Converting a Fraction to a Percentage Denominator of 4, 5, or 10

Introduction

Consider any fraction with a denominator of 4, 5 or 10. Such fractions can be converted to fractions with a denominator of 100. Then it would be easy to write those fractions as percentages as shown below in examples

Rules to convert a fraction into a percentage with 4, 5 or 10 as denominator

• If the fraction has a denominator 4, we multiply and divide the fraction with 25. For example: 34=(3×25)(4×25)=7510034=(3×25)(4×25)=75100
• If the fraction has a denominator 5, we multiply and divide the fraction with 20. For example: 25=(2×20)(5×20)=4010025=(2×20)(5×20)=40100
• If the fraction has a denominator 10, we multiply and divide the fraction with 10. For example: 710=(7×10)(10×10)=70100710=(7×10)(10×10)=70100
• The fractions with 100 as denominator are converted to percentages. For example: 7510075100 = 75%; 4010040100 = 40%; 7010070100 = 70%

Example 1

Write the following fraction as a percentage

1414

Solution

Step 1:

The given fraction 1414 has a denominator 4.

We multiply and divide the fraction by 25

14=(1×25)(4×25)=2510014=(1×25)(4×25)=25100

Step 2:

Writing this fraction as a percentage

By definition, 2510025100 = 25%

Step 3:

So, 1414 = 25%Example 2

Write the following fraction as a percentage

4545

Solution

Step 1:

The given fraction 4545 has a denominator 5.

We multiply and divide the fraction by 20

45=(4×20)(5×20)=8010045=(4×20)(5×20)=80100

Step 2:

Writing this fraction as a percentage

By definition, 8010080100 = 80%

Step 3:

So, 4545 = 80%Example 3

Write the following fraction as a percentage

910910

Solution

Step 1:

The given fraction 910910 has a denominator 10.

We multiply and divide the fraction by 10

910=(9×10)(10×10)=90100910=(9×10)(10×10)=90100

Step 2:

Writing this fraction as a percentage

By definition, 9010090100 = 90%

Step 3:

So, 910910 = 90%