**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