Finding a fraction of a number and vice versa

In this publication, we will consider how you can find a fraction of a whole number and vice versa – how to find a number if you know what a certain fraction of it is equal to. We will also analyze examples of solving problems for a better understanding and consolidation of theoretical material.

Content

Finding a fraction from a number

To find the part of a whole number n, which is represented by a fraction, you need this fraction (for example, a/b) for a given number n.

Fraction from a number = n
a/b

 =  

n ⋅ a/b

 

Example 1

Will find
5/12

from the number 24.

 

Solution

5/12

⋅ 24 =

5⋅24/12

=

120/12

= 10

 

Example 2

Will find
4/9

from the number 7.

 

Solution

4/9

⋅ 7 =

4⋅7/9

=

28/9

=3

1/9

 

Thus, the result of finding a fraction of a number is not always an integer.

Note: if the fraction is mixed, it should first be represented in the form and only then the multiplication should be performed.

Finding a number by the value of a fraction

If you know how many n ranks among m, and this fraction is expressed as a fraction, then to find the number m the formula is used:

m = m :
a/b

 

Example:

One row of the cinema hall accommodates 20 seats, which is
2/5

from the total capacity of the hall. Determine how many seats there are in the hall.

 

Solution

The total number of seats is:

In 20:
2/5

= 20 ⋅

5/2

=

20⋅5/2

= 50

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