**Multiply and divide rational numbers word problems :**

Here we are going to see some examples based on the concept multiplying and dividing rational numbers.

**Example 1 :**

The product of two rational numbers is 2/9. If one of the number is 1/2, find the other rational number.

**Solution :**

Product of two rational numbers = 2/9

One rational number = 1/2

Given number x required number = 2/9

(1/2) x required number = 2/9

required number/2 = 2/9

Multiplying by 2 on both sides

2 x (required number/2) = (2/9) x 2

required number = 4/9

**Example 2 :**

The product of two rational numbers is 6. If one of the number is 14/3, find the other number.

**Solution :**

Product of two rational numbers = 6

One rational number = 14/3

Given number x required number = 6

(14/3) x required number = 6

(14 x required number)/3 = 6

Multiply by 3 on both sides

[(14 x required number)/3] x 3 = 6 x 3

14 required number = 18

Divide by 14 on both sides

14 required number /14 = 18/14

required number = 9/7

**Example 3 :**

What number should be multiply 7/2 to get 21/4 ?

**Solution :**

Required number x (7/2) = 21/4

(7 x required number) /2 = 21/4

Multiply 2 on both sides

7 x required number = (21/4) x 2

= 21/2

Divide by 7 on both sides

required number = (21/2) x (1/7)

= 3/2

**Example 4 :**

John reads 1/3 part of a book in 1 hour. How much part of the book will he read in 2 1/5 hours?

**Solution :**

The part of the book read by John in 1 hour = 1/3

So, the part of the book read by him in 2 1/5 hours

= 2 1/5 x (1/3)

= (11/5) x (1/3)

= 11/15

**Example 5 :**

Suzy plants 4 saplings, in a row, in her garden. The distance between two adjacent saplings is 3/4 m. Find the distance between the first and the last sapling.

**Solution :**

**Number of saplings in a garden = 4 **

**The distance between two adjacent saplings = 3/4 m**

**T****he distance between the first and the last sapling **

**= 4 x (3/4) m**

** = 3 m**

**Example 6 :**

Lipika reads a book for 1 3/4 hours every day. She reads the entire book in 6 days. How many hours in all were required by her to read the book?

**Solution :**

Time taken by Lipika for reading a book in one day

= 1 3/4

Converting the mixed fraction into improper fraction, we get 7/4

Number of days taken by Lipika to read the entire book

= 6

Total number of hours taken by her to complete the entire book = 6 x (7/4) = 21/4

= 10 1/2 hours.

After having gone through the stuff given above, we hope that the students would have understood "Multiply and divide rational numbers word problems".

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