MULTIPLY AND DIVIDE RATIONAL NUMBERS WORD PROBLEMS

Problem 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

Problem 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

Problem 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) 

required number  =  3/2

Problem 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 

Problem 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

The distance between the first and the last sapling 

=  4 x (3/4) m

  =  3 m

Problem 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.

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