NCERT Solutions Class 6th Maths Chapter – 7 Fractions Exercise – 7.4

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

(c) Show 2/4, 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

Solution – 

(a) Total number of divisions = 8
(i) Number of shaded parts = 3
∴ Fraction = 3/8

(ii) Total number of divisions = 8
Number of shaded parts = 6
∴ Fraction = 6/8

(iii) Total number of divisions = 8
Number of shaded parts = 4
∴ Fraction = 4/8

(iv) Total number of divisions = 8
Number of shaded part = 1
∴ Fraction = 1/8
Now the fractions are- 3/8, 6/8, 4/8 and 1/8 with same denominator.
Ascending Order – 1/8 < 3/8 < 4/8 < 6/8
Descending Order – 6/8 > 4/8 > 3/8 > 1/8

(b) (i) Total number of divisions = 9
Number of shaded parts = 8
∴ Fraction = 8/9

(ii) Total number of divisions = 9
Number of shaded parts = 4
∴ Fraction = 4/9

(iii) Total number of divisions = 9
Number of shaded parts = 3
∴ Fraction = 3/9

(iv) Total number of divisions = 9
Number of shaded parts = 6
∴ Fraction = 6/9
∴ Fractions are 8/9, 4/9, 3/9, 6/9 with same denominator.

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

Solution –

(a) 3/6 ▢ 5/6 
Here, the denominators of the two fractions are the same and 3 < 5.

Here, numerators of the fractions are the same and 7 > 4.

Here, the denominators of the two fractions are the same and 4 < 5.

Here, the numerators of the two fractions are the same, and 5 < 7.

Solution –

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

Solution – 

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 ▢ 4/5
(k) 5/7 ▢ 15/21

Solution – 

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

Solution – 

(a) 2/12 = 1/6
(b) 3/15 = 1/5
(c) 8/50 = 4/25
(d) 16/ 100 = 4/25
(e) 10 / 60 = 1/6
(f) 15/75 = 1/5
(g) 12/60 = 1/5
(h) 16/96 = 1/6
(i) 12/75 = 4/25
(j) 12/72 = 1/6
(k) 3/18 = 1/6
(l) 4/25 = 4/25

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 ?

Solution – 

(a) 5/9 and 4/5
By cross-multiplying, we get
5 x 5 = 25 and 4 x 9 = 36
Since 25 ≠ 36
∴ 5/6 is not equal to 4/5.

(b) 9/16 and 5/9
By cross-multiplying, we get
9 x 9 = 81 and 16 x 5 =80
Since 81 ≠ 80
∴ (b) 9/16 is not equal to 5/9.

(c) 4/5 and 16/20
By cross-multiplying, we get
4 x 20 = 80 and 5 x 16 = 80
Since 80 = 80
∴ 4/5 is equal to 16/20.

(d) 1/15 and 4/30
By cross-multiplying, we get
1 x 30 = 30 and 4 x 15 = 60
∴ 1/15 is not equal to 4/30

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

Solution –

Ila reads 25 pages out of 100 pages.
∴ fraction = 25/100 = 25 ÷ 25/100 ÷ 25 = 1/4
Lalita reads 2/5 of the same book.
Comparing 1/4 and 2/5, we get
1 x 5 = 5 and 2 x 4 = 8
Since 5 < 8
∴ 1/4 < 2/5
Hence Ila reads less pages.

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?

Solution –

Rafiq exercised for 3/6 of an hour.
Rohit exercised for 3/4 of an hour.
Comparing 3/6 and 3/4, we get
3 x 4 = 12 and 3 x 6 = 18
Since 12 < 18
∴ 3/4 > 3/6
Hence Rohit exercised for a longer time.

Question 10. In class A of 25 students, 20 passed in first class; in another class B of 30 students, 24 passed in first class. In which class was a greater fraction of students getting first class?

Solution –

In class A, 20 students passed in first-class out of 25 students.

∴ Fraction of students getting first class
= 20/25 = 20 ÷ 5/125 ÷ 5 = 4/5

In class B, 24 students passed in first-class out of 30 students.

∴ Fraction of students getting first class
= 24/30 = 24 ÷ 6/30 ÷ 6 = 4/5

Comparing the two fractions, we get 4/5 = 4/5
Hence, both classes A and B have the same fractions.