FRACTIONS
EXERCISE – 7.4
EX 7.4 QUESTION 1.
Solution:
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:
(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
Now the fractions are:
EX 7.4 QUESTION 2.
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) Here both fractions have same denominators. So, the fraction 3 < 5.
∴ 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
∴ 1 / 7 < 1 / 4
(c) Here both fractions have same denominators. So, the fraction 4 < 5.
∴ 4 / 5 < 5 / 5
(d) Here both numerators are the same. So, the fraction having less denominator will be the highest factor
∴ 3 / 7 < 3 / 5
EX 7.4 QUESTION 3.
Make five more such pairs and put appropriate signs.
Solution:
(a) 2 / 7 > 2 / 11
(b) 6 / 8 > 3 / 8
(c) 4 /9 > 3/ 9
(d) 1 / 9 < 5 / 9
(e) 4 /10 < 6 / 10
EX 7.4 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
Solutions:
(a) 1 / 6 < 1 / 3
(b) 3 / 4 > 2 / 6
(c) 2 / 3 > 2 / 4
(d) 5 / 6 < 5 / 5
EX 7.4 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
Solutions:
EX 7.4 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
Solutions:
(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 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
Solutions:
(a) 5 / 9, 4 / 5
By cross-multiplying,
5 x 5 = 25 and 4 x 9 = 36
25 ≠ 36
Hence, 5 / 9 is not equal to 4 / 5
(b) 9 / 16, 5 / 9
By cross-multiplying,
9 x 9 = 81 and 16 x 5 =80
81 ≠ 80
Hence, 9 / 16 is not equal to 5 / 9
(c) 4 / 5, 16 / 20
By cross-multiplying
4 x 20 = 80 and 5 x 16 = 80
80 = 80
Hence, 4 / 5 is equal to 16 / 20
(d) 1 / 15, 4 / 30
By cross-multiplying,
1 x 30 = 30 and 4 x 15 = 60
Hence, 1 / 15 is not equal to 4 / 30
EX 7.4 QUESTION 8.
Ila read 25 pages of a book containing 100 pages. Lalita read 2 / 5 of the same book. Who read less?
Solutions:
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.
EX 7.4 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?
Solutions:
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
∴ 3 / 4 > 3 / 6
Therefore Rohit exercised for a longer time than Rafiq.
EX 7.4 QUESTION 10.
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?
Solutions:
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
∴ An equal fraction of students passed in first class in both the classes
