Practice Questions on Addition and Subtraction of Rational Numbers

Rational numbers are part of basic curriculum mathematical lessons and are used as a base and starting point for various complicated mathematical operations. Since the addition and subtraction of rational numbers form a strong foundation for learners, learners must master it.

In this article, we will explain rational numbers along with some examples and practice questions based on the addition and subtraction of rational numbers.

What is Addition and Subtraction of Rational Numbers?

Addition and subtraction of rational numbers can be defined as operations that involve combining or removing quantities that are in the form of the ratio of two integers. Addition and subtraction of rational numbers involve adding or subtracting fractions or decimals.

Rational numbers include fractions, integers, and any numbers of the form a/b where a and b are integers and b ≠ 0.

Important Related Formulas / Concepts

Addition or Subtraction of Rational Number with the Same Denominator

a/b + c/b = a+c/b

Or

a/b - c/b = a-c/b

Addition or Subtraction of Rational Number with Different Denominators

a/b + c/d = ad+bc/bd

Or

a/b - c/d = ad-bc/bd

Addition or Subtraction of Rational Number and a Whole Number

a/b + c = a+cb/b

Or

a/b - c = a-cb/b

Addition and Subtraction of Rational Numbers: Practice Questions with Solutions

Question 1: Add 3/4 + 2/5.

Solution :

We are using this formula, a/b + c/d = (a ✕d + c ✕ b ) / b ✕ d

Putting the values of a, b,c and d in the formula

3/4 + 2/5 = (3 ✕ 5 + 2 ✕ 4 ) / 4 ✕ 5 ⇒ (15+8) / 20 ⇒ 23/20

Question 2: Subtract 7/8 - 3/5.

Solution :

We are using this formula , a/b - c/d = (a ✕d - c ✕ b ) / b ✕ d

Putting the values of a, b,c and d in the formula

7/8 - 3/5 = ( 7 ✕ 5 - 3 ✕ 8) / 8 ✕ 5 ⇒ (35-24)/40 ⇒ 11 /40

Question 3: Add 1/2 + (-3)/4

Solution :

We are using this formula , a/b + c/d = (a ✕d + c ✕ b ) / b ✕ d

Putting the values of a, b,c and d in the formula

1/2 + (-3)/4 = (1 ✕ 4 + (-3) ✕ 2 ) / 2 ✕ 4 ⇒ (4-6)/8 ⇒ -2/8 ⇒ -1/4

Question 4: Subtract -5/6 - 1/3

Solution :

We are using this formula, a/b - c/d = (a ✕d - c ✕ b ) / b ✕ d

Putting the values of a, b,c and d in the formula

-5/6 - 1/3 = (-5 ✕ 3 - 1 ✕ 6) / 6 ✕ 3 ⇒ (-15 - 6)/18 ⇒ -21/18 ⇒ -7/6

Question 5: Add 4/9 + 7/12.

Solution :

We are using this formula, a/b + c/d = (a ✕d + c ✕ b ) / b ✕ d

Putting the values of a, b,c and d in the formula

4/12 + 7/12 = (4 ✕ 12 + 7✕ 9 ) / 9 ✕ 12 ⇒ (48+63) / 108 ⇒ 111/108

⇒ 37/36

​Question 6: Subtract 5/8 - 1/2.

Solution :

We are using this formula , a/b - c/d = (a ✕d - c ✕ b ) / b ✕ d

Putting the values of a, b,c and d in the formula

5/8 - 1/2 = ( 5 ✕ 2 - 1 ✕ 8) / 8 ✕ 2 ⇒ (10-8)/16 ⇒ 1 /8

Question 7: Add -2/3 + 5.

Solution :

We are using this formula, a/b + c = (a + c ✕ b ) / b

Putting the values of a, b,c and d in the formula

-2/3 + 5 = (-2 + 5✕ 3 ) / 3 ⇒ (-2 + 15) / 3 ⇒ 13/3

Question 8: Subtract 9 - 2/5.

Solution :

We are using this formula , a- c/d = (a ✕d - c ) / d

Putting the values of a, b,c and d in the formula

9 - 2/5 = ( 9 ✕ 5 - 2 ) / 5 ⇒ (45 - 20)/50 ⇒ 25/5

⇒ 5

Question 9: Add 3/7 + 4/9.

Solution :

We are using this formula, a/b + c/d = (a ✕d + c ✕ b ) / b ✕ d

Putting the values of a, b,c and d in the formula

3/7 + 4/9 = (3 ✕ 9 + 4 ✕ 7) / 7 ✕ 9 ⇒ (27 + 28) / 63 ⇒ 55/63

Question 10: Subtract -3/8 - 5/8.

Solution :

We are using this formula , a/b - c/b = (a - c ) / b

Putting the values of a, b,c and d in the formula

-3/8 - 5/8 = ( -3 - 5 ) / 8 ⇒ -8/8

⇒ -1

Addition and Subtraction of Rational Numbers: Practice Questions

Solve the following questions:

Answer Key:

1. 19/12

2. 1/15

3. -3/8

4. -2/9

5. 41/35

6. -73/88

7. 3/10

8. -1/20

9. -1 /8

10. 40/63

Also Check,

• Practice Questions on Decimals
• Practice Questions on Symmetry
• Practice Questions on Congruence of Triangles