In his post we will learn that the fraction can be written in the form of division.

**Representing Fraction as Division**

Consider the fraction \mathtt{\frac{1}{4}} .

The above fraction can be written in division form as: **1 ÷ 4**

i.e, \mathtt{\frac{1}{4}} ⟹ (1 ÷ 4)

We can generally express the property as:

**But how is this possible?**

How can fraction be represented like that?

To understand this we have to review the basics of fraction.

Consider the below circle of unit 1.

Now divide the circle into 4 equal parts.

In order to split the circle you will divide 1 by 4 and after solving you get \mathtt{\frac{1}{4}} as quotient.

i.e. \mathtt{1\ \div \ 4\ \ =\ \ \frac{1}{4}}

Observe that the division of numbers results in fraction of same numbers. Hence, fraction and division can be used interchangeably.

**Let us consider another example.**

Given above is the rectangle with unit 1.

Divide the rectangle into 7 parts.

Division of rectangle is given as 1 ÷ 7 .

When you do the calculation, you will get \mathtt{\frac{1}{7}} as quotient.

Hence,

\mathtt{1\ \div \ 7\ \ =\ \ \frac{1}{7}}

Conclusion: The fraction can be represented as division or vice versa.

**Examples of Fraction as Division**

\mathtt{( a) \ \frac{1}{7} \ =\ 1\div \ 7}\\\ \\ \mathtt{( b) \ \frac{2}{9} \ =\ 2\ \div \ 9}\\\ \\ \mathtt{( c) \ \frac{13}{41} \ =\ 13\div \ 41}\\\ \\ \mathtt{( d) \ \frac{6}{17} \ =\ 6\div 17}\\\ \\ \mathtt{( e) \ \frac{1}{81} \ =\ 1\div \ 81}
**How this property is helpful?**

Fraction as division property help to solve complex algebraic problem in fast and effective way.

For Example;

Calculate the value of x in below equation

\mathtt{x\ =\ \frac{4}{5} \ \times \ 15}

Here the fraction (4/5) is multiplied by whole number 15.

Converting fraction as division and rewriting the equation.

\mathtt{x\ =\ \frac{4\ \times 15}{5}}\\\ \\ \mathtt{x\ =\ \frac{60}{5}}\\\ \\ \mathtt{x\ =\ 12}

Hence, the value of x is 12.

That’s how converting fraction into multiplication help solve equation fast.