Fraction as Division || How to represent fraction as a division?

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:

Representing fraction as division

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.

Property of fraction

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.

Changing fraction into division

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.

\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.

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