Percent to fraction

Percent to fraction
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Percent to fraction conversion is needed to make use of the value of percentage in a calculation. In any calculation, the percent value has to be changed by removing the percent symbol. Removing the percent symbol simply changes it into a fraction. For x%, on removing the % symbol changes to x/100, which is its fractional form. This is the simple format of changing a percent into a fraction.

Changing a percent into a fraction is a much-needed step in mathematical calculation. A percentage has to be necessarily changed to a fraction to be used for further calculations.  In this lesson you will learn how to convert percent to fraction, convert mixed fractions into a percentage, as well as decimals to fractions.

Table of Contents

What is meant by Percent to Fraction?

Percent means per hundred or for every hundred. We represent it as %. A percentage is simple to understand as it is on a scale of 1 to 100. The percent to fraction is the conversion of percentage values to a fraction. As per formula the percentage can be converted into a fraction by removing the % symbol and then writing the value in the form of a fraction with a 100 in the denominator. A percentage value of 21% is equal to a fraction of 21/100. Any percent is easy to be converted to fraction and vice versa.

An example of converting a percentage to a fraction is 45% = 45/100, 37% = 37/100. Also, a fraction or a decimal can be converted into a percentage. 48/100 = 48%, 0.27 = 27/100 = 27%. Thus fraction, decimal and percent are related to each other.

How to convert Percent to Fraction?

There are three simple steps to convert percent to fraction. Let us look at these three steps below.

  • Step 1:  Drop the percent symbol % 
  • Step 2:  Divide it by 100
  • Step 3:  Reduce the fraction so obtained.

Example: Mira has 20 items on her shopping list. She checks with her list and finds that she has completed 40% of her shopping. Can you say how many more items she has to buy? She has done 40% of her shopping which is 2/5 of 20 items. 2/5 × 20 = 8. Therefore, more items she has to buy is 20 - 8 = 12.

Conversion of Percent to fraction

Percent Conversions

The conversion of a percent to a fraction is very simple and convenient. Further, it depends on the numerical value of the percentage. The numeric value of the percentage could be a whole number, a fraction, or a decimal. In all the cases the percentage symbol is dropped and the numeric value is divided by the number 100. Let us now look at the following conversions from one form to another form.

Whole Number Percent to Fraction

To convert the whole number percent to a fraction, the following steps can be used:

  • Step 1: Remove the percent symbol and divide it by 100.
  • Step 2: Reduce the fraction with 100 as the denominator, into a simple fraction.

Let us look at a simple example to understand more. If there are 45 girls out of 100 students in the class, we mean 45% of the students are girls. 45%= 45/100 = 9/20. 

Mixed Number Percent to Fraction

To convert mixed number percent to fraction, follow the steps given below. Consider \(12 \dfrac{1}{2}\)%

  • Step 1: Convert it into an improper fraction. \(12 \dfrac{1}{2}\)% =  25/2 %
  • Step 2:  Drop the percent symbol %, multiplying by 100.  25/2 % = 25/2 × 1/100 = 25/200
  • Step 3: Reduce it to the lowest form. 25/200 = 1/8

Percentage to Fraction

To convert percent to fraction, follow the steps given below. Consider 120%.

  • Step 1: Express percent with the denominator 100. 120% = 120/100
  • Step 2: Reduce it to the lowest form. 12/10 = 6/5

Decimal to Fraction

To convert decimal percent to fraction, follow the steps given below. Consider the percentage value 7.5%.

  • Step 1: Drop the % symbol and divide it by100. 7.5% = 7.5/100.
  • Step 2: Drop the decimal place in the numerator. Multiply both numerator and denominator by 10. (7.5 × 10)/(100 × 10) = 75/1000. 
  • Step 3: Reduce this fraction to its lowest form by finding the GCF between numerator and denominator. (75 ÷ 25)/(1000 ÷ 25) = 3/40.

Given below is a simple percent conversion table for the most frequently used percent conversions.

Percent Fraction
5% 5/100
0.5% 5/1000
\(5 \frac{1}{2}\)% 11/200

Percent to Fraction Conversion Table

Percent to fraction conversion is very helpful in calculations. The process to convert a percent to a fraction is to remove the percent symbol and divide the remaining value with 100. The numerical value is in the numerator and the number 100 is in the denominator and it forms the fraction. Further, reduce the fraction to obtain the simplest fraction value. Also as per need some of the percentage values are also converted into decimals too. Here let us look at the converted values of percentage into fractions in the below table. 

Percent Fraction
10% 10/100 = 1/10
20% 20/100 = 1/5
25% 25/100 = 1/4
50% 50/100 = 1/2
75% 75/100 = 3/4
100% 100/100 = 1/1 = 1

Important Points

  • While converting fraction to percent, we multiply by 100.
  • While converting percent to fraction, we divide by 100.
  • To convert decimal percent to fraction, remove the decimal point and then divide by 100.
  • To convert mixed number percent to fraction, convert mixed to an improper fraction and then divide it by 100.

Important Topics

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


FAQs on Percent to Fraction 

What is the Difference Between Percent and Fraction?

The percentage value has a symbol of % and is on a scale of 1 to 100. Further, a fraction has a numerator and a denominator. A percentage value can be a whole number, fraction, or decimal, but a fraction is always in the form of numerator/denominator. A value of 4% is equal to a fraction of 4/100.

How To Convert Mixed Percent to Fraction? 

The process to convert a mixed percent to a fraction is very simple. The steps given below are to be followed to convert a mixed percent to a fraction:

  • Convert the mixed percentage into a simple fraction form of a percentage.
  • Divide with a 100, and remove the percentage symbol.
  • The fraction is simplified to obtain the answer fraction.

Let us look at a simple example to understand more of this explanation. 12½% = 25/2% = 25/2 × 1/100 = 25/200 = 1/8.

How To Convert Decimal Percent to Fraction?

The decimal percent can be easily converted into a fraction by following the steps given below:

  • Convert the decimal percentage into a fraction percentage.
  • Remove the percentage symbol by dividing the fraction by 100.
  • Simplify the fraction to obtain the required answer fraction. 

Let us solve a simple example to clearly understand this explanation. 2.5% = 25/10% = 25/10 × 1/100 = 25/1000 = 1/40

What is Percent to Fraction?

Percent to a fraction is the interpretation of percentage into a fraction. Here we need to convert a percent to a fraction. For this we can simply remove the percentage symbol and replace it with a 100 in the denominator, to obtain the required fraction. As an example 25% = 25/100 = 1/4.

How to Find Percent for any Fraction?

A percent can be conveniently be converted into a fraction. First, remove the percent symbol and replace it with a 100 in the denominator of the value. Further, reduce the fraction to a simple fraction. As an example, let us consider that a 15% of the apples are rotten. To know the fraction of apples that are rotten, we need to convert this percentage into a fraction. Here 15% = 15/100 = 3/20.

How is it Helpful to Write a Fraction as a Percent?

It is always helpful to write fractions as a percent. Writing a fraction as percent helps to convert the given fractions into a single scale of percentage and it is easy to compare and understand. Let us look at two fractions 1/2 and 1/3. It is difficult to understand and analyze these fractions. But on conversion to a percentage, the values of these fractions is 50% and 33.33% and it is simple to understand.

Can a Percent and Fraction Be Equal?

A percent and a fraction are not equal. They differ by a percent symbol %. Removal of a percent symbol replaces it with a fraction. For example, 40% is equal to a fraction of 40/100 = 4/10 = 2/5.


Solved Examples

Example 1: Andrew is given the assignment of finding the values of A, B, C, D. Can you help him find the answers?

Percent Decimal Fraction
150% A B
C 0.12 D

Solution:

A) Percent to Decimal: 150% = 150/100 = 15/10 = 1.5

B) Percent to Fraction: 150%= 150/100 = 15/10= 3/2 = \(1\frac{1}{2}\)

C) Decimal to Percent: 0.12 = 12/100 =12%

D) Percent to Fraction: 12/100 = 3/25

Therefore A = 1.5, B=\(1 \frac{1}{2}\), C= 12/100, D=3/25

Example 2: Steve has 4 shapes in his sheet. He is asked to find which shape is shaded 25%. How will he come up with the correct answer?

Percent Shading of Figures

Solution:

25% = 25/100 = 1/4. The fourth shape shows the fraction 1/4. Thus, 4th shape shows 25 %.

Therefore, the 4th shape shows 25%.

Example 3: A sugar solution of 1 liter contains 0.8%of sugar. Ryan wants to know what fraction of sugar is in the solution.

Solution:

Convert 0.8% to a fraction. To convert to percent divide the given decimal by 100 after dropping the % symbol. 0.8 ÷ 100 = 0.8/100. To move one decimal point, multiply both 0.8 and 100 by 10. (0.8 × 10)/(100 × 10)= 8/1000. Further, the GCF of 8 and 1000, is 8. (8 ÷ 8)/(1000 ÷ 8) = 1/125.

Therefore, 0.8% is equal to 1/125 of sugar in the solution.

Example 4: James gives 14.28% of discount on the laptop worth $2500. What will be a fraction of the discounted price?

Solution:

Removing the % symbol, we get  14.28 ÷100. Taking away the decimal places in the numerator, we get 14.28 ÷100 = (14.28 x 100)/(100 × 100) = 1428/10000. We find the GCF is 2. (1428 ÷ 2)/(10000 ÷ 2) = (714 ÷ 2)/(5000 ÷ 2) = 357/2500.

Therefore, the fraction of  the discounted price is 357/2500

Practice Problems 

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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