Fraction to Percent

Fraction to Percent
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We usually use fractions and percents to compare two quantities. A fraction is a relationship between a part and a whole whereas a percent is a type of fraction with 100 as a whole. Consider a situation where two siblings are arguing over who has done better in their math test. One had scored 42 out of 50 whereas the other had scored 33 out of 40. Can you guess who scored better? While both of them have scored exceptionally well, we need to calculate the percentage of marks that both scored to determine who did better. To determine who scored more, we will convert the fraction to a percentage.

Table of Contents

What is Fraction?

The word fraction is derived from the Latin word "fractio" which means 'to break'. Fractions are represented as a numerical value, can be defined as the parts of a whole. A fraction can be a portion or section of any quantity out of a whole, where, the whole can be any number, a  specific value, or a thing.

What is Percent?

"Percent means a part or a portion out of hundred." In other words, we can say that percent is the ratio calculated out of 100 or percent is a fraction with the denominator as 100. It is represented by %.

The percent is another name for indicating hundredths. Thus, 1% is one hundredth. To find the percentage of a whole, work out the value of 1% and then multiply it by the percent we need to find.

What is Fraction to Percent?

Converting a fraction to percent means to convert the whole part into 100 and find how many are considered out of 100. Say, for example, Fraction = 3/5 which means 3 parts are shaded out of 5.

Fraction to Percent Illustration with Example

To find the percent for this fraction, we have to find the number of parts that would be shaded out of 100. To convert a fraction to percent, we multiply it by 100/100. Since 100/100 = 1, multiplying 3/5 by 100/100 doesn't change its value.

3/5 = 3/5 × 100/100

= 300/5 %

= 60 %

There are other ways to convert a fraction to percent.

  • Fraction to Percent using decimals
  • Fraction to Percent using proportion

Percentage Formula

The percentage formula is used to find the share of a whole in terms of 100. Using this formula, you can represent a number as a fraction of 100

Percentage = (Value/Total Value) × 100

For example, out of 20 beads, the number of 8 beads are red. So, out of 100, the number of red beads are

8/20 × 100 = 40%

In short, to convert a fraction to percent, multiply it by the number 100 followed by the symbol %.

Conversion of Fraction to Percent

Let's discuss the first way to convert fraction to percent, that is, fraction to percent using decimals.

Fraction to Percent Using Decimals

Follow the steps mentioned below to convert fraction to percent using decimals.

Consider the fraction 3/5. We will perform the long division to convert the fraction in decimal form.

Fraction to Percent Using Decimals

So, 3/5 = 0.6 Finally, we will multiply 0.6 by 100 to express the fraction 3/5 in percent.

0.6 = 0.6 × 100 % = 60 %

Flow Chart to Explain Fraction to Percent Using Decimals

Fraction to Percent Using Proportions

When two ratios a/b and c/d are equal, the numbers a, b, c, and d are said to be in proportion. If we have the fraction a/b, we need to convert this ratio into the form x/100

Let's consider the same fraction 3/5,

3/5 = x/100

x = 3/5 × 100

x = 60

Thus, 3/5 = 60 %

We can also convert a mixed fraction to percent using the above methods. For example, we have \(2\dfrac{1}{5}\) which can be written as 11/5.

To convert this into percent, you can follow any of the methods shown below.

Method 1:

11/5 = 11/5 × 100 %

= 1100/5 %

=220 % 

Method 2:

11/5 = x/100

(11 × 20) (5 × 20) = x/100

2200/100 = x/100

x = 220 %

Fraction to Percent Conversion Table

The fraction to percent conversion table helps you to quickly find out the percent value of a fraction. Look at a few fractions that are converted to percent in the fraction to percent chart below:

Fraction Decimal Percent
1/8 0.125 12.5 %
2/8 0.25 25 %
3/8 0.375 37.5%
4/8 0.5 50 %
5/8 0.625 62.5 %
6/8 0.75 75 %
7/8 0.875 87.5 %
8/8 1 100 %

Important Topics

Given below is the list of topics that are closely connected to fraction to percent. These topics will also give you a glimpse of how such concepts are covered in Cuemath.


FAQs on Fraction to Percent

How do you Convert Fractions to a Percent?

To find the percent of a fraction, we have to find the number of parts that would be shaded out of 100. For example to convert (1/5) to percent, multiply 1/5 by 100 that is (1/5) × 100 = 20 %.

How do you Turn a Fraction into a Decimal and Percent?

Multiply the denominator and the numerator of the fraction with the same number such that the product of the denominator becomes 100. Then the numerator gives the percentage value. The decimal value of that fraction is calculating by dividing the percentage value by 100. Then place the decimal point before two digits from the right of the numerator.

Can we Express All Fractions in Percent Form?

Yes, all fractions can be written as a percentage. To convert any fraction to a percent, just multiply the fraction by 100/100 or 100 %

Why do we Convert Fraction to Percent?

We convert fraction to percent to compare the two different quantities appropriately. Suppose person X scored 44 out of 50 and person B scored 28 out of 30. Can you tell who scored better and why? If we convert their scores in percentage, then it would be easy for us to identify who among them scored better.

What are the Ways to Convert a Fraction to Percent?

There are two ways of converting a fraction to a percent:

  • By using decimals: In this method, we first convert the fraction in the decimal form and then multiply the decimal number by 100 %
  • By using proportion: In this method, we form an equation in variable x such that the fraction is equal to x %

What Fraction is Equal to 70%?

Since a percent is a fraction with a denominator of 100. We can write 70 % as 70/100 and this is equal to 7/10. So, 70 % = 70/100 = 7/10.

How do you Turn the Fraction 3/8 into a Percentage?

To convert a fraction to percent, we simply multiply the fraction by 100. So, 3/8 = 3/8 × 100= 37.5 %.


Solved Examples on Converting Fraction to Percent

Example 1:

Cathy wants to convert the fraction 48/60, to percent by first converting it into decimal form. Help her do the conversion.

Solution

We will first simplify the fraction 48/60 and convert it into a decimal by placing a decimal point after one skipping one digit from the right side of the numerator, then multiply the decimal by 100 to convert it to percent.

48/60 = 8/10

          = 0.8

          = 0.8 × 100 %

          = 80 %

So, 48/60 = 80 %

Example 2:

Mia participated in several sports events and she won 8 out of 12 of them. What was her winning percent?

Solution

The ratio of the number of events she won over the total number of events is 8 out of 12.

8/12 = 8/12 × 100 %

  = 2/3 × 100

= 66.67 %

So, Mia won 66.67% of the races.

Practice Questions on Converting Fraction to Percent

Here are a few activities for you to practice.

Select/Type your answer and click the "Check Answer" button to see the result.

 

 
 
 
 
 
  
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