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# Converting Fractions

Top
 Sub Topics A fraction represents a part of a whole and a fraction has a numerator and a denominator. It is of the form $\frac{a}{b}$ where a and b are non zero integers, a is called the numerator and b is called the denominator. It is easy to convert fractions and can be converted into many other number forms of number system. In this page we'll learn how to convert fractions to decimals, percents, whole numbers, mixed numbers etc.,

## Converting Fraction to Decimals

Decimals and fractions represent the same things, numbers that are not whole numbers.
Steps to convert fractions to decimals is explained below.
1. Divide the numerator with the denominator or Make an equivalent fraction whose denominator is in terms of 10, 100, 1000 and so on.
2. Write the new fraction as a decimal.
Example: What is $\frac{3}{4}$ as a decimal?

Solution: Given $\frac{3}{4}$

We have to multiply the denominator by 25 to get 100. Multiply and divide the fraction by 25

= $\frac{3}{4}$ $\times$ $\frac{25}{25}$

= $\frac{75}{100}$

= 0.75

## Converting Fractions to Percents

When converting fractions to percents, follow the below steps.
• Firstly, convert the denominators of the given fraction to 100. (By multiplying)
• Secondly by a common factor, multiply both the numerator and the denominator.
Example 1: What is $\frac{8}{10}$ as a percent?

Solution: Given $\frac{8}{10}$

= $\frac{8}{10}$ $\times$ $\frac{10}{10}$

= $\frac{80}{100}$

= 80 %

Therefore, $\frac{3}{4}$ = 80 %

We can also use proportions to do the conversion and is explained below.

$\frac{Top\ of\ Fraction}{Bottom\ of\ Fraction}$ = $\frac{Percent}{100}$

Percent = $\frac{Top\ of\ Fraction * 100}{Bottom\ of\ Fraction}$

Example: Convert $\frac{7}{15}$ to percent.

Solution: Given $\frac{7}{15}$

The given fraction can be written as

$\frac{7}{15}$ = $\frac{Percent}{100}$

$\rightarrow$ $\frac{7*100}{15}$

= 46.67 %

Therefore, $\frac{7}{15}$ = 46.67 %

## Converting Fraction to Binary

To convert a fraction to binary first change the fraction to a decimal and then convert the decimal to a binary. The conversion process is explained below with simple steps.

We convert a given fractional decimal number to its equivalent binary fraction.

Let the converting fractions be $\frac{3}{4}$ which is equivalent to 0.75 so to convert fractions into binary we follow the below steps:
1). Convert the fraction into a decimal by simple division i.e, $\frac{3}{4}$ = 0.75

2). Multiply 0.75 by the binary 2 i.e, 0.75 * 2 = 1.5

3). Take the value to the right of the point that is 1 and multiply the 0.5 again by 2 i.e, 0.5 * 2=1

4). Here we will again take 1 which is to the left of decimal point but as after decimal point we got 0 we will stop. So the resultant binary value of the fraction is (0.11)$_{2}$
Therefore, $\frac{3}{4}$ = (0.11)$_{2}$

## Converting Fractions to Whole Numbers

Whole numbers are numbers without fractions, percentages or decimals. The set of whole numbers is denoted by W. Zero is neither a fraction nor a decimal, so zero is a whole number.

Fractions are representations of the part of a whole.

Given below are the examples of fraction converted to a whole number.
Example 1: Convert $\frac{150}{10}$ to a whole number?

Solution: Given $\frac{150}{10}$

$\frac{150}{10}$

= 15

Example 2: Convert $\frac{36}{6}$ to a whole number?

Solution: Given $\frac{36}{6}$

= $\frac{36}{6}$

= 6

## Converting Fractions to Mixed Numbers

We can convert improper fraction to mixed numbers. An improper fraction will have the numerator greater than or equal to the denominator whereas the mixed number consists of an integer followed by a proper fraction.

Example 1: Convert $\frac{12}{5}$ to a mixed number

Solution: Given $\frac{12}{5}$

$\Rightarrow$ 2$\frac{2}{5}$

Therefore, $\frac{12}{5}$ = 2$\frac{2}{5}$

Example 2: Convert $\frac{27}{4}$ to a mixed number.

Solution: Given $\frac{27}{4}$

$\Rightarrow$ 6 $\frac{3}{4}$

Therefore, $\frac{27}{4}$ = 6$\frac{3}{4}$