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.
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.
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 ?
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
Divide by 7 on both sides
required number = (21/2) x (1/7)
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?
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)
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.
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
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?
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
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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