Converting a Percentage to a Fraction in Simplest Form

Introduction

Any per cent can be written as a fraction with a denominator of 100 as follows

x% = x100�100; 50% = 5010050100

Similarly, 8% = 81008100; 10% = 1010010100; 24% = 2410024100 and so on The fraction can be reduced to simplest form as follows

50% = 5010050100

We divide the numerator and the denominator with their highest common factor HCF���. Here the HCF of 50 and 100 is 50

50% = 5050÷10050=125050÷10050=12

So, 50% = 1212

Rules to convert a percentage into a fraction in simplest form

• The percentage is written as a fraction with 100 as denominatorFor example, 30% = 3010030100
• This fraction is then simplified and reduced to lowest termsFor example, 30% = 30100=31030100=310

Example 1

Write the percent as a fraction in the simplest form

24%

Solution

Step 1:

The percent written in fraction form

24% = 2410024100

Step 2:

The fraction can be reduced to simplest form as follows

We divide the numerator and the denominator with their highest common factor. Here the HCF of 24 and 100 is 4

24% = 244÷1004=625244÷1004=625

Step 3:

So, 24% = 625625 in simplest formExample 2

Write the percent as a fraction in the simplest form

55%

Solution

Step 1:

The percent written in fraction form

55% = 5510055100

Step 2:

The fraction can be reduced to simplest form as follows

We divide the numerator and the denominator with their highest common factor. Here the HCF of 55 and 100 is 5

55% = 555÷1005=1120555÷1005=1120

Step 3:

So, 55% = 11201120 in simplest formExample 3

Write the percent as a fraction in the simplest form

6%

Solution

Step 1:

The percent written in fraction form

6% = 61006100

Step 2:

The fraction can be reduced to simplest form as follows

We divide the numerator and the denominator with their highest common factor. Here the HCF of 6 and 100 is 2

6% = 62÷1002=35062÷1002=350

Step 3:

So, 6% = 350350 in simplest form