Fractions Practice Questions with Solutions (Medium)

Fractions are a way of representing parts of a whole. They express a number in terms of a numerator and a denominator, where:

• Numerator: The top number, represents how many parts we are considering.
• Denominator: The bottom number, represents the total number of equal parts that make up the whole.

Types of Fractions:

1. Proper Fraction: The numerator is smaller than the denominator (e.g., 3/4).
2. Improper Fraction: The numerator is equal to or larger than the denominator (e.g., 5/4).
3. Mixed Number: A whole number combined with a proper fraction (e.g., ).

Learn About: Fractions
Read More: Fun Facts about Fractions

Solved Practice Questions on Fractions (Medium)

Question 1: Add the following fractions: 5/6 + 11/9
Solution:

To add fractions, we need a common denominator. The least common denominator (LCD) of 6 and 9 is 18, to make the denominator same we need to multiply the first fraction with 3 and the second fraction with 2.

= (5 × 3)/(6 × 3)+ (11 × 2)/(9 × 2)
= 15/18 + 22/18
= 37/18

Question 2: Add the following fractions: 52/16 + 12/32
Solution:

To add fractions, we need a common denominator. The least common denominator (LCD) of 16 and 32 is 32, to make the denominator same we need to multiply the second fraction with 2.

= (52 × 2)/(16 × 2)+ (12)/(32)
= 104/32 + 12/32
= 116/32

Question 3: Subtract the following fractions: 23/4 - 23/3
Solution:

To subtract the fractions, we need a common denominator. The least common denominator (LCD) of 4 and 3 is 12, to make the denominator same we need to multiply the first fraction with 3 and the second fraction with 4.

= (23 × 3)/(4 × 3) - (23 × 4)/(3 × 4)
= 69/12 - 92/12
= -13/12

Question 4: Subtract the following fractions: 33/4 - 32/5
Solution:

To subtract the fractions, we need a common denominator. The least common denominator (LCD) of 4 and 5 is 20, to make the denominator same, we need to multiply the first fraction with 5 and the second fraction with 4.

= (33 × 5)/(4 × 5) - (32 × 4)/(5 × 4)
= 165/20 -128/20
= 37/20

Question 5: Multiply the following fractions: 33/7 × 63/11
Solution:

To multiply fractions, multiply the numerators and multiply the denominators: 33/7 × 63/11

= 2079/77
= 189/7
= 27

Question 6: Divide the following fractions: 44/15 ÷ 33/46
Solution:

To divide fractions, multiply the first fraction by the reciprocal of the second fraction: 44/15 ÷ 33/46

= 44/15 × 46/33
= 2024/495
= 184/45

Question 7: Solve for x: 22/x = 121/3
Solution:

To solve for x, cross-multiply:

22 × 3 = 121 × x
66 = 121x
x = 66/121
x = 6/11

Question 8: Solve for y: y/64 = 25/8
Solution:

To solve for y, cross-multiply:

y × 8 = 64 × 25
8y = 1600
y = 200

Question 9: Solve for x: 3/4 ​+ x/5 ​= 7/10 ​− 1/2​
Solution:

First, simplify the right-hand side of the equation:

7/10 ​− 1/2
=1/5

Now the equation becomes:

3/4 + x/5 = 1/5​
x/5 = 1/5 - 3/4
x/5 = -11/20
x = -55/20
x = -11/4

Question 10: Solve for y: 8/3 - 3/y = 4/3 × 5/9
Solution:

First, simplify the right-hand side:

4/3 × 5/9
20/27

Now the equation becomes:

8/3 - 3/y =20/27
8/3 - 20/27 = 3/y
52/27 = 3/y
y = 81/52

Question 11: Write two equivalent fractions of 3/39.
Solution:

Equivalent fraction by multiplying with the same number, lets multiply by 2:
(3 × 2)/(39 × 2) = 6/78

Equivalent fraction by division with the same number, here, both numerator and denominator are divisible by 3, dividing by 3:
(3 ÷ 3)/(39 ÷ 3) = 1/13

Question 12: Write two equivalent fractions of 5/9
Solution:

Equivalent fraction by multiplying with the same number, lets multiply by 3:
(5 × 3)/(9 × 3) = 15/27

Equivalent fraction by multiplying with the same number, lets multiply by 2:
(5 × 2)/(9 × 2) = 10/18

Unsolved Practice Questions Fractions(Medium)

Question 1: Add the following fractions: 7/8 + 9/10

Question 2: Add the following fractions: 44/12 + 15/28

Question 3: Subtract the following fractions: 9/5 − 7/6

Question 4: Subtract the following fractions: 25/8 − 13/12

Question 5: Multiply the following fractions: 7/11 × 18/19

Question 6: Divide the following fractions: 12/25 ÷ 30/40

Question 7: Solve for x: 15/x = 5/2

Question 8: Solve for y: y/72 = 18/6

Question 9: Solve for x: 2/3 + x/4 = 5/6 − 1/2

Question 10: Solve for y: 5/4 − 2/y = 85 × 37

Question 11: Write two equivalent fractions for 4/32​.

Question 12: Write two equivalent fractions for 8/15​.

Answer key

1. 113/80
2. 211/84
3. 17/30
4. 47/24
5. 126/209
6. 16/25
7. x = 6
8. y = 216
9. x = 1/6
10. y = 7
11. 1/8, 2/16
12. 16/30, 24/45