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.

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.

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

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

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

What are rational numbers?

The rational numbers are numbers in the form of a ratio, which is an integer divided by another integer without the second integer being 0.

How do you add rational numbers with different denominators?

Make them to be of the same denominator and the sum of the numerators is while the denominator remains constant.

What is the common denominator?

The multiple is normally the least common multiple of the denominators of two or more fractions.

How do you subtract rational numbers?

The same like addition, first bring all to the same denominator and then deduct the numbers on the numerator.

Can rational numbers be negative?

Yes, rational numbers can be negative if either the numerator or the denominator is negative.