### Fraction of an amount

To find the fraction of a number / amount , or the exact opposite, to find the whole number of a fraction it is important to know unit fractions.

• Fractions are made up of equal parts
• One of the equal parts is called a unit fraction

For example;  the unit fraction of $$\displaystyle \frac{4}{6}$$  is $$\displaystyle \frac{1}{6}$$

$$\displaystyle \frac{4}{6}$$ is made up of 4 ,  $$\displaystyle \frac{1}{6}$$

Our goal is to find the value of unit component of the fraction.
If you can find the value of unit fraction you can calculate the value of several pieces of the fraction.

What is the $$\displaystyle \frac{1}{4}$$ th of 20 ?

We must divide 20 into 4 equal parts and find the value of unit fraction.

$$\displaystyle 20:4=5$$

$$\displaystyle \frac{1}{4}$$ of 20 = 5

Let us find  the $$\displaystyle \frac{7}{9}$$ ths of 36 ?

Let sum of 9 pieces are equal to 36we must find the value of a single piece ( unit fraction ) , (  $$\displaystyle \frac{1}{9}$$  ) Then, multiply with 7we will find the value of 7 pieces that is required .

$$\displaystyle 36:9=4$$
this is the value of a piece $$\displaystyle \frac{1}{9}=4$$

To find the value of 7 let us multiply by 7,

$$\displaystyle 7.4=28$$

$$\displaystyle \frac{7}{9}$$ of 36 = 28

## Finding the whole number of a fraction

if $$\displaystyle \frac{4}{6}$$ of number is 100 , what is the whole value of the number?

First let’s understand what we have and what is wanted?

If the value of 4 pieces is 100, let us divide 100 by 4 to find the value of 1 piece.

$$\displaystyle 100:4=25$$

The value of $$\displaystyle \frac{1}{6}$$ =25

Our goal is to find the whole value of $$\displaystyle \frac{6}{6}$$ If one piece is 25 then;

$$\displaystyle 6.25=150$$

The whole number = 150

if   $$\displaystyle \frac{5}{8}$$ ’th of a number is 40 what is the whole value of the number?

If the value of 5 pieces is 40, let us divide 40 by 5.

$$\displaystyle 40:5=8$$ is the value of single part.

$$\displaystyle \frac{1}{8}=8$$

The whole of it, $$\displaystyle \frac{8}{8}=64$$