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# Chapter 1: Rational Numbers Exercise – 1.7

### Question: 1

Divide: ### Solution: ### Question: 2

Find the value and express as a rational number in standard form: ### Solution: ### Question: 3

The product of two rational numbers is 15. If one of the numbers is -10. Find the other number.

### Solution:

Let, the other number be x. ### Question: 4

The product of two rational numbers is −8/9. If one of the number is −4/15, Find the other number.

### Solution:

Let, the other number be x. ### Question: 5

By what number should we multiply −1/6 so that the product may be −23/9?

### Solution:

Let, the number be x. ### Question: 6

By what number should we multiply −15/28 so that the product may be −5/7?

### Solution:

Let, the number be x. ### Question: 7

By what number should we multiply −8/13 so that the product may be 24?

### Solution:

Let, the number be x. ### Question: 8

By what number should -3/4 be multiplied in order to produce 2/3?

### Solution:

Let, the number be x. ### Question: 9

Find (x + y) ÷ (x – y), if ### Solution:  ### Question: 10

The cost of 7(2/3) metres of rope is Rs 12(3/4). Find its cost per metres.

### Solution:

The cost of 7(2/3) metres of rope is Rs. 7(2/3).

Therefore, ### Question: 11

The cost of 2(1/3) metres of cloth is Rs. 75(1/4). Find the cost of cloth per metres.

### Solution:

The cost of 2(1/3) metres of cloth is Rs. 75(1/4). ### Question: 12

By what number should −33/16 be divided to get -1/14?

### Solution: ### Question: 13

Divide the sum of 13/5 and 12/7 by the product of 3/17 and 1/2?

### Solution: ### Question: 14

Divide the sum of 65/12 and 12/7 by their differences.

### Solution: ### Question: 15

If 24 trousers of equal size can be prepared in 54 meters of cloth, what length of cloth is required for each trouser?

### Solution:

Cloth needed to prepare 24 trousers = 54 m

So,

Length of the cloth required for each trousers = 54 ÷ 24 = 54/24 = 9/4 m = 2(1/4) metres.