MULTIPLY FRACTIONS WORD PROBLEMS

About "Multiply fractions word problems"

Here we are going to see, how to solve multiply fractions word problems. 

Examples

To learn solving multiply fractions word problems, let us look at some examples. 

Example 1 :

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

Solution :

Let "x" be the numerator. 

"The denominator of the fraction is 9/4 of the numerator"

From the above information, we have the fraction = x / [(9/4)x] 

= x / [(9x/4)]

= x . 4/(9x)

= 4/9

Hence, the required fraction is 4/9

Let us look at  the next problem on "multiply fractions word problems"

Example 2 :

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

Solution :

No. of boys in the school = 450 x 2/3 = 300

Total no. of students = 450. 

Then no. of girls = 450 - 300 = 150

Hence the numbers girls in the school = 150 

Let us look at  the next problem on "multiply fractions word problems"

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. 

"If the fraction is multiplied by 3, it becomes 5/4"

From the above information, we have 3(x/y) = 5/4

3x / y = 5/4 -------> 12x = 5y --------> 12x - 5y = 0 ---------(1)

"Sum of the numerator and denominator is 17"

From the above information, we have x + y = 17 ---------(2)

Solving (1) and (2), we get x = 5 and y = 12

So, x/y = 5/12

Hence, the required fraction is 5/12

Let us look at  the next problem on "multiply fractions word problems"

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.

From the information given in the question, we have

x + y = 16 ----------(1)

and 1/5(x)  =  (1/3)y ---------> 3x = 5y -------> 3x - 5 y = 0 --------(2)

Solving (1) and (2), we get x = 10 and y = 6.

Hence, the two numbers are 10 and 6

Let us look at  the next problem on "multiply fractions word problems"

Example 5 :

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

Solution :

Let "x" be the required number. 

Fourth part of the number = (1/4)x = x/4

Sixth part of the number = (1/6)x = x/6 

According to the question, we have x/4 - x/6 = 4

3x/12 - 2x/12 = 4 ------> (3x - 2x) / 12 = 4 -----> x / 12 = 4 ------> x = 48

Hence, the required number is 48

Let us look at  the next problem on "multiply fractions word problems"

Example 6 :

The width of the rectangle is 2/3 of its length. If the perimeter of the rectangle is 80 cm. Find its area. 

Solution :

Let "x" be the length of the rectangle. 

Then, width of the rectangle = (2/3)x

Perimeter = 80 cm -----> 2(l + w) = 80 -------> l + w = 40

l + w = 40 -------> x + (2/3)x = 40 -------> (3x+2x) / 3 = 40

(3x+2x) / 3 = 40 ------> 5x = 120 ------> x = 24

So, length = x = 24 cm

and width = (2/3)x = (2/3)24 = 16 cm

Area = l x w = 24x16 = 384 square cm.

Hence, area of the rectangle is 384 square cm

Let us look at  the next problem on "multiply fractions word problems"

Example 7 :

If a number of which the half is greater than 1/5 th of the number by 15, find the number. 

Solution :

Let "x" be the required number.

Half of the number = (1/2)x 

1/5 the of the number = (1/5)x

According to the question, we have  (1/2)x - (1/5)x = 15

(1/2)x - (1/5)x = 15 ------> (5x - 2x) / 10 = 15 -------> 3x = 150

3x = 150 ----------> x = 50

Hence, the required number is 50

Let us look at  the next problem on "multiply fractions word problems"

Example 8 :

David's salary is $1800. David spent 2/3 of the total money for salary. He spent 1/2 of the remaining for his kids education and saved the rest. How much did he save ?  

Solution :

Money spent on food = 1800x2/3 = 1200

Remaining = 1800 - 1200 = 600 -------(1)

Money spent on kids education = 1/2 of remaining = (1/2)x600

(1/2) x 600 = 300 --------(2)

Then, his savings = (1) - (2) = 600 - 300 = 300

Hence, his savings is $300

Let us look at  the next problem on "multiply fractions word problems"

Example 9 :

A, B and C are friends. A has 1/3 of money that B has. C has 1/2 of money that A has. If they all together have  $450. How much money do A, B and C have separately ? 

Solution :

Let us assume that B has the money "x". 

Then, A = (1/3)x = x/3    

C = 1/2 of A = (1/2) x (x/3) = x/6

Given : A + B + C = 300 -------> x/3 + x + x/6 = 450

4x/12 + 12x/12 + 2x/12 = 450 -------> (4x+12x+2x)/12 = 450

(4x+12x+2x)/12 = 450 -------->18x/12 = 450-------> x = 300 

Now, A = x/3 = 300/3 = 100

B = x = 300

C = x/6 = 300/6 = 50

Hence, A has $100, B has $450 and C has $50

Let us look at  the next problem on "multiply fractions word problems"

Example 10 :

John's present age is 1/3 of David's age  5 years back.If David is 20 years old now, find the present age  of John.  

Solution :

Present age of David = 20 years

David's age 5 years back = 20 - 5 = 15 years

John's present age = 1/3 of David's age  5 years back

John's present age = 1/3 of 15 years = (1/3)x15 = 5 years. 

Hence, John's present age is 5 years. 

After having gone through the examples explained above, we hope that students would have understood "Multiply fractions word problems".

Apart from the examples, if you want to know more about "Multiply fractions word problems", please click here.

Please click the below links to know "How to solve word problems in each of the given topics"

1. Solving Word Problems on Simple Equations

2. Solving Word Problems on Simultaneous Equations

3. Solving Word Problems on Quadratic Equations

4. Solving Word Problems on Permutations and Combinations

5. Solving Word Problems on HCF and LCM

6. Solving Word Problems on Numbers

7. Solving Word Problems on Time and Work

8. Solving Word Problems on Trains

9. Solving Word Problems on Time and Work.

10. Solving Word Problems on Ages.

11.Solving Word Problems on Ratio and Proportion

12.Solving Word Problems on Allegation and Mixtures.

13. Solving Word Problems on Percentage

14. Solving Word Problems on Profit and Loss

15. Solving Word Problems Partnership

16. Solving Word Problems on Simple Interest

17. Solving Word Problems on Compound Interest

18. Solving Word Problems on Calendar

19. Solving Word Problems on Clock

20. Solving Word Problems on Pipes and Cisterns

21. Solving Word Problems on Modular Arithmetic

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