Fractions Questions

Fractions questions are given here will help the students to understand how to perform arithmetic operations on fractions. We know that fractions is one of the most important concepts of Class 7 Maths. In this article, you will get the questions on fractions, along with their solutions, based on the latest NCERT curriculum.

What are Fractions?

In maths, a fraction is defined as a part of the whole thing, and it can be written in the form a/b, where a and b are whole numbers, also, b ≠ 0. Based on the numerical values of numerator and denominator, we can define different types of fractions.

Proper fraction: A proper fraction is a number representing a part of a whole. This whole may be a single object or a group of objects.

Improper fraction: An improper fraction is a number in which the numerator is greater than the denominator.

Mixed fraction: A mixed fraction is a combination of a whole number and a proper fraction.

Learn more about fractions here.

Fractions Questions and Answers

1. How many 2/3 kg pieces can be cut from a cake of weight 4 kg?

Solution:

Let p be the number 2/3 kg pieces that are cut from a 4 kg cake.

So, p × (2/3) = 4

p = 4 × (3/2)

= 2 × 3

= 6

Therefore, six 2/3 kg pieces can be cut from a cake of weight 4 kg.

2. What is the product of 5/129 and its reciprocal?

Solution:

Given fraction: 5/129

Here, numerator = 5

Denominator = 129

Reciprocal of 5/129 = 129/5

The product of 5/129 and its reciprocal = (5/129) × (129/5) = 1.

3. Sunita and Rehana want to make dresses for their dolls. Sunita has 3/4 m of cloth, and she gave 1/3 of it to Rehana. How much did Rehana have?

Solution:

Length of cloth Sunita has = 3/4 m

According to the given,

Sunita has 3/4 m of cloth, and she gave 1/3 of it to Rehana.

Therefore, the length of cloth Rehana has

= 1/3 of 3/4 m

= (1/3) x (3/4) m

= 1/4 m

4. Anuradha can do a piece of work in 6 hours. What part of the work can she do in 1 hour, in 5 hours, in 6 hours?

Solution:

Let m be the whole work to be done.

The part of work done by Anuradha in 6 hours = m

Thus, the part of work done by her in 1 hour = m/6

The part of work done by her in 5 hours = (m/6) x 5 = 5m/6

The part of work done by her in 6 hours = (m/6) x 6 = m

Therefore, Anuradha can do 1/6 part of work in 1 hour, 5/6 part of work in 5 hours and the complete work in 6 hours.

5. Multiply the following fractions.

(i) (⅖) × 5 ¼

(ii) 2 ⅗ × 3

Solution:

(i) (⅖) × 5 ¼

Here, 5 ¼ is a mixed fraction.

Let us convert this mixed fraction into an improper fraction.

5 ¼ = [(5 × 4) + 1]/4 = 21/4

Thus, (⅖) × 5 ¼ = (⅖) × (21/4) = 21/10

(ii) 2 ⅗ × 3

Here, 2 ⅗ is a mixed fraction.

Let us convert this mixed fraction into an improper fraction.

2 ⅗ = [(2 × 5) + 3]/5 = 13/5

Therefore, 2 ⅗ × 3 = (13/5) × 3 = 39/5

6. Divide 3/10 by (1/4 of 3/5).

Solution:

1/4 od 3/5 = (1/4) × (3/5) = 3/(4 × 5) = 3/20

3/10 ÷ (1/4 of 3/5)

= 3/10 ÷ 3/20

= (3/10) × (20/3)

= 2

Solution:

First, simplify the denominators.

and

Now,

= (7/30) + (13/50) + (9/5)

= (35 + 39 + 270)/150 {since the LCM of 30, 50 and 5 is 150}

= 344/150

= 172/75

8. Evaluate the following:

(i) 3 ½ ÷ 4

(ii) 4 ⅓ ÷ 3

Solution:

(i) 3 ½ ÷ 4

Here, 3 ½ is a mixed fraction.

3 ½ = (3 × 2 + 1)/2 = 7/2

3 ½ ÷ 4 = 7/2 ÷ 4 = (7/2) × (¼) = 7/8

(ii) 4 ⅓ ÷ 3

Here, 4 ⅓ is a mixed fraction.

4 ⅓ = (4 × 3 + 1)/3 = 13/3

4 ⅓ ÷ 3 = 13/3 ÷ 3 = (13/3) × (⅓) = 13/9

9. 1/8 of a number equals 2/5 ÷ 1/20. What is the number?

Solution:

Let p be the number.

According to the given,

(1/8) × p = 2/5 ÷ 1/20

p/8 = (2/5) × (20/1)

p/8 = 2 × 4

p = 8 × 8

p = 64

Hence, 64 is the required number.

10. Raj travels 360 km on three-fifths of his petrol tank. How far would he travel at the same rate with a full tank of petrol?

Solution:

Distance travelled by Raj with three-fifths (i.e. ⅗) of petrol tank = 360 km

Distance travelled by him with a full petrol tank = (360 ÷ 3/5) km

= (360 x 5)/3 km

= 120 x 5 km

= 600 km.

Video Lesson on Fractions

Practice Questions on Fractions

1. The weight of an object on the moon is 1/6 its weight on the Earth. If an object weighs 5 3/5 kg on the Earth, how much would it weigh on the moon?

2. Lipika reads a book for 1 ¾ hour every day. She reads the entire book in 6 days. How many hours in all were required by her to read the book?

3. Multiply and reduce to the lowest form (if possible).

1. 11/2 × 3/10
2. 4/5 × 12/7

4.  Arrange the following in descending order:

1. 2/9, 2/3, 8/21
2. 1/5, 3/7, 7/10

5. Write five equivalent fractions of 8/11.