# NCERT Class 6 Maths Chapter 7 ‘Fractions’: Notes and Solutions (Free PDF)

In this chapter, students will understand everything related to fractions. The chapter is very important is it lays the foundation for understanding the fractions for complex calculations. Students will learn concepts like Proper, Improper, and Mixed Fractions. In Chapter 7 of Class 6 Maths, students will learn how to divide a whole figure into a mentioned number of parts. Read through for CBSE NCERT Class 6 Maths Chapter 7 Fractions Notes, Exercise, and Important Questions.

## NCERT Class 6 Maths Chapter 7 Fractions Notes – Free PDF Download

Below we have given topic-wise notes for the CBSE NCERT Class 6 Maths Chapter 7 Fractions. We have also provided a downloadable free PDF at the end of these notes so you can download and take a printout to study later when you need quick revision before going to the exam hall.

### Topic 1: Fractions

• Fractions: A fraction means a part of a group or of a region. A fraction can be represented by a/b.

### Topic 2: Proper Fraction

• Proper Fraction: In a proper fraction the numerator is always less than the denominator. So, all these fractions lie to the left of 1 as they are less than 1.

For eg, ⅘, ⅔, ½, and so on.

### Topic 3: Improper Fractions

• Improper Fractions: The fractions, where the numerator is bigger than the denominator are called improper fractions.

For eg, 5/4, 3/2, 99/98, and so on.

### Topic 4: Mixed Fractions

• Mixed Fractions: A mixed fraction has a combination of a whole and a part.

For eg, 2½, 3⅔, 1⅘, and so on.

### Topic 5: Equivalent Fractions

• Equivalent Fractions: Different fractions that have the same value but different sets o numerator and denominator.

For eg, ½, 2/4, and 3/6. All these fractions have the same value, i.e. ½ but they differ in numerator and denominator.

### Topic 6: How to Find an Equivalent Fraction?

There are two ways to find the equivalent fraction of a given fraction.

1. To find an equivalent fraction of a given fraction, you may multiply both the numerator and the denominator of the given fraction by the same number. For eg,
1. To find an equivalent fraction, we may divide both the numerator and the denominator by the same number. For eg,

### Topic 6: Comparing Like and Unlike Fractions

• Like Fractions: Two fractions are like fractions if they have the same denominators.

For eg, ½, 3/2, 5/2, and so on.

• Unlike Fractions: Two fractions are unlike if they have different denominators.

For eg, ½, ⅔, ¾, and so on.

Key Takeaways:

1. If the numerator is the same in two unlike fractions, the fraction with the smaller denominator is greater of the two. For example,
1. For like fractions, we should try to change the denominators of the given fractions, so that they become equal. In this case, we must determine the lowest common multiple of the two denominators and convert both the denominators as their LCM by multiplying with a suitable number. This practice will give us the same denominator and then, the fraction with a greater value of the numerator will be greater in value.

For eg, consider fractions ⅔ and ¾, the LCM of 3 and 4 is 12.

So let’s multiply the whole fraction ⅔ with 4 and fraction ¾ with 3, this gives us:

Now, we know that

### Topic 7: Addition and Subtraction of Fractions

2. Retain the denominators.
3. Write the fraction as :

For eg, let’s take ⅗ and ⅖

• Subtraction of Like Fractions: Just like addition, subtraction of the like fractions will be carried out in the same way.

For eg, let’s consider two fractions 5/6 and 2/6.

• Addition and Subtraction of Unlike Fractions: Just like we have studied earlier, the addition and subtraction of unlike fractions can be made easier by making their denominators the same.

## Important Questions in NCERT Class 6 Maths Chapter 7: Free PDF Download

Below we have provided some important exercise questions and their solutions from Chapter 7 of CBSE NCERT Maths for Class 6.

### Exercise 7.1

Q 1. Write the fraction representing the shaded portion.

1.
2.
3.

Ans. The fractions representing the shaded portions are given below.

1. Total number of parts in the given figure = 4

Number of shaded regions = 2

∴ fraction = 2/4

1. Total number of parts in the given figure = 4

Number of shaded regions = 1

∴ fraction = 1/4

1. Total number of parts in the given figure = 8

Number of shaded regions = 4

∴ fraction = 4/8

1. Total number of parts in the given figure = 8

Number of shaded regions = 4

∴ fraction = 4/8

Q 2. What fraction of a day is 8 hours?

Ans. The total number of hours in a day is 24. We have to find the fraction of the day in 8 hours.

So, the required fraction is 8/24 = ⅓.

Q 3. Kanchan dyes dresses. She had to dye 30 dresses. She has so far finished 20

dresses. What fraction of dresses has she finished?

Ans. Total number of dresses that Kanchan had to dye = 30

Dresses dyed so far = 20

So, the fraction of dresses she has finished dyeing = 20/30 = ⅔.

Q 4. Write the natural numbers from 2 to 12. What fraction of them are prime numbers?

Ans. The natural numbers from 2 to 12 are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Hence, the total numbers are 11.

Prime numbers from natural numbers 2 to 12 are 2, 3, 5, 7, 11 = 5 prime numbers.

So, the fraction of prime numbers is 5/11

### Exercise 7.2

Q 1.  Express the following as improper fractions :

1. 7¾
2. 5⅔

Ans. Let us see the improper fractions below.

1. 7¾ = (7 × 4 + 3)/4 = 31/4
2. 5⅔ = (5 × 3 + 2)/3 = 17/3

### Exercise 7.3

Q 1. Replace ☐ in each of the following by the correct number:

(a) 2 / 7 = 8 / ☐

(b) 5 / 8 = 10 / ☐

(c) 3 / 5 = ☐ / 20

Ans. The answers are given below.

1. On cross multiplication, we get:

☐ = (8 × 7)/2

= 56/2 = 28

1. On cross multiplication, we get:

☐ = (8 × 10)/5

= 80/5 = 16

1. On cross multiplication, we get:

☐ = (3 × 20)/5

= 60/5 = 12

Q 2.   Find the equivalent fraction of 3 / 5 having

1. denominator 20
2. numerator 9

Ans: One way of obtaining an equivalent fraction is either by dividing or by multiplying the denominator and numerator of the given fraction with a same number. Hence, the answers are:

1. As the desired denominator of the required equivalent fraction is 20. We will multiply the numerator and denominator of the given fraction with 4.

Hence, (⅗ × 4/4) = 12/20

1. The desired numerator can be achieved if we multiply the whole fraction by 3. So, this gives us:

(⅗ × 3/3) = 9/15

### Exercise 7.4

Q 1. Compare the fractions and put an appropriate sign.

1. 3/6 ☐ 5/6
2. 1/7 ☐ 1/4
3. ⅘ ☐ 5/5
4. ⅗ ☐ 3/7

Ans. The comparisons are given below.

1. <
2. Since the given are unlike fractions, we will convert them into like factors by converting both of the denominators into their lowest common multiple, i.e. 28.

1/7 × 4/4 = 4/28

¼ × 7/7 = 7/28

Now we know, 4/28 < 7/28

1. <
2. Equaising denominators:

⅗ × 7/7 = 21/35

3/7 × 5/5 = 15/35

So, 21/35 > 15/35

Q 2. Ila read 25 pages of a book containing 100 pages. Lalita read 2/5 of the same book. Who reads less?

Ans. Total number of pages in the book = 100

Ila read 25 pages, this resulted in the fraction 25/100 = ¼

Now, to compare both fractions, let’s convert them into like fractions.

¼  × 5/5 = 5/20

⅖ × 4/4 = 8/20

Now, 5/20 < 8/20

So, this suggests that Ila has read less.

### Exercise 7.5

Q 1. Shubham painted 2/3 of the wall space in his room. His sister Madhavi helped

and painted 1/3 of the wall space. How much did they paint together?

Ans. To find the whole area painted by Shubham and Madahavi, let us add the areas of the wall painted by them separately.

⅔ + ⅓ = (2 + 1)/3 = 3/3 = 1

So, Shubham and Madhavi together have painted the whole wall.

Q 2. Javed was given 5/7 of a basket of oranges. What fraction of oranges was left in the basket?

Ans. The whole of a fraction is 1.

Fraction of the basket of oranges given to Javed = 5/7

Farctions of oranges left in the basket = 1 – 5/7 = (7-5)/7 = 2/7

### Exercise 7.6

Q 1. Sarita bought 2/5 metre of ribbon and Lalita 3/4 metre of ribbon. What is the total length of the ribbon they bought?

Ans. To determine the total ribbon bought, we must add both fractions.

Q 2. Jaidev takes 2(⅕) minutes to walk across the school grounds. Rahul takes 7/4 minutes to do the same. Who takes less time and by what fraction?

Ans. Time taken by Jaidev to walk across the ground = (2 × 5 + 1)/5 = 11/5 minutes

Time taken by Rahul to walk across the ground = 7/4 minutes

Converting both the fractions into like fractions:

11/5 × 4/4 = 44/20

7/4 × 5/5 = 35/20

Now we know: 44/20 > 35/20

Difference: 44/20 – 35/20 = 9/20

Hence, Rahul takes 9/20 less minutes than Jaidev to walk across the ground.

Also See:

Class 6 Maths Chapter 1 Knowing Our Numbers Notes and Important Questions – Free PDF

CBSE NCERT Class 6 Maths Chapter 2 Whole Numbers Notes, Exercise and Important Questions – Free PDF

Class 6 Maths Chapter 3 Playing With Numbers Notes and Important Exercise Questions and Answers – Free PDF

Class 6 Maths Chapter 4 Basic Geometrical Ideas Notes and Important Exercise Questions and Answers – Free PDF

Class 6 Maths Chapter 5 Understanding Elementary Shapes Notes and Important Exercise Questions and Answers – Free PDF

Class 6 Maths Chapter 6 Integers Notes and Important Exercise Questions and Answers – Free PDF

## FAQs

Q.1. What are fractions?

Ans: A fraction means a part of a group or of a region. A fraction can be represented by a/b.

Q.2. What are Proper Fractions?

Ans: In a proper fraction, the numerator is always less than the denominator. So, all these fractions lie to the left of 1 as they are less than 1. For eg, ⅘, ⅔, ½, and so on.

Q.3. What are Improper Fractions?

Ans: The fractions, where the numerator is bigger than the denominator are called improper fractions. For eg, 5/4, 3/2, 99/98, and so on.

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