MULTIPLY FRACTIONS WORD PROBLEMS

Multiply Fractions Word Problems : 

In this section, you will learn, how to solve word problems on multiplying fractions. 

Multiply Fractions Word Problems

Example 1 :

The denominator of a fraction is 9/4 of the numerator. Find the fraction. 

Solution :

Let x be the numerator. 

Given : The denominator of the fraction is 9/4 of the numerator.

Then, the denominator is 9x/4.

Therefore, the required fraction is 

=  x / (9x/4)

=  x ⋅ (4/9x)

=  (x ⋅ 4) / 9x

=  (1 ⋅ 4) / 9

=  4/9

Example 2 :

In a school, there are 450 students in total. If 2/3 of the total strength is boys, find the number of girls in the school. 

Solution :

Given : 2/3 of the total strength is boys

Then, the number of boys in the school is 

=  2/3 ⋅ 450

=  (2 ⋅ 450) / 3

=  (2 ⋅ 150) / 1

=  300

Therefore, the number of girls in school is 

=  Total strength - No. of boys

=  450 - 300

=  150

Example 3 :

If the fraction is multiplied 3, it becomes 5/4. And sum of the numerator and denominator is 17. Find the fraction. 

Solution :

Let x/y be the required fraction.

Given : If the fraction is multiplied 3, it becomes 5/4.

Then, we have

⋅ x/y  =  5/4

3x/y  =  5/4

12x  =  5y

12x - 5y  =  0 -----(1)

Given : Sum of the numerator and denominator is 17.

x + y  =  17 -----(2)

Solving (1) and (2), we get

x  =  5  and  y  =  12

x/y  =  5/12

So, the required fraction is 5/12.

Example 4 :

Of two numbers, 1/5th of a the greater equal to 1/3rd of the smaller and their sum is 16. Find the numbers.  

Solution :

Let x and y be the required two numbers such that x > y.

Given : 1/5th of a the greater equal to 1/3rd of the smaller.

Then, we have 

x/5  =  y/3

3x  =  5y

3x - 5y  =  0 -----(1)

Given : Sum of the numbers is 16. 

Then, we have 

x + y  =  16 -----(2)

Solving (1) and (2), we get

x  =  10  and  y  =  6

So, the numbers are 6 and 10.

Example 5 :

The fourth part of a number exceeds the sixth part by 4. Find the number.

Solution :

Let x be the required number.

Then,

Fourth part of the number  =  x/4

Sixth part of the number  =  x/6

Given : The fourth part of a number exceeds the sixth part by 4

Then, we have 

x/4  =  x/6 + 4

x/4 - x/6  =  4

3x/12 - 2x/12  =  4 

(3x - 2x) / 12  =  4

x/12  =  4

x  =  48

So, the number is 48.

Example 6 :

A work was assigned to A and B. A completed 2/3 of the work and B completed 5/8 of the remaining work. What fraction of the original word completed by B ?  

Solution :

Given : A completed 2/3 of the work.

Remaining  =  1/3

Given : B completed 5/8 of the remaining work

Then, the part of the work completed by B is  

=  5/8 ⋅ 1/3

=  (5 ⋅ 1) / (8 ⋅ 3)

=  5/24

=  5/24

So, B completed 5/24 of the original work. 

Example 7 :

Rachel bought a pizza and ate 2/5 of it. If he had given 2/3 of the remaining to his friend, what fraction of the original pizza will be remaining now ?

Solution :

Given : Rachel 2/5 of a pizza. 

Remaining  =  3/5

Given : He gave 2/3 of the remaining to his friend.

Then, Amount of pizza given to his friend is 

=  2/3 ⋅ 3/5

=  (2 ⋅ 3) / (3 ⋅ 5)

=  (2 ⋅ 1) / (1 ⋅ 5)

=  2/5

Now, we have

Remaining pizza

=

Total amount of pizza

-

(Amount of pizza eaten by Rachel + Amount of Pizza given to his friend)

Then, we have 

Remaining pizza  =  1 - (2/5 + 2/5)

Remaining pizza  =  1 - 4/5

Remaining pizza  =  5/5 - 4/5

Remaining pizza  =  1/5

So, 1/5 of the original pizza will be remaining. 

Example 8 :

A work was  assigned to David. He completes 1/9 of the work each day. If the total work is considered to be 450 units, how many units will he complete in 5 days ? 

Solution :

Given : David completes 1/9 of work each day.

Then, the fraction of work completed by him in 5 days is 

=  5 ⋅ 1/9

=  (5 ⋅ 1) / 9

=  5/9

Given : The total work is considered to be 450 units.

Then, the number of units completed in 5 days is 

=  5/9 ⋅ 450

=  (5 ⋅ 450) / 9

=  (5 ⋅ 50) / 1

=  250/1

=  250

So, David will complete 250 units of work in 5 days. 

After having gone through the stuff given above, we hope that the students would have understood, how to solve word problems on multiplying fractions. 

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