2/7)**
**Solution:
This can be written as
=3/8+2/7
LCM of 8 and 7 is 56
=(3×7+2×8) / 56
=(21+16) / 56
=37/16
****(vi) -4/13 - (-5/26)**
**Solution:
This can be written as
=-4/13+5/26
LCM of 13 and 26 is 26
=(-4×2+5×1) / 26
=(-8+5) / 26
=(-3) / 26
****(vii)-5/14 - (-2/7)**
**Solution:
This can be written as
=-5/14+2/7
LCM of 14 and 7 is 14
=(-5×1+2×2) / 14
=(-5+4) / 14
=(-1) / 14
****(viii)13/15 - 12/25**
**Solution:
15=3×5
25=5×5
LCM is 5×5×3=75
=(13×5-12×3) / 75
=(65-36) / 75
=(29) / 75
****(ix) -6/13 - (-7/13)**
**Solution:
This can be written as
=-6/13+7/13
As denominators are same
=(-6+7) / 13
=1/13
****(x) 7/24 - 19/36**
**Solution:
24=2×2×2×3
36=2×2×3×3
LCM is 2×2×2×3×3 =72
=(7×3-19×2) / 72
=(21-38) / 72
=(-17) / 72
****(xi) 5/63 - (-8/21)**
**Solution:
This can be written as
=5/63+8/21
LCM of 21 and 63 is 63
=(5×1+8×3) / 63
=(5+24) / 63
=29/63
**Question 3. Sum of two numbers is 5/9. If one of the numbers is 1/3, **find the other.
**Solution:
Let the other number be x
1/3+x=5/9 (As sum is 5/9)
x=5/9-1/3 (On transposing 1/3)
LCM of 3 and 9 is 9
x=(5×1-1×3) / 9
x=(5-3) / 9
x=2/9
Therefore, other number is 2/9
**Question 4. The sum of two numbers is -1/3. If one of the numbers is -12/3,find the other.
**Solution:
Let the other number be x
-12/3+x=-1/3 (As -1/3 is the sum)
x=-1/3+12/3(Transposing -12/3)
x=(-1+12) / 3
x=11/3
Therefore, the other number is 11/3
**Question 5. The sum of the two numbers is -4/3. If one of the numbers is -5, find the other.
**Solution:
Sum of two numbers = -4/3
One of the number = -5/1
-5+x=-4/3
x=-4/3+5/1 (Transposing -5)
LCM of 3 and 1 is 3
x= (-4×1+5×3) / 3
= (-4 + 15)/3
= 11/3
The other number is 11/3
**Question 6. The sum of the two rational numbers is -8. If one of the numbers is -15/7, find the other.
**Solution:
Sum of two rational numbers = -8/1
One of the number = -15/7
Let the other rational number as x
x + -15/7 = -8
7 is the LCM
(7x -15) / 7 = -8
Transposing 7 to the right side
7x -15 = -8×7
7x — 15 = -56
7x = -56+15
x = -41/7
Other number is -41/7
**Question 7. What should be added to -7/8 to get 5/9?
**Solution:
Let the number to be added be x
-7/8+x=5/9
x=5/9+7/8 (Transposing -7/8)
LCM of 9 and 8 is 72
x=(5×8+7×9) / 72
x=(40+63) / 72
x=103/72
Therefore, 103/72 should be added
**Question 8. What number should be added to -5/11 to get 26/33?
**Solution:
Let the number to be added be x
-5/11+x=26/33
x=26/33+5/11 (Transposing 5/11)
LCM of 33 and 11 is 33
x=(26×1+5×3) / 33
x=(26+15) / 33
x=41/33
Therefore, 41/33 should be added
**Question 9. What number must be added to -5/7 to get -2/3?
**Solution:
Let the number be x
-5/7+x=-2/3
x=-2/3+5/7 (Transposing -5/7)
LCM of 3 and 7 is 21
x=(-2×7+5×3) / 21
x=(-14+15) / 21
x=1/21
Therefore, 1/21 should be added
**Question 10. What number should be subtracted from -5/3 to get 5/6?
**Solution:
Let the number be x
-5/3 - x = 5/6
-x = 5/6 + 5/3 (Transposing 5/3)
LCM of 3 and 6 is 6
-x = (5 × 1 + 5 × 2) / 6
-x=(5+10) / 6
-x=15/6
x=-15/6
x=-5/2
Therefore, -5/2 should be subtracted.
Chapter 1 Rational Numbers - Exercise 1.3 | Set 2
Conclusion
Understanding rational numbers is fundamental to the mastering basic arithmetic and algebra. By solving Exercise 1.3 | Set 1 students practice essential operations such as the addition, subtraction, multiplication and division with the rational numbers. These exercises help build a strong foundation for the more advanced topics in the mathematics.