Exercise 7.1 Exercise 7.2 Exercise 7.3 Exercise 7.4 Exercise 7.5 Exercise 7.6 |

**NCERT Answers for Class 6 Maths Chapter 7 Fractions Ex 7.4**

**Ex 7.4 Class 6 Maths Question 1. Write shaded portion as fraction. Arrange them in ascending and descending order using correct sign ‘<’, ‘=’, ‘>’ between the fractions:**

**Answer **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

**Answer**

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

The arranged fractions are:

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

**(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**

**Answer** 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

**Ex 7.4 Class 6 Maths Question 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**

Answer

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

Therefore 3 / 6 < 5 / 6

**(b)** Multiply by 4

1 / 7 = (1 × 4) / (7 × 4)

= 4 / 28

Multiply by 7

1 / 4 = (1 × 7) / (4 × 7)

= 7 / 28

Here 4 < 7

Therefore 1 / 7 < 1 / 4

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

Therefore 4 / 5 < 5 / 5

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

Therefore 3 / 7 < 3 / 5

**Ex 7.4 Class 6 Maths Question 3. Make five more such pairs and put appropriate signs.**

**(i) **5 / 8 < 6 / 8

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

**(ii)** 5 / 8 > 2 / 8

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

**(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

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

**(v)** 9 / 50 < 9 / 45

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

**Ex 7.4 Class 6 Maths Question 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**

**Answer**

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

Therefore 1 / 6 < 1 / 3

**(b)** 3 / 4 = (3 × 3) / (4 × 3)

= 9 / 12

2 / 6 = (2 × 2) / (6 × 2)

= 4 / 12

Between 4 / 12, 9 / 12

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

Therefore 9 / 12 > 4 / 12

3 / 4 > 2 / 6

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

Therefore 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

Therefore 5 / 6 < 5 / 5

**Ex 7.4 Class 6 Maths Question 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**

**Answer**

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

Therefore 1 / 2 > 1 / 5

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

Therefore 2 / 4 = 3 / 6

**(c)** 3 / 5 = (3 × 3) / (5 × 3)

= 9 / 15

2 / 3 = (2 × 5) / 3 × 5)

= 10 / 15

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

Therefore 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

Therefore 3 / 4 > 2 / 8

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

Therefore 3 / 5 < 6 / 5

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

Therefore 7 / 9 > 3 / 9

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

Hence, 1 / 4 = 2 / 8

**(h)** 6 / 10 = (3 × 2) / (5 × 2)

= 3 / 5

Between 3 / 5 and 4 / 5

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

Therefore 6 / 10 < 4 / 5

**(i)** 3 / 4 = (3 × 2) / (4 × 2)

= 6 / 8

Between 6 / 8 and 7 / 8

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

Therefore 3 / 4 < 7 / 8

**(j)** 6 / 10 = (3 × 2) / (5 × 2)

= 3 / 5

Therefore 6 / 10 = 3 / 5

**(k)** 5 / 7 = (5 × 3) / (7 × 3)

= 15 / 21

Therefore 5 / 7 = 15 / 21

**Ex 7.4 Class 6 Maths Question 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**

**Answer (a) **2 / 12 = (1 × 2) / (6 × 2)

= 1 / 6

**(b)** 3 / 15 = (1** **× 3) / (5 × 3)

= 1 / 5

**(c)** 8 / 50 = (4 × 2) / (25 × 2)

= 4 / 25

**(d)** 16 / 100 = (4 × 4) / (25 × 4)

= 4 / 25

**(e)** 10 / 60 = (1 × 10) / (6 × 10)

= 1 / 6

**(f)** 15 / 75 = (1 × 15) / (5 × 15)

= 1 / 5

**(g)** 12 / 60 = (1 × 12) / (5 × 12)

= 1 / 5

**(h)** 16 / 96

= (1 × 16) / (6 × 16)

= 1 / 6

**(i)** 12 / 75 = (4 × 3) / (25 × 3)

= 4 / 25

**(j)** 12 / 72 = (1 × 12) / 6 × 12)

= 1 / 6

**(k)** 3 / 18 = (1 × 3) / (6 × 3)

= 1 / 6

(l) 4 / 25

Totally there are 3 groups of equivalent fractions.

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

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

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

**Ex 7.4 Class 6 Maths Question 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**

**Answer**

**(a) 5 / 9, 4 / 5**

Convert these fractions into like fractions

5 / 9 = (5 / 9) × (5 / 5)

= 25 / 45

4 / 5 = (4 / 5) × (9 / 9)

= 36 / 45

Therefore 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)

= 81 / 144

5 / 9 = (5 / 9) × (16 / 16)

= 80 / 144

Therefore 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

Therefore 4 / 5 = 16 / 20

Hence, 4 / 5 is equal to 16 / 20

**(d)** 1 / 15, 4 / 30

4 / 30 = (2 × 2) / (15 × 2)

= 2 / 15

Therefore 1 / 15 ≠ 4 / 30

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

**Ex 7.4 Class 6 Maths Question 8. Ila read 25 pages of a book containing 100 pages. Lalita read 2 / 5 of the same book. Who read less?**

**Answer**

Total number of pages a book has = 100 pages

Lalita read = 2 / 5 × 100 = 40 pages

Ila read = 25 pages

Therefore Ila read less than Lalita.

**Ex 7.4 Class 6 Maths Question 9. Rafiq exercised for 3 / 6 of an hour, while Rohit exercised for 3 / 4 of an hour. Who exercised for a longer time?**

**Answer**

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)

= 6 / 12

3 / 4 = (3 × 3) / (4 × 3)

= 9 / 12

Clearly, 9 / 12 > 6 / 12

Therefore 3 / 4 > 3 / 6

Therefore Rohit exercised for a longer time than Rafiq.

**Ex 7.4 Class 6 Maths Question 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?**

**Answer**

Total number of students in Class A = 25

Students passed in first class in Class A = 20

Hence, fraction = 20 / 25

= 4 / 5

Total number of students in Class B = 30

Students passed in first class in Class B = 24

Hence, fraction = 24 / 30

= 4 / 5

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