### Chapter 1 Rational Numbers – Exercise 1.7 | Set 1

**Problem 11. The cost of 2 1/3 meters of cloth is Rs 75 ¼. Find the cost of cloth per meter.**

**Solution**:

2 1 / 3 = 7 / 3 meters of cloth = Rs 301 / 4

Let us consider a number = x

x (7 / 3) = 301 / 4

x = (301 / 4) / (7 / 3)

= (301 / 4) × (3 / 7)

= (301 × 3) / (4 × 7)

7 is the common factor

= (43 × 3) / (4 × 1)

= 129 / 4

= 32.25

Cost of cloth per meter is Rs 32.25

**Problem 12. By what number should -33/16 be divided to get -11/4?**

**Solution**:

Let us consider a number = x

(-33 / 16) / x = -11 / 4

-33 / 16 = x (-11 / 4)

x = (-33 / 16) / (-11 / 4)

= (-33 / 16) × (4 / -11)

4 and 11 are the common factors

= (-33 × 4) / (16 × -11)

= (-3 × 1) / (4 × -1)

= 3 / 4

The number should be divided by 3 / 4

**Problem 13. Divide the sum of -13/5 and 12/7 by the product of -31/7 and -1/2.**

**Solution**:

Sum of -13 / 5 and 12 / 7

= -13 / 5 + 12 / 7

LCM is 35

= ((-13 × 7) + (12 × 5)) / 35

= (-91 + 60) / 35

= -31 / 35

Product of -31 / 7 and -1 / 2

= -31 / 7 × -1 / 2

= (-31 × -1) / (7 × 2)

= 31 / 14

Dividing the sum and the product,

= (-31 / 35) / (31 / 14)

= (-31 / 35) × (14 / 31)

= (-31 × 14) / (35 × 31)

31 and 7 is the common factor

= -2 / 5

**Problem 14. Divide the sum of 65/12 and 12/7 by their difference.**

**Solution**:

Sum = 65 / 12 + 12 / 7

LCM is 84

= (65 × 7 + 12 × 12) / 84

= (455 + 144) / 84

= 599 / 84

Difference i = 65 / 12 – 12 / 7

= (65 × 7 – 12 × 12) / 84

= (455 – 144) / 84

= 311 / 84

After dividing, (599 / 84) / (311 / 84)

= (599 / 84) × (84 / 311)

84 is the common factor

= 599 / 311

**Problem 15. If 24 trousers of equal size can be prepared in 54 meters of cloth, what length of cloth is required for each pair of** **trousers?**

**Solution**:

Total number trousers = 24

The total length of the cloth = 54 m

Length of the cloth required for each trouser = total length of the cloth / number of trousers = 54 / 24

6 is the common factor

Hence it can be written as 9 / 4

9 / 4 meters is required for each trouser.