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Grade 6 Fractions Worksheets

Grade 6 maths fractions multiple choice questions (mcqs).

• CBSE Worksheets for Class 6 Maths Fractions Assignment 1
• CBSE Worksheets for Class 6 Maths Fractions Assignment 2
• CBSE Worksheets for Class 6 Maths Fractions Assignment 3
• CBSE Worksheets for Class 6 Maths Fractions Assignment 4
• CBSE Worksheets for Class 6 Maths Fractions Assignment 5
• CBSE Worksheets for Class 6 Maths Fractions Assignment 6
• CBSE Worksheets for Class 6 Maths Fractions Assignment 7
• CBSE Worksheets for Class 6 Maths Fractions Assignment 8

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Maths fractions worksheets for grade 6

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6th Grade Fractions Worksheets

6th grade fractions worksheets are used to give students a better idea of the kind of problems that can be framed on the topic. These 6th grade math worksheets consist of questions on applying arithmetic operators to different types of fractions, word problems, converting fractions, and identifying different types of fractions.

Benefits of 6th Grade Math Worksheets Fractions

There are several topics associated with fractions such as ratios and proportions, percentages, etc. If students have clear concept of fractions, they can solve problems based on other topics easily. 6th grade fractions worksheets help kids in achieving their goal of mastering the topic of fractions by providing several practice sums. The answer keys included with the worksheets detail the step-by-step solution to all problems, enabling students to check their answers.

☛ Practice : Grade 6 Interactive Fractions Worksheets

Printable PDFs for Grade 6 Fractions Worksheets

6th Grade fractions math worksheets are free to download, interactive, easy to use, and are available in PDF format.

• Fractions Math Worksheet for Grade 6
• 6th Grade Fraction Math Worksheet
• Fractions Math Worksheet for 6th Grade
• Fractions Worksheet Grade 6

Interactive 6th Grade Fractions Worksheets

• Grade 6 Types of Fractions Worksheet
• Equivalent Fractions Worksheet for Grade 6
• Grade 6 Multiplication of Fractions by Fractions Worksheet
• Multiplication of Fractions by Whole Numbers 6th Grade Worksheet
• A Recap to Fractions Worksheet for Grade 6

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• Chapter 7: Fractions

NCERT Solutions For Class 6 Maths Chapter 7 Fractions

Subject experts at BYJU’S have prepared the NCERT Solutions For Class 6 Maths Chapter 7 Fractions as per the latest CBSE Syllabus for Class 6, so that students can practise well for the final exams. A fraction is a number representing part of a whole. The whole may be a single object or a group of objects where the parts have to be equal. Also, a fraction is said to be in the simplest (or lowest) form if its numerator and denominator have no common factor except 1. Learning and practising the NCERT Solutions is supposed to help the students in gaining the confidence to solve all the problems related to fractions they come across. The topics and sub-topics covered in Chapter 7 Fractions are as follows:

• 7.1 – Introduction
• 7.2 – A Fraction
• 7.3 – Fraction on the Number Line
• 7.4 – Proper Fractions
• 7.5 – Improper and Mixed Fractions
• 7.6 – Equivalent Fractions
• 7.7 – Simplest Form of a Fraction
• 7.8 – Like Fractions
• 7.9 – Comparing Fractions
• 7.10 – Addition and Subtraction of Fractions

Download Exclusively Curated Chapter Notes for Class 6 Maths Chapter 7 – Fractions

Download most important questions for class 6 maths chapter 7 – fractions.

• Chapter 1 Knowing our Numbers
• Chapter 2 Whole Numbers
• Chapter 3 Playing With Numbers
• Chapter 4 Basic Geometrical Ideas
• Chapter 5 Understanding Elementary Shapes
• Chapter 6 Integers
• Chapter 7 Fractions
• Chapter 8 Decimals
• Chapter 9 Data Handling
• Chapter 10 Mensuration
• Chapter 11 Algebra
• Chapter 12 Ratio And Proportion
• Chapter 13 Introduction To Symmetry
• Chapter 14 Practical Geometry
• Exercise 7.1 Chapter 7 Fractions
• Exercise 7.2 Chapter 7 Fractions
• Exercise 7.3 Chapter 7 Fractions
• Exercise 7.4 Chapter 7 Fractions
• Exercise 7.5 Chapter 7 Fractions
• Exercise 7.6 Chapter 7 Fractions

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

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Access NCERT Solutions for Class 6 Chapter 7: Fractions

Exercise 7.1 page no: 135

1. Write the fraction representing the shaded portion.

(i) Number of parts = 4

Shaded portion = 2

∴ Fraction = 2 / 4

(ii) Number of parts = 9

Shaded portion = 8

∴ Fraction = 8 / 9

(iii) Number of parts = 8

Shaded portion = 4

∴ Fraction = 4 / 8

(iv) Number of parts = 4

Shaded portion = 1

∴ Fraction = 1 / 4

(v) Number of parts = 7

Shaded portion = 3

∴ Fraction = 3 / 7

(vi) Number of parts = 12

∴ Fraction = 3 / 12

(vii) Number of parts = 10

Shaded portion = 10

∴ Fraction = 10 / 10

(viii) Number of parts = 9

∴ Fraction = 4 / 9

(ix) Number of parts = 8

(x) Number of parts = 2

∴ Fraction = 1 / 2

2. Colour the part according to the given fraction.

3. Identify the error, if any.

(i) The shaded portion is not half

Hence, this is not 1 / 2

(ii) Since the parts are not equal

∴ Shaded portion is not 1 / 4

(iii) Since the parts are not equal

∴ Shaded portion is not 3 / 4

4. What fraction of a day is 8 hours?

There are 24 hours in a day

We have 8 hours

Hence, required fraction is 8 / 24

5. What fraction of an hour is 40 minutes?

There are 60 minutes in 1 hour

∴ 1 hour = 60 minutes

Hence, required Fraction = 40 / 60

6. Arya, Abhimanyu, and Vivek shared lunch. Arya has brought two sandwiches, one made of vegetable and one of jam. The other two boys forgot to bring their lunch. Arya agreed to share his sandwiches so that each person will have an equal share of each sandwich.

(a) How can Arya divide his sandwiches so that each person has an equal share?

(b) What part of a sandwich will each boy receive?

(a) Arya has divided the sandwich into 3 equal parts. So each person will get one part.

(b) Each boy receive 1 / 3 part

∴ Required Fraction is 1 / 3

7. Kanchan dyes dresses. She had to dye 30 dresses. She has so far finished 20 dresses. What fraction of dresses has she finished?

Total number of dresses Kanchan has to dye = 30 dresses

Number of dresses she has finished = 20 dresses

∴ Required Fraction = 20 / 30 = 2 / 3

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

Natural numbers from 2 to 12 are

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

Total number of natural numbers given= 11

Number of prime numbers = 5

∴ Required Fraction = 5 / 11

9. Write the natural numbers from 102 to 113. What fraction of them are prime numbers?

Natural numbers from 102 to 113 are

102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113

Total number of natural numbers given = 12

∴ Required Fraction = 4 / 12 = 1 / 3

10. What fraction of these circles have Xs in them?

Total number of circles in the figure = 8

Number of circles having Xs in them = 4

∴ Required Fraction = 4 / 8 = 1 / 2

11. Kristin received a CD player for her birthday. She bought 3 CDs and received 5 others as gifts. What fraction of her total CDs did she buy and what fraction did she receive as gifts?

Number of CDs Kristin bought from the market = 3

Number of CDs received as gifts = 5

Total number of CDs Kristin have = 3 + 5 = 8

∴ Fraction of CD she bought = 3 / 8

∴ Fraction of CDs received as gifts = 5 / 8

Exercise 7.2 page no: 141

1. Draw number lines and locate the points on them:

(a) 1 / 2, 1 / 4, 3 / 4, 4 / 4

(b) 1 / 8, 2 / 8, 3 / 8, 7 / 8

(c) 2 / 5, 3 / 5, 8 / 5, 4 / 5

Here divide the number line from 0 to 1 into four equal parts

C = 2 / 4 = 1 / 2

D = 3 / 4 and

E = 4 / 4 = 1

Divide the number line from 0 to 1 into eight equal parts

From the given number line, we have

2. Express the following as mixed fractions:

3. Express the following as improper fractions:

(a) (7 × 4 + 3) / 4 = 31 / 4

∴ The improper form is 31 / 4

(b) (5 × 7 + 6) / 7 = 41 / 7

∴ The improper form is 41 / 7

(c) (2 × 6 + 5) / 6 = 17 / 6

∴ The improper form is 17 / 6

(d) (10 × 5 + 3) / 5 = 53 / 5

∴ The improper form is 53 / 5

(e) (9 × 7 + 3) / 7 = 66 / 7

∴ The improper form is 66 / 7

(f) (8 × 9 + 4) / 9 = 76 / 9

∴ The improper form is 76 / 9

Exercise 7.3 page no: 146

1. Write the fractions. Are all these fractions equivalent?

(i) The shaded portion is 1 / 2

(ii) The shaded portion is 2 / 4 = (2 / 2) / (4 / 2) = 1 / 2

(iii) The shaded portion is 3 / 6 = (3 / 3) / (6 / 3) = 1 / 2

(iv) The shaded portion is 4 / 8 = (4 / 4) / (8 / 4) = 1 / 2

Hence, all fractions are equivalent.

(i) The shaded portion is 4 / 12 = (4 / 4) / (12 / 4) = 1 / 3

(ii)The shaded portion is 3 / 9 = (3 / 3) / (9 / 3) = 1 / 3

(iii) The shaded portion is 2 / 6 = (2 / 2) / (6 / 2) = 1 / 3

(iv) The shaded portion is 1 / 3

(v) The shaded portion is 6 / 15 = (6 / 3) / (15 / 3) = 2 / 5

All the fractions in their simplest form are not equal

Hence, they are not equivalent fractions.

2. Write the fractions and pair up the equivalent fractions from each row.

(b) 4 / 6 = (4 / 2) / (6 / 2)

(c) 3 / 9 = (3 / 3) / (9 / 3)

(d) 2 / 8 = (2 / 2) / (8 / 2)

(i) 6 / 18 = (6 / 6) / (18 / 6)

(ii) 4 / 8 = (4 / 4) / (8 / 4)

(iii) 12 / 16 = (12 / 4) / (16 / 4)

(iv) 8 / 12 = (8 / 4) / (12 / 4)

(v) 4 / 16 = (4 / 4) / (16 / 4)

The following are the equivalent fractions

(a) and (ii) = 1 / 2

(b) and (iv) = 2 / 3

(c) and (i) = 1 / 3

(d) and (v) = 1 / 4

(e) and (iii) = 3 / 4

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

(a) 2 / 7 = 8 / ☐

(b) 5 / 8 = 10 / ☐

(c) 3 / 5 = ☐ / 20

(d) 45 / 60 = 15 / ☐

(e) 18 / 24 = ☐ / 4

2 / 7 = 8 / ☐

2 × ☐ = 7 × 8

☐ = (7 × 8) / 2

5 / 8 = 10 / ☐

☐ = (8 × 10) / 5

3 / 5 = ☐ / 20

☐ = (3 × 20) / 5

45 / 60 = 15 / ☐

☐ = (15 × 60) / 45

18 / 24 = ☐ / 4

☐ = (18 × 4) / 24

4. Find the equivalent fraction of 3 / 5 having

(a) denominator 20

(b) numerator 9

(c) denominator 30

(d) numerator 27

(a) We require denominator 20

Let M be the numerator of the fractions

∴ M / 20 = 3 / 5

5 × M = 20 × 3

M = (20 × 3) / 5

Therefore, the required fraction is 12 / 20

(b) We require numerator 9

Let N be the denominator of the fractions

∴ 9 / N = 3 / 5

3 × N = 9 × 5

N = (9 × 5) / 3

Therefore, the required fraction is 9 / 15

(c) We require denominator 30

Let D be the numerator of the fraction

∴ D / 30 = 3 / 5

5 × D = 3 × 30

D = (3 × 30) / 5

Therefore, the required fraction is 18 / 30

(d) We require numerator 27

Let N be the denominator of the fraction

∴ 27 / N = 3 / 5

3 × N = 5 × 27

N = (5 × 27) / 3

Therefore, the required fraction is 27 / 45

5. Find the equivalent fraction of 36 / 48 with

(a) numerator 9

(b) denominator 4

(a) Given numerator = 9

∴ 9 / D = 36 / 48

D × 36 = 9 × 48

D = (9 × 48) / 36

Hence, the equivalent fraction is 9 / 12

(b) Given, denominator = 4

∴ N / 4 = 36 / 48

N × 48 = 4 × 36

N = (4 × 36) / 48

Hence, the equivalent fraction is 3 / 4

6. Check whether the given fractions are equivalent:

(a) 5 / 9, 30 / 54

(b) 3 / 10, 12 / 50

(c) 7 / 13, 5 / 11

(a ) Given 5 / 9 and 30 / 54

We have 5× 54 = 270

9 × 30 = 270

5 × 54 = 9 × 30

Hence, 5 / 9 and 30 / 54 are equivalent fractions

(b) Given 3 / 10 and 12 / 50

We have 3 × 50 = 150

10 × 12 = 120

3 × 50 ≠ 10 × 12

Hence, 3 / 10 and 12 / 50 are not equivalent fractions

(c) Given 7 / 13 and 5 / 11

We have 7 × 11 = 77

5 × 13 = 65

7 × 11 ≠ 5 × 13

Hence, 7 / 13 and 5 / 11 are not equivalent fractions

7. Reduce the following fractions to simplest form:

(a) 48 / 60

(b) 150 / 60

(c) 84 / 98

(d) 12 / 52

(a) 48 / 60 = (12 × 4) / (12 × 5)

(b) 150 / 60 = (30 × 5) / (30 × 2)

(c) 84 / 98 = (14 × 6) / (14 × 7)

(d) 12 / 52 = (3 × 4) / (13 × 4)

(e) 7 / 28 = 7 / (7 × 4)

8. Ramesh had 20 pencils, Sheelu had 50 pencils and Jamaal had 80 pencils. After 4 months, Ramesh used up 10 pencils, Sheelu used up 25 pencils and Jamaal used up 40 pencils. What fraction did each use up? Check if each has used up an equal fraction of her/his pencils.

Total number of pencils Ramesh had = 20

Number of pencils used by Ramesh = 10

∴ Fraction = 10 / 20 = 1 / 2

Total number of pencils Sheelu had = 50

Number of pencils used by Sheelu = 25

∴ Fraction = 25 / 50 = 1 / 2

Total number of pencils Jamaal had = 80

Number of pencils used by Jamaal = 40

∴ Fraction = 40 / 80 = 1 / 2

Yes, each has used up an equal fraction of pencils i.e 1 / 2

9. Match the equivalent fractions and write two more for each.

(i) 250 / 400 (a) 2 / 3

(ii) 180 / 200 (b) 2 / 5

(iii) 660 / 990 (c) 1 / 2

(iv) 180 / 360 (d) 5 / 8

(v) 220 / 550 (e) 9 / 10

(i) 250 / 400

= (5 × 50) / (8 × 50)

25 / 40 and 30 / 48 are two more fractions

(ii) 180 / 200

= (9 × 20) / (10 × 20)

18 / 20 and 27 / 30 are two more fractions

(iii) 660 / 990

= (2 × 330) / (3 × 330)

20 / 30 and 200 / 300 are two more fractions

(iv) 180 / 360

= (1 × 180) / (2 × 180)

20 / 40 and 30 / 60 are two more fractions

(v) 220 / 550

= (2 × 110) / (5 × 110)

20 / 50 and 40 / 100 are two more fractions

∴ The equivalent fractions are

(i) 250 / 100 = (d) 5 / 8

(ii) 180 / 200 = (e) 9 / 10

(iii) 660 / 990 = (a) 2 / 3

(iv) 180 / 360 = (c) 1 / 2

(v) 220 / 550 = (b) 2 / 5

Exercise 7.4 page no: 152

1. Write shaded portion as fraction. Arrange them in ascending and descending order using correct sign ‘’ between the fractions:

(c) Show 2 / 6, 4 / 6, 8 / 6 and 6 / 6 on the number line. Put appropriate signs between the fractions given.

5 / 6 ☐ 2 / 6, 3 / 6 ☐ 0, 1 / 6 ☐ 6 / 6, 8 / 6 ☐ 5 / 6

(a) First circle shows 3 shaded parts out of 8 equal parts. Hence, the fraction is 3 / 8

Second circle shows 6 shaded parts out of 8 equal parts. Hence, the fraction is 6 / 8

Third circle shows 4 shaded parts out of 8 equal parts. Hence, the fraction is 4 / 8

Fourth circle shows 1 shaded parts out of 8 equal parts. Hence, the fraction is 1 / 8

The arranged fractions are:

1 / 8 < 3 / 8 < 4 / 8 < 6 / 8

(b) First square shows 8 shaded parts out of 9 equal parts. Hence, the fraction is 8 / 9

Second square shows 4 shaded parts out of 9 equal parts. Hence, the fraction is 4 / 9

Third square shows 3 shaded parts out of 9 equal parts. Hence, the fraction is 3 / 9

Fourth square shows 6 shaded parts out of 9 equal parts. Hence, the fraction is 6 / 9

3 / 9 < 4 / 9 < 6 / 9 < 8 / 9

(c) Each unit length should be divided into 6 equal parts to represent the fractions 2 / 6, 4 / 6, 8 / 6 and

6 / 6 on number line. These fractions can be represented as follows:

5 / 6 > 2 / 6

3 / 6 > 0

1 / 6 < 6 / 6

8 / 6 > 5 / 6

2. Compare the fractions and put an appropriate sign.

(a) 3 / 6 ☐ 5 / 6

(b) 1 / 7 ☐ 1 / 4

(c) 4 / 5 ☐ 5 / 5

(d) 3 / 5 ☐ 3 / 7

(a) Here both fractions have same denominators. So, the fraction with greater numerator is the highest factor

∴ 3 / 6 < 5 / 6

(b) Multiply by 4

1 / 7 = (1 × 4) / (7 × 4)

Multiply by 7

1 / 4 = (1 × 7) / (4 × 7)

Here 4 < 7

∴ 1 / 7 < 1 / 4

(c) Here both fractions have same denominators. So, the fraction with greater numerator is the highest factor

∴ 4 / 5 < 5 / 5

(d) Here both numerators are same. So, the fraction having less denominator will be the highest factor

∴ 3 / 7 < 3 / 5

3. Make five more such pairs and put appropriate signs.

(a) 5 / 8 < 6 / 8

Here, the denominators are same. So, the fraction having greater numerator is the highest factor

(ii) 5 / 8 > 2 / 8

(iii) 6 / 13 > 6 / 18

Here, the numerators are same. So, the fraction having lesser denominator will be the highest factor

(iv) 5 / 25 > 3 / 25

(v) 9 / 50 < 9 / 45

4. Look at the figures and write ‘<’ or ‘>’, ‘=’ between the given pairs of fractions.

(a) 1 / 6 ☐ 1 / 3

(b) 3 / 4 ☐ 2 / 6

(c) 2 / 3 ☐ 2 / 4

(d) 6 / 6 ☐ 3 / 3

(e) 5 / 6 ☐ 5 / 5

(a) Here, the numerators are same. So, the fraction having lesser denominator is the greater

∴ 1 / 6 < 1 / 3

(b) 3 / 4 = (3 × 3) / (4 × 3)

2 / 6 = (2 × 2) / (6 × 2)

Between 4 / 12, 9 / 12

Both fractions have same denominators. So, the fraction having greater numerator will be the greater

∴ 9 / 12 > 4 / 12

3 / 4 > 2 / 6

(c) Here, the numerators are same. So, the fraction having lesser denominator is the greater

∴ 2 / 3 > 2 / 4

(d) We get 6 / 6 = 1 and 3 / 3 = 1

So, 6 / 6 = 3 / 3

(e) Here, the numerators are same. So, the fraction having lesser denominator is the greater

∴ 5 / 6 < 5 / 5

5. How quickly can you do this? Fill appropriate sign. ( ‘<’, ‘=’, ‘>’)

(a) 1 / 2 ☐ 1 / 5

(b) 2 / 4 ☐ 3 / 6

(c) 3 / 5 ☐ 2 / 3

(d) 3 / 4 ☐ 2 / 8

(e) 3 / 5 ☐ 6 / 5

(f) 7 / 9 ☐ 3 / 9

(g) 1 / 4 ☐ 2 / 8

(h) 6 / 10 ☐ 4 / 5

(i) 3 / 4 ☐ 7 / 8

(j) 6 / 10 ☐ 3 / 5

(k) 5 / 7 ☐ 15 / 21

(a) Here, the numerators are same. So, the fraction having lesser denominator is greater

∴ 1 / 2 > 1 / 5

(b) 2 / 4 = 1 / 2 and 3 / 6 = 1 / 2

∴ 2 / 4 = 3 / 6

(c) 3 / 5 = (3 × 3) / (5 × 3)

2 / 3 = (2 × 5) / 3 × 5)

Here, between 9 / 15 and 10 / 15 both have same denominators. Hence, the fraction having greater numerator will be the greater.

∴ 3 / 5 < 2 / 3

(d) Here, 2 / 8 = 1 / 4

As, 3 / 4 and 1 / 4 have same denominators. Hence, the fraction having greater numerator will be the greater

∴ 3 / 4 > 2 / 8

(e) Here, the denominators are same. So, the fraction having greater numerator will be the greater

∴ 3 / 5 < 6 / 5

(f) Here, the denominators are same. So, the fraction having greater numerator will be the greater

∴ 7 / 9 > 3 / 9

(g) We know 2 / 8 = 1 / 4

Hence, 1 / 4 = 2 / 8

(h) 6 / 10 = (3 × 2) / (5 × 2)

Between 3 / 5 and 4 / 5

Both have same denominators. So, the fraction having greater numerator will be greater

∴ 6 / 10 < 4 / 5

(i) 3 / 4 = (3 × 2) / (4 × 2)

Between 6 / 8 and 7 / 8

∴ 3 / 4 < 7 / 8

(j) 6 / 10 = (3 × 2) / (5 × 2)

∴ 6 / 10 = 3 / 5

(k) 5 / 7 = (5 × 3) / (7 × 3)

∴ 5 / 7 = 15 / 21

6. The following fractions represent just three different numbers. Separate them into three groups of equivalent fractions, by changing each one to its simplest form.

(a) 2 / 12 (b) 3 / 15 (c) 8 / 50 (d) 16 / 100 (e) 10 / 60 (f) 15 / 75

(g) 12 / 60 (h) 16 / 96 (i) 12 / 75 (j) 12 / 72 (k) 3 / 18 (l) 4 / 25

(a) 2 / 12 = (1 × 2) / (6 × 2)

(b) 3 / 15 = (1 × 3) / (5 × 3)

(c) 8 / 50 = (4 × 2) / (25 × 2)

(d) 16 / 100 = (4 × 4) / (25 × 4)

(e) 10 / 60 = (1 × 10) / (6 × 10)

(f) 15 / 75 = (1 × 15) / (5 × 15)

(g) 12 / 60 = (1 × 12) / (5 × 12)

(h) 16 / 96

= (1 × 16) / (6 × 16)

(i) 12 / 75 = (4 × 3) / (25 × 3)

(j) 12 / 72 = (1 × 12) / 6 × 12)

(k) 3 / 18 = (1 × 3) / (6 × 3)

Totally there are 3 groups of equivalent fractions.

1 / 6 = (a), (e), (h), (j), (k)

1 / 5 = (b), (f), (g)

4 / 25 = (c), (d), (i), (l)

7. Find answers to the following. Write and indicate how you solved them.

(a) Is 5 / 9 equal to 4 / 5?

(b) Is 9 / 16 equal to 5 / 9?

(c) Is 4 /5 equal to 16 / 20?

(d) Is 1 / 15 equal to 4 / 30?

(a) 5 / 9, 4 / 5

Convert these fractions into like fractions

5 / 9 = (5 / 9) × (5 / 5)

4 / 5 = (4 / 5) × (9 / 9)

∴ 25 / 45 ≠ 36 / 45

Hence, 5 / 9 is not equal to 4 / 5

(b) 9 / 16, 5 / 9

Convert into like fractions

9 / 16 = (9 / 16) × (9 / 9)

5 / 9 = (5 / 9) × (16 / 16)

∴ 81 / 144 ≠ 80 / 144

Hence, 9 / 16 is not equal to 5 / 9

(c) 4 / 5, 16 / 20

16 / 20 = (4 × 4) / (5 × 4)

∴ 4 / 5 = 16 / 20

Hence, 4 / 5 is equal to 16 / 20

(d) 1 / 15, 4 / 30

4 / 30 = (2 × 2) / (15 × 2)

∴ 1 / 15 ≠ 4 / 30

Hence, 1 / 15 is not equal to 4 / 30

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

Total number of pages a book has = 100 pages

Lalita read = 2 / 5 × 100 = 40 pages

Ila read = 25 pages

∴ Ila read less than Lalita.

9. Rafiq exercised for 3 / 6 of an hour, while Rohit exercised for 3 / 4 of an hour. Who exercised for a longer time?

Rafiq exercised = 3 / 6 of an hour

Rohit exercised = 3 / 4 of a hour

3 / 6, 3 / 4

Convert these into like fractions

3 / 6 = (3 × 2) / (6 × 2)

3 / 4 = (3 × 3) / (4 × 3)

Clearly, 9 / 12 > 6 / 12

∴ 3 / 4 > 3 / 6

Therefore Rohit exercised for a longer time than Rafiq.

10. In a class A of 25 students, 20 passed with 60% or more marks; in another class B of 30 students, 24 passed with 60% or more marks. In which class was a greater fraction of students getting with 60% or more marks?

Total number of students in Class A = 25

Students passed in first class in Class A = 20

Hence, fraction = 20 / 25

Total number of students in Class B = 30

Students passed in first class in Class B = 24

Hence, fraction = 24 / 30

∴ An equal fraction of students passed in first class in both the classes

Exercise 7.5 page no: 157

1. Write these fractions appropriately as additions or subtractions:

(a) Total number of parts each rectangle has = 5

No. of shaded parts in the first rectangle = 1 i.e 1 / 5

No. of shaded parts in the second rectangle = 2 i.e 2 / 5

No. of shaded parts in the third rectangle = 3 i.e 3 / 5

Clearly, the fraction represented by the third rectangle = Sum of the fractions represented by first and second rectangle

Hence, 1 / 5 + 2 / 5 = 3 / 5

(b) Total number of parts each circle has = 5

We may observe that the first, second and third circles represent 5, 3 and 2 shaded parts out of 5 equal parts respectively. Clearly, fraction represented by the third circle is the difference between the fractions represented by the first and second circles.

Hence, 5 / 5 – 3 / 5 = 2 / 5

(c) Here we may observe that first, second and third rectangles represents 2, 3 and 5 shaded parts out of 6 equal parts, respectively. Clearly, fraction represented by the third rectangle is the sum of fractions represented by the first and second rectangles.

Hence, 2 / 6 + 3 / 6 = 5 / 6

(a) 1 / 18 + 1 / 18

(b) 8 / 15 + 3 / 15

(c) 7 / 7 – 5 / 7

(d) 1 / 22 + 21 / 22

(e) 12 / 15 – 7 / 15

(f) 5 / 8 + 3 / 8

(g) 1 – 2 / 3 (1 = 3 / 3)

(h) 1 / 4 + 0 / 4

(i) 3 – 12 / 5

= (1 + 1) / 18

= (8 + 3) / 15

= (7 – 5) / 7

= (1 + 21) / 22

(e) 12 /15 – 7 / 15

= (12 – 7) / 15

= (5 + 3) / 8

(g) 1 – 2 / 3

= 3 / 3 – 2 / 3

= (3 – 2) / 3

(h) 1 / 4 + 0

= 15 / 5 – 12/ 5

= (15 – 12) / 5

3. 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?

Wall space painted by Shubham in a room = 2 / 3

Wall space painted by Madhavi in a room = 1 / 3

Total space painted by both = (2 / 3 + 1 / 3)

= (2 + 1) / 3

∴ Shubham and Madhavi together painted 1 complete wall in a room.

4. Fill in the missing fractions.

(a) 7 / 10 – ▯ = 3 / 10

(b) ▯ – 3 / 21 = 5 / 21

(c) ▯ – 3 / 6 = 3 / 6

(d) ▯ + 5 / 27 = 12 / 27

(a) Given 7 / 10 – ▯ = 3 / 10

▯ = 7 / 10 – 3 / 10

▯ = (7 – 3) / 10

(b) Given ▯ – 3 / 21 = 5 / 21

▯ = 5 / 21 + 3 / 21

▯ = (5 + 3) / 21

(c) Given ▯ – 3 / 6 = 3 / 6

▯ = 3 / 6 + 3 / 6

▯ = (3 + 3) / 6

(d) Given ▯ + 5 / 27 = 12 / 27

▯ = 12 / 27 – 5 /27

▯ = (12 – 5) / 27

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

Fraction of oranges given to Javed = 5 / 7

Fraction of oranges left in the basket = 1 – 5 / 7

= 7 / 7 – 5 / 7

Exercise 7.6 page no: 160

(a) 2 / 3 + 1 / 7

(b) 3 / 10 + 7 / 15

(c) 4 / 9 + 2 / 7

(d) 5 / 7 + 1 / 3

(e) 2 / 5 + 1 / 6

(f) 4 / 5 + 2 / 3

(g) 3 / 4 – 1 / 3

(h) 5 / 6 – 1 / 3

(i) 2 / 3 + 3 / 4 + 1 / 2

(j) 1/ 2 + 1 / 3 + 1 / 6

(m) 16 / 5 – 7 / 5

(n) 4 / 3 – 1 / 2

(a) 2 / 3 + 1/ 7

= (14 + 3) / 21

Taking LCM 30

= [(3 × 3) + (7 × 2)] / 30

= (9 + 14) / 30

(c) 4 / 9 + 2/ 7

Taking LCM 63

= [(4 × 7) + (2 × 9)] / 63

= (28 + 18) / 63

Taking LCM 21

= [(5 × 3) + (1 × 7)] / 21

= (15 + 7) / 21

= [(2 × 6) + (1 × 5)] / 30

= (12 + 5) / 30

Taking LCM 15

= [(4 × 3) + (2 × 5)] / 15

= (12 + 10) / 15

Taking LCM 12

= [(3 × 3) – (1 × 4)] / 12

= (9 – 4) / 12

Taking LCM 6

= [(5 × 1) – (1 × 2)] / 6

= (5 – 2) / 6

= [(2 × 4) + (3 × 3) + (1 × 6)] / 12

= (8 + 9 + 6) / 12

(j) 1 / 2 + 1 / 3 + 1 / 6

= [(1 × 3) + (1 × 2) + (1 × 1)] / 6

= (3 + 2 + 1) / 6

= [(3 × 1) + 1] / 3 + [(3 × 3) + 2] / 3

= (3 + 1) / 3 + (9 + 2) / 3

= 4/ 3 + 11 / 3

= (4 + 11) / 3

= [(3 × 4) + 2] / 3 + [(3 × 4) + 1] / 4

= 14 / 3 + 13 / 4

= [(14 × 4) + (13 × 3)] / 12

= (56 + 39) / 12

= (16 – 7) / 5

(n) 4 /3 – 1 / 2

= [(4 × 2) – (1 × 3)] / 6

= (8 – 3) /6

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

Ribbon length bought by Sarita = 2 / 5 metre

Ribbon length bought by Lalita = 3 / 4 metre

Total length of the ribbon bought by both of them = 2 / 5 + 3 / 4

Taking LCM 20

= [(2 × 4) + (3 × 5)] / 20

= (8 + 15) / 20

= 23 / 20 metre

∴ Total length of the ribbon bought by both Sarita and Lalita is 23 / 20 metre

Total amount of cake given to both of them = 3 / 2 + 4 / 3

= [(3 × 3) + (4 × 2)] / 6

= (9 + 8) / 6

4. Fill in the boxes:

(a) ▯ – 5 / 8 = 1 / 4

(b) ▯ – 1 / 5 = 1 / 2

(c) 1 / 2 – ▯ = 1 / 6

▯ = 1 / 4 + 5 / 8

▯ = [(1 × 2 + 5)] / 8

▯ = 1 / 2 + 1 / 5

▯ = [(1 × 5) + (1 × 2)] / 10

▯ = (5 + 2) / 10

▯ = 1 / 2 – 1 / 6

▯ = [(1 × 3) – (1 × 1)] / 6

▯ = (3 – 1) / 6

5. Complete the addition and subtraction box.

(a) 2 / 3 + 4 / 3

= (2 + 4) / 3

1 / 3 + 2 / 3

= (1 + 2) / 3

2 / 3 – 1 / 3

= (2 – 1) / 3

4 / 3 – 2 / 3

= (4 – 2) / 3

Hence, the complete given box is

(b) 1 / 2 + 1 / 3

= [(1 × 3) + (1 × 2)] / 6

= (3 + 2) / 6

1 / 3 + 1 / 4

= [(1 × 4) + (1 × 3)] / 12

= (4 + 3) / 12

1 / 2 – 1 / 3

= [(1 × 3) – (1 × 2)] / 6

= (3 – 2) / 6

1 / 3 – 1 / 4

= [(1 × 4) – (1 ×3)] / 12

= (4 – 3) / 12

1 / 6 + 1 / 12

= [(1 × 2) + 1] / 12

= (2 + 1) / 12

6. A piece of wire 7 / 8 metre long broke into two pieces. One piece was 1 / 4 metre long. How long is the other piece?

Total length of wire = 7 / 8 metre

Length of one piece of wire = 1 / 4 metre

Length of other piece of wire = Length of the original wire and this one piece of wire

= 7 / 8 – 1 / 4

= [(7 × 1) – (1 × 2)] / 8

= (7 – 2) / 8

∴ Length of the other piece of wire = 5 / 8 metre

7. Nandini’s house is 9 / 10 km from her school. She walked some distance and then took a bus for 1 / 2 km to reach the school. How far did she walk?

Distance of the school from house = 9 / 10 km

Distance she travelled by bus = 1 / 2 km

Distance walked by Nandini = Total distance of the school – Distance she travelled by bus

= 9 / 10 – 1 / 2

= [(9 × 1) – (1 × 5)] / 10

= (9 – 5) / 10

∴ Distance walked by Nandini is 2 / 5 km

8. Asha and Samuel have bookshelves of the same size partly filled with books. Asha’s shelf is 5 / 6 th full and Samuel’s shelf is 2/ 5 th full. Whose bookshelf is more full? By what fraction?

Fraction of Asha’s bookshelf = 5 / 6

Fraction of Samuel’s bookshelf = 2 / 5

5 / 6 = 5 / 6 × 5 / 5

= (5 × 5) / (6 × 5)

2 / 5 = 2 / 5 × 6 / 6

= (2 × 6) / (5 × 6)

25 / 30 > 12 / 30

5 / 6 > 2 / 5

∴ Asha’s bookshelf is more full than Samuel’s bookshelf

Difference = 5 / 6 – 2 / 5

= 25 / 30 – 12 / 30

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

11 / 5 = 11 / 5 × 4 / 4

= (11 × 4) / (5 × 4)

7 / 4 = 7 / 4 × 5 / 5

= (7 × 5) / (4 × 5)

Clearly, 44 / 20 > 35 / 20

11 / 5 > 7 / 4

∴ Rahul takes less time than Jaidev to walk across the school ground

Difference = 11 / 5 – 7 / 4

= 44 / 20 – 35 / 20

Hence, Rahul walks across the school ground by 9 / 20 minutes

Frequently Asked Questions on NCERT Solutions for Class 6 Maths Chapter 7

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NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12

Fractions Class 6 Extra Questions Maths Chapter 7

June 11, 2019 by Bhagya

Extra Questions for Class 6 Maths Chapter 7 Fractions

Fractions Class 6 Extra Questions Very Short Answer Type

Question 6. Write all the natural numbers from 1 to 15. What fraction of them are prime numbers? Solution: Natural numbers from 1 to 15 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 and 15 Prime numbers from 1 to 15 are 2, 3, 5, 7, 11, 13, i.e., 6 prime numbers. ∴ Fraction of prime numbers = \(\frac { 6 }{ 15 }\)

Fractions Class 6 Extra Questions Short Answer Type

Question 12. Write any (a) three proper and three improper fractions with denominator 7. (b) two proper and two improper fractions with numerator 9. Solution: (a) Proper fractions with denominator 7 are: \(\frac { 2 }{ 7 }\) , \(\frac { 3 }{ 7 }\) and \(\frac { 5 }{ 7 }\) Improper fractions with denominator 7 are: \(\frac { 9 }{ 7 }\) , \(\frac { 11 }{ 7 }\) and \(\frac { 13 }{ 6 }\)

(b) Proper fractions with numerator 9 are: \(\frac { 9 }{ 11 }\) and \(\frac { 9 }{ 17 }\) Improper fractions with numerator 9 are: \(\frac { 9 }{ 2 }\) and \(\frac { 9 }{ 5 }\)

Fractions Class 6 Extra Questions Higher Order Thinking Skills (HOTS)

Extra Questions for Class 6 Maths

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Important Questions for CBSE Class 6 Maths Chapter 7 - Fractions

• Class 6 Important Question
• Chapter 7: Fractions

CBSE Class 6 Maths Important Questions Chapter 7 - Fractions - Free PDF Download

Class 6 maths chapter 7 important questions PDF consists of specially curated and previous year questions that help students get a rough idea of the types of questions that can be asked in their semester examinations. Important Questions For Class 6 Maths Chapter 7 help students in revising what they have studied in an orderly manner, making sure that they don’t miss any important topics.  The subject matter experts at Vedantu have made sure to cover all the important concepts and necessary points for Class 6 Maths chapter 7.

You can download important questions on fractions for class 6 from Vedantu, on your laptop, PC or phone and study at your convenience, whenever and wherever. It is portable.

Given below is a summarized version of fractions class 6 important questions. It is advised to brush up on all the topics before you start attempting important questions on fractions for class 6. Vedantu is a platform that provides free CBSE Solutions (NCERT) and other study materials for students. You can also register Online for NCERT Class 6 Science tuition on Vedantu.com to score more marks in CBSE board examination.

Download CBSE Class 6 Maths Important Questions 2024-25 PDF

Also, check CBSE Class 6 Maths Important Questions for other chapters:

Study Important Questions for Class 6 Maths Chapter 7 - Fraction

Very short answer questions                                                1 mark.

1. Write fraction representing the shaded portion

Ans: Given- A figure with some shaded squares in it.

We have to find fractions for the shaded portion.

Total number of squares $=12$

Number of shaded boxes $=6$

$\therefore $ the shaded portion $=\dfrac{6}{12}$

2. Shade in the given figure: $\dfrac{5}{9}$

Ans: Given: A figure having $9$ boxes.

We have to shade 5 boxes out of a total 9 boxes.

3. Write in fraction form of eight-ninths.

Ans: We are given eight-ninths

To find: the fraction form of eight-ninths

Eight - ninths means eight parts out of nine

So, the fraction will be $\dfrac{8}{9}$

4. Write down the fraction with numerator 3, denominator 9

Ans: Given, numerator =3

Denominator =9

We have to find the fraction.

We know that the numerator is the above part of a fraction and the denominator is the below part of the fraction.

$\therefore$ The fraction is $\dfrac{3}{9}$.

5. Fill up the blanks

$\mathbf{\dfrac{1}{12}\square 1}$

Ans: Given: $\dfrac{1}{12}\square 1$

We have to put a sign between the terms like $<,>,=$

Solve, $\dfrac{1}{12}$

We can see that the value is less than one.

$\therefore \dfrac{1}{12}<1$

$\mathbf{\dfrac{6512}{6512}\square 1}$

Ans: Given: $\dfrac{6512}{6512}\square 1$

Solve, $\dfrac{6512}{6512}$

$\dfrac{6512}{6512}=1$

6. Compare $\mathbf{\dfrac{4}{5}}$ and $\mathbf{\dfrac{3}{5}}$

Ans: Given: two terms $\dfrac{4}{5},\,\dfrac{3}{5}$

We have to compare the given terms.

We can see that the denominator of both the terms is the same. So we will compare the numerators only.

Here, 

 $\therefore \dfrac{4}{5}>\dfrac{3}{5}$

Short Answer Questions                                                           2 Marks

1. Find $\mathbf{\dfrac{3}{4}}$ of $\mathbf{12.}$

Ans: Given, two terms $\dfrac{3}{4},12$

We have to find $\dfrac{3}{4}$ of $12.$

We know that $x$ of $y$ means $x\times y$

$\therefore \dfrac{3}{4}$ of $12$\[\]

$ =\dfrac{3}{4}\times 12 $

2. What fraction of an hour is 35 minutes?

Ans: Given, a time

We have to find $35$ minutes will be what fraction of an hour.

We know that $1$ hour $=60$ minutes

$\therefore $ fraction will be $\dfrac{35}{60}.$

3. The figure given can be written in the fraction form as $\mathbf{\dfrac{2}{3}.}$ Say true or false.

Ans: Given: figure

We have to find if the figure shows fraction $\dfrac{2}{3}.$

As we can see that all parts of the figure are not similar. Therefore, it cannot be represented as a fraction. So, the statement is False.

4. Name the numerator and denominator in the $\mathbf{\dfrac{16}{20}}$

Ans: Given: $\dfrac{16}{20}$

To find: numerator and denominator

We know that the numerator is the above part of the fraction and the denominator is the below part.

$\therefore $ Numerator $=16$

Denominator $=20$

5. Convert $\mathbf{\dfrac{30}{8}}$ into a mixed fraction

Ans: Given: $\dfrac{30}{8}$

To find: mixed fraction of the given expression.

We got mixed fraction by dividing the fraction

We know if  $\dfrac{x}{y}=z$ then mixed fraction is $z\dfrac{x}{y}$

$\therefore $ $\dfrac{30}{8}$

$ =3\dfrac{6}{8} $

$ =3\dfrac{3}{4}$

6. Convert $\mathbf{6\dfrac{7}{9}}$ into improper fraction.

Ans: Given: $6\dfrac{7}{9}$

To find the improper form of the given expression

We know that \[z\dfrac{x}{y}=\dfrac{y\times z+x}{y}\]

So, $6\dfrac{7}{9}=9\times 6+7$ as numerator

Therefore, the improper fraction will be $\dfrac{61}{9}.$

7. Fill in the blanks $\mathbf{\dfrac{54}{63}=\dfrac{6}{\square }}$

Ans:  Given: $\dfrac{54}{63}=\dfrac{6}{\square }$

We need to fill the blank

On Left Hand Side, divide numerator and denominator y by $9$

Thus, $\dfrac{54}{63}\div \dfrac{9}{9}$

$=\dfrac{6}{7}$

Thus, the number which has to be filled at blank is $7.$

8. Simplify:

$\mathbf{\dfrac{3}{8}+\dfrac{4}{8}+\dfrac{2}{8}}$

Ans: Given: $\dfrac{3}{8}+\dfrac{4}{8}+\dfrac{2}{8}$

We have to simplify the fractions by adding them

As the denominator of each fraction is same then the $\text{L}\text{.C}\text{.M}$ will be $8.$

Now, simply add the numerator of each fraction, we get

$=\dfrac{3+4+2}{8}$ $=\dfrac{9}{8}.$

$\mathbf{\dfrac{8}{9}-\dfrac{6}{9}}$

Ans: We have to find the difference between the fractions.

We can see that the denominator of both fractions is same then the $\text{L}\text{.C}\text{.M}$will be $9.$

Now, simply subtract the numerators, we get

$ \dfrac{8-6}{9} $

$ =\dfrac{2}{9} $

Short Answer Questions                                                           3 Marks

1. Seema has 28 books. She gave $\mathbf{\dfrac{4}{10}}$ to Meera. How many books does Meena has? How much is left with Seema?

Ans: Given: Total books Seema has $=28$

Seema gave books to Meera $\dfrac{4}{10}$ of $28$

$\therefore $ Books with Meena $=\dfrac{4}{10}\times 28$

$=11$ Books

Now, books left with Seema $=28-11$

$=17$ Books

2. Represent $\mathbf{3\dfrac{2}{5}}$ on the number line.

Ans: Given: $3\dfrac{2}{5}$

We have to represent the fraction on the number line.

We can write the fraction as,

$3\dfrac{2}{5}=3+\dfrac{2}{5}$

Therefore, we represent it on the number line as 

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3. Write a fraction equivalent to $\mathbf{\dfrac{4}{5}}$ with numerator 16.

Ans: Given: $\dfrac{4}{5}$

We have to find a fraction so that the numerator of fraction is $16.$

Multiply the numerator and denominator of the given fraction with $4$to get the required fraction.

$ \dfrac{4}{5}\times \dfrac{4}{4} $ 

$ =\dfrac{16}{20} $

4. Write a fraction equivalent to $\mathbf{\dfrac{42}{60}}$ with denominator 10.

Ans: Given: $\dfrac{42}{60}$

We have to find a fraction so that the denominator of fraction is $10.$

Divide the numerator and denominator of the given fraction with $6$ to get the required fraction.

$ \therefore \dfrac{42}{60}\div \dfrac{6}{6} $

$ =\dfrac{7}{10} $

5. Simplify $\mathbf{\dfrac{7}{10}}$ into the simplest form.

Ans: Given: $\dfrac{7}{10}$

We have to find the simplest form of the fraction.

The HCF of the terms \[7\text{ }\!\!\And\!\!\text{ }10\] is \[1.\]

Thus, the fraction $\dfrac{7}{10}$ is already in its simplest form.

6. Simplify \[\mathbf{2\dfrac{7}{9}+\dfrac{11}{15}+\dfrac{9}{24}-3\dfrac{1}{4}}\]

Ans: Given: \[2\dfrac{7}{9}+\dfrac{11}{15}+\dfrac{9}{24}-3\dfrac{1}{4}\]

We need to simplify the given expression. So we’ll find \[\text{LCM}\]and then simplify the expression.

\[\text{LCM}\]of numbers \[9,15,24,4=360\]

$ 2\dfrac{7}{9}+\dfrac{11}{15}+\dfrac{9}{24}-3\dfrac{1}{4} $ 

$ =\dfrac{25}{9}+\dfrac{11}{15}+\dfrac{9}{24}-\dfrac{13}{4} $

$ =\dfrac{1000+264+135-1170}{360} $

$ =\dfrac{1399-1170}{360} $

$ =\dfrac{229}{360} $

7. Subtract $\mathbf{3\dfrac{7}{8}-5\dfrac{1}{6}}$

Ans: Given: $3\dfrac{7}{8}-5\dfrac{1}{6}$

\[\text{LCM}\] of the numbers $6,8=24$

$ 3\dfrac{7}{8}-5\dfrac{1}{6} $

$ =\dfrac{31}{6}-\dfrac{31}{8}$ 

$ =\dfrac{31\times 4-31\times 3}{24} $

$ =\dfrac{124-93}{24} $

$ =\dfrac{31}{24} $

Long  Answer Questions                                                           4 Marks

1. Write four equivalent fraction for each of the following:

$\mathbf{\dfrac{3}{7}}$

 Ans: Given: $\dfrac{3}{7}$

To find: four equivalent fraction

Multiply and divide numerator and denominator with four different numbers

$ \dfrac{3}{7}\times \dfrac{2}{2}=\dfrac{6}{14} $

$ \dfrac{3}{7}\times \dfrac{3}{3}=\dfrac{9}{21} $

$ \dfrac{3}{7}\times \dfrac{4}{4}=\dfrac{12}{28} $

$ \dfrac{3}{7}\times \dfrac{5}{5}=\dfrac{15}{35} $

$\mathbf{\dfrac{300}{900}}$

Ans: To find four equivalent fraction

$ \dfrac{300}{900}\div \dfrac{2}{2}=\dfrac{150}{450}$ 

$ \dfrac{300}{900}\div \dfrac{3}{3}=\dfrac{100}{300} $

$ \dfrac{300}{900}\div \dfrac{5}{5}=\dfrac{60}{180} $

$ \dfrac{300}{900}\div \dfrac{10}{10}=\dfrac{30}{90} $ 

2. Show that $\mathbf{\dfrac{6}{7}}$ and $\mathbf{\dfrac{42}{49}}$ are equivalent fractions.

Ans: Given: Fractions, $\dfrac{6}{7}$, $\dfrac{42}{49}$

We need to show that both the fractions are equivalent.

Thus, $\dfrac{6}{7}=\dfrac{42}{49}$

Cross multiply, we get

$ 6\times 49=249........(1) $

$ 7\times 42=294........(2) $

$ \Rightarrow (1)=(2) $

Therefore, we can say that the given fractions are equivalent.

3. Reduce into simplest form: $\mathbf{\dfrac{225}{500}}$

Ans: Given: $\dfrac{225}{500}$

We need to find the simplest form of the given fraction.

Divide by \[5,\] we get

$\dfrac{225}{500}\div \dfrac{5}{5}=\dfrac{45}{100}$

Again, divide by \[5,\] we get

$\dfrac{45}{100}\div \dfrac{5}{5}=\dfrac{9}{20}$

We can see that the HCF of the terms of the fraction is $1$

$\therefore \dfrac{9}{20}$ is the simplest form of the given fraction.

4. Convert \[\mathbf{\dfrac{1}{4},\dfrac{5}{8},\dfrac{13}{24}}\] into like fractions.

Ans: Given: \[\dfrac{1}{4},\dfrac{5}{8},\dfrac{13}{24}\]

We need to convert the given fractions into like fractions.

The LCM of the denominators will be

\[\begin{align} & 4\left| \!{\underline {\, 4,8,24 \,}} \right.  \\ & 2\left| \!{\underline {\, 1,2,6 \,}} \right.  \\ & \left| \!{\underline {\, 1,1,3 \,}} \right.  \\ \end{align}\]

Therefore, LCM = $4\times 2\times 3$ 

$\quad\quad\quad\quad\quad\quad=24$ 

$=\dfrac{\left( 6\times 1 \right),\left( 5\times 3 \right),\left( 13 \right)}{24}$ 

$=\dfrac{6,15,13}{24}$

So, the required like fractions are $\dfrac{6}{24},\dfrac{15}{24},\dfrac{13}{24}$

5. Compare $\mathbf{\dfrac{8}{13}\text{and}\dfrac{8}{7}}$

Ans: Given: fractions $\dfrac{8}{13}\text{and}\dfrac{8}{7}$

We need to compare the fractions.

To compare the fractions the denominator of the fractions must be the same.

To convert into like terms, take LCM then we get

$ =13\times 7 $

$ \therefore \dfrac{8\times 7,8\times 13}{91} $

$ =\dfrac{56,104}{91} $

$ \therefore \dfrac{56}{91}<\dfrac{104}{91} $

6. Roshni bought a material of length $\mathbf{3\dfrac{2}{5}\text{m}}$ and one more piece of length $\mathbf{2\dfrac{7}{10}\text{m}\text{.}}$ How much material did she purchase in all?

Ans: Given: Length of first material bought by Roshni $=3\dfrac{2}{5}\text{m}$

Length of second material bought by Roshni $=2\dfrac{7}{10}\text{m}$

Total length of material purchased by Roshni will be

$ =3\dfrac{2}{5}+2\dfrac{7}{10} $

$ =3+\dfrac{2}{5}+2+\dfrac{7}{10} $

$ =5+\dfrac{2\times 2+7}{10} $

$ =5+\dfrac{4+7}{10} $

$ =5+\dfrac{11}{10} $

$ =\dfrac{61}{10} $

$ =6\dfrac{1}{10}\text{m} $

7. Ram bought $\mathbf{6\dfrac{1}{2}}$ litres of milk. Out of this $\mathbf{5\dfrac{1}{4}}$ litres was used. How much is the remaining milk?

Ans: Total milk bought by Ram $=6\dfrac{1}{2}\text{litres}$

Milk Used $=5\dfrac{1}{4}\text{litres}$

Remaining milk with Ram will be

$ =6\dfrac{1}{2}-5\dfrac{1}{4} $

$ =6+\dfrac{1}{2}-\left[ 5+\dfrac{1}{4} \right] $

$ =6-5+\left[ \dfrac{1}{2}-\dfrac{1}{4} \right] $

$ =1+\dfrac{1}{4} $

$ =1\dfrac{1}{4}\text{litres} $

Very Long  Answer Questions                                             6 Marks

1.  Classify each of the following into proper, improper and mixed fractions.

$\mathbf{\dfrac{1}{5}}$

 Ans: Proper fraction

$\mathbf{12}$

Ans: Improper fraction

$\mathbf{3\dfrac{1}{5}}$

Ans: Proper fraction

$\mathbf{\dfrac{15}{6}}$

$\mathbf{\dfrac{15}{20}}$

2. Compare $\mathbf{\dfrac{5}{8}}$ and $\mathbf{\dfrac{4}{9}}$

Ans: Given: $\dfrac{5}{8}$ and $\dfrac{4}{9}$

We need to compare the given fractions so we will convert both fractions into like fractions by taking LCM.

$ \text{LCM = 72} $

$ \text{=}\dfrac{5\times 9,4\times 8}{72} $

$ =\dfrac{45,32}{72} $

$ =\dfrac{5}{8}>\dfrac{4}{9} $

3. Arrange the following in ascending and descending order $\mathbf{\dfrac{2}{3},\dfrac{3}{4},\dfrac{7}{10},\dfrac{8}{15},\dfrac{5}{8}}$

Ans: Given: fractions $\dfrac{2}{3},\dfrac{3}{4},\dfrac{7}{10},\dfrac{8}{15},\dfrac{5}{8}$

We need to find the ascending and descending order of the fractions.

We will first convert the fractions in like terms and then find the order.

To convert into like terms. LCM will be

$\begin{align} & 4\left| \!{\underline {\, 3,4,10,15,8 \,}} \right.  \\ & 5\left| \!{\underline {\, 3,1,10,15,2 \,}} \right.  \\ & 3\left| \!{\underline {\, 3,1,2,3,2 \,}} \right.  \\ & 2\left| \!{\underline {\, 1,1,2,1,2 \,}} \right.  \\ & \left| \!{\underline {\, 1,1,1,1,1 \,}} \right.  \\ & \text{LCM = 4}\times \text{5}\times \text{3}\times \text{2} \\ & \text{=120} \\ \end{align}$

Then the fractions will be

$ \dfrac{2\times 20,3\times 30,7\times 12,8\times 8,5\times 15}{120} $

$ =\dfrac{80,90,84,64,75}{120}$

$=\dfrac{80}{120},\dfrac{90}{120},\dfrac{84}{120},\dfrac{64}{120},\dfrac{75}{120} $

Ascending order will be

$=\dfrac{64}{120},\dfrac{75}{120},\dfrac{80}{120},\dfrac{84}{120},\dfrac{90}{120} $

$ =\dfrac{8}{15},\dfrac{5}{8},\dfrac{2}{5},\dfrac{7}{10},\dfrac{3}{4} $

Descending order will be

$=\dfrac{90}{120},\dfrac{84}{120},\dfrac{80}{120},\dfrac{75}{120},\dfrac{64}{120} $

$ =\dfrac{3}{4},\dfrac{7}{10},\dfrac{2}{3},\dfrac{5}{8},\dfrac{8}{15} $

Definition of Fraction:

A fraction is a number that represents a part of a whole number. Fractions represent equal parts of a whole or a collection.

Representation of Fraction:

A fraction is represented by two parts separated by the “/” symbol. The number written above the line is called the numerator. It helps us to know how many equal parts of the whole or collection are taken. The number written below the line is known as the denominator. With the help of fraction, we can know the total number of equal parts which are there in a collection.

Types of Fractions

Proper fractions

Improper fractions

Mixed fractions

Like fractions

Unlike fractions

Equivalent fractions

Proper Fractions

The proper fractions are those fractions where the numerator is less than the denominator.

Example: 5/9 will be a proper fraction since “numerator < denominator”.

Improper Fractions

The improper fraction is a fraction where the numerator is greater than the denominator.

Example: 9/5 will be an improper fraction since “denominator < numerator”.

Mixed Fractions

The combination of the integer part and a proper fraction is called a mixed fraction also known as a mixed number.

Example: \[3\frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{7}{2}\]

Like Fractions

Like fractions are a fraction that has two or more fractions that have the same denominator. Example- Take ½ and 2/4, they are alike fractions since if we simplify it mathematically, we will get the same fraction.

Unlike Fractions

Unlike fractions are fractions that have different denominators.

Example: ½ and ⅓ are unlike fractions.

Equivalent Fractions

Two fractions are said to be equivalent to each other if after simplification either of two fractions is equal to the other one.

Example: ⅔ and 4/6 are equivalent fractions.

Since, 4/6 = (2 × 2)/(2 × 3) = ⅔

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There are some basic rules we should know before solving the problems based on fractions.

Before performing addition or subtraction on fractions, we must make sure that the denominators are equal. Hence, addition and subtraction of fractions are possible only when the denominator is common.

If we have multiplied two fractions, then the numerators are multiplied as well as the denominators are multiplied. Later, simplify the fraction.

When we divide a fraction from another fraction, we need to find the reciprocal of the other fraction and then multiply it to the first one to get the answer.

Addition of Fractions

The addition of fractions is easy when they have a common denominator, we need to just add the numerators here.

Example: ⅔ + 8/3 = (2 + 8)/3 = 10/3

If the denominators of the two fractions are different then we have to simplify them by finding the LCM of denominators and then making it common for both fractions.

Example: ⅔ + ¾

Here, the denominators are 3 and 4.

Hence, LCM of 3 and 4 is 12.

Therefore, we multiply  ⅔ by 4/4 and ¾ by 3/3, we get,

= 8/12 + 9/12

= (8 + 9)/12

Subtraction of Fractions

The rule for subtracting two or more fractions is the same as for addition. We should make denominators common to subtract two fractions.

Example: 9/2 – 7/2 = (9-7)/2 = 2/2 = 1

If the denominators of the two fractions are different, then we have to simplify them by finding the LCM of denominators after that making it common for both fractions.

For example ⅔ – ¾

8/12 – 9/12

= (8 – 9)/12

Multiplication of Fractions

As per rule 2, when two fractions are multiplied, then the top part (numerators) and the bottom part (denominators) are multiplied together.

Suppose a/b and c/d are two different fractions, then the multiplication of a/b and c/d will be:

(a/b) × (c/d) = (a × c)/(b × d) = (ac/bd)

Example: Multiply ⅔ and 3/7.

= (⅔) × (3/7) = (2 × 3)/(3 × 7) = 2/7

Division of Fractions

As per rule 3, if we have to divide any two fractions where we need to multiply the first fraction to the reciprocal of the second fraction.

Suppose, a/b and c/d are two different fractions, then the division a/b by c/d can be expressed as:

(a/b) ÷ (c/d) = (a/b) × (d/c) = (ad/bc)

Example: Divide ⅔ by 3/7.

(⅔) ÷ (3/7) = (⅔) × (7/3) = (2 × 7)/(3 × 3) = 14/9

What are the Benefits of Important Questions from Vedantu for Class 7 Math Chapter 7 - Fractions

Focus on key topics for efficient studying.

Prepares students for exams and reduces anxiety.

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Teaches effective time management.

Enables self-assessment and progress tracking.

Strategic approach for higher scores.

Covers a wide range of topics for comprehensive understanding.

Supports exam preparation and boosts confidence.

Conclusion:

Fractions are a part of our day-to-day life. Fractions make the calculations easier. Also, fractions can be converted into decimals which are heavily used in our monetary system.

After going through the above-given summary, students are advised to attempt the questions provided in Class 6 maths chapter 7 important questions . Students can easily understand the concept behind the question and solve it easily.

Important Related Links for CBSE Class 6 Maths 

FAQs on Important Questions for CBSE Class 6 Maths Chapter 7 - Fractions

1. What is a fraction Class 6?

A fraction is a part of the whole. It is a numerical quantity which is not whole. Fractional numbers are used to represent a part of something. Some examples of fractions could be one-third, three-fourth etc.  A fraction is described in the form of p/q. The letter p expresses the numerator of the fraction whereas the letter q expresses the denominator of the fraction. In a fraction 3/8, 3 is the numerator and 8 is the denominator. It represents 3 portions of the 8.

2. What are types of fractions?

The chapter introduces you to the concept of fraction. The chapter explains five types of fractions, namely, proper fractions, improper fractions, mixed fractions, like fractions and unlike fractions. Proper fraction is when the denominator is greater than the numerator. Improper is when the denominator is less than a numerator. Mixed fractions are those which consist of a whole number and a fraction. Two fractions are called when they have the same denominators. Two fractions are unlike fractions if they have different denominators. 

3. Do whole numbers also have denominators?

Fractions are numbers expressed in the form of p/q. If a number can be expressed in the p/q form, it is called a fraction. Whole numbers are those numbers that can be drawn on a number line. It is possible to write whole numbers in the form of p/q. Numbers that are whole have the denominator 1. So, a number as 3 can also be written as 3/1, where 3 is the numerator and 1 is the denominator. Writing a whole number in the fraction form helps in our calculation immensely. 

4. What fraction of a day is 8 hours?

A day has 24 hours. So, 24 will be the denominator that represents the whole. When we want to find a fraction of 8 hours, 8 will be our nominator. So, our fraction will be 8/24. What we are trying to find will come in the place of numerator and what we already know will come in the place of denominator. 8 and 24 are both divisible by 8, so we can simplify the fraction by dividing both numerator and denominator by 8. 8/8 will give us 1, which will be our new numerator. 24/8 will give us 3, our new denominator. So, our new fraction will be the new numerator/new denominator. Our answer is ⅓. 8 hours is one-third of 24 hours. 

5. What is the difference between proper and improper fractions?

A fraction consists of a numerator and a denominator. A number that occupies the place above the line is the numerator. The number that occupies the bottom is the denominator. A proper fraction is one in which the denominator is greater than the numerator. For example, 4/7 (7 is greater than 4), 3/11 (11 is greater than 3). However, if the numerator is greater than the denominator, then the fraction is called an improper fraction. For example, 8/7 and 13/6 where 8 and 13 are greater than 7 and 6 respectively.

Chapter wise Important Questions for CBSE Class 6 Maths

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Unit 5: Fractions

Fractions on the number line.

• Fractions on a number line (Opens a modal)
• Fractions greater than 1 on the number line (Opens a modal)
• Fractions on the number line Get 5 of 7 questions to level up!
• Fractions greater than 1 on the number line Get 3 of 4 questions to level up!

Improper and mixed fractions

• Writing mixed numbers as improper fractions (Opens a modal)
• Writing improper fractions as mixed numbers (Opens a modal)
• Write mixed numbers and improper fractions Get 5 of 7 questions to level up!

Equivalent fractions

• Equivalent fractions (Opens a modal)
• Equivalent fractions and different wholes (Opens a modal)
• Equivalent fractions Get 5 of 7 questions to level up!
• Equivalent fractions and different wholes Get 5 of 7 questions to level up!
• Simplify fractions Get 5 of 7 questions to level up!

Comparing fractions

• Comparing fractions with like numerators and denominators (Opens a modal)
• Comparing fractions 2 (unlike denominators) (Opens a modal)
• Compare fractions with the same numerator or denominator Get 5 of 7 questions to level up!
• Compare fractions with different numerators and denominators Get 5 of 7 questions to level up!

Adding or subtracting like fractions

• Adding fractions with like denominators (Opens a modal)
• Subtracting fractions with like denominators (Opens a modal)
• Add fractions with common denominators Get 5 of 7 questions to level up!
• Subtract fractions with common denominators Get 5 of 7 questions to level up!

Adding or subtracting unlike fractions

• Adding fractions with unlike denominators (Opens a modal)
• Subtracting fractions with unlike denominators (Opens a modal)
• Add fractions with unlike denominators Get 5 of 7 questions to level up!
• Subtracting fractions with unlike denominators Get 5 of 7 questions to level up!

Fractions word problems

• Adding fractions word problem: paint (Opens a modal)
• Subtracting fractions word problem: tomatoes (Opens a modal)
• Add and subtract fractions word problems Get 3 of 4 questions to level up!

Visualising fractions (bonus)

• Visualizing equivalent fractions (Opens a modal)
• Decomposing a fraction visually (Opens a modal)
• Visually adding fractions: 5/6+1/4 (Opens a modal)
• Equivalent fractions (fraction models) Get 3 of 4 questions to level up!
• Decompose fractions visually Get 3 of 4 questions to level up!
• Visually add and subtract fractions Get 3 of 4 questions to level up!

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Grade 6 - Fractions

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Contents: Fractions

Fractions - Fractions - Mixed Review, Word Problems.

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