Fraction to Percentage Conversion

Fractions and percentages are two different ways of expressing a number and are generally used for comparing quantities. The fractions can be converted to percentages and vice versa.

Let us consider that in a test Rosy got 5 out of 6 while John got 6 out of 8. So, can you determine who has the better marks percentage? For that, we need to calculate their marks percentage first. So, we need to convert the given fractions to percentages.

Fraction to Percentage Converter

You can convert any fraction to a percentage using the following converter:

Converting Fractions to Percentage

To convert a fraction to a percentage we need to divide the given fraction to obtain a decimal and then Multiply the decimal by 100 to get the percentage lastly add a percentage sign (%) to the result

Fraction to Percentage Conversion Formula

Fraction to percentage conversion can be done using this formula. It helps in finding the share of a whole expressed in terms of 100.

x = p/q × 100

Percentage = Fraction × 100

where, 
p represents the numerator,
q represents the denominator, and
x represents the required percentage

For example, out of 50 coins, we have 15 gold coins. So, in terms of a fraction, we can write this as 15/50. Now, to convert it into a fraction, multiply it by 100 and add the percent symbol.

Thus, 15/50 × 100 = 30% , so, 30% of the total coins we have are gold coins .

Steps to convert Fractions to Percentage Using Decimals

Follow the steps given below to convert fractions to percentages using decimals:

Step 1 : First, divide the numerator by the denominator.
Step 2 : Now, multiply the obtained result by 100.
Step 3 : Add the percent symbol to the result obtained in the above step.

Example: Convert 4/9 to percentage by first converting it into decimal form.

Solution:

Step 1: Divide the numerator by the denominator, i.e., divide 4 by 9. 4 ÷ 9 = 0.444445
Step 2: Multiply the 0.444445 by 100, i.e., 0.444445 × 100 = 44.4445.
Step 3: Add the percent symbol to the result obtained in the above step.
So, 4/9 = 44.4445%

Steps for Fraction to Percentage conversion Using Proportions

Let a/b and c/d be equal ratios, so the numbers a, b, c, and d are said to be in proportion. To convert a fraction a/b into a percent, we should convert it into the form of x/100, where x is the required percentage.

Step 1 : Write the given fraction in proportion format.

a/b = x/100

Step 2 : Solve the above proportion using the cross-multiplication method and simplify it further to obtain the required percent.

Required percent (x) = (a/b) × 100

Example: Convert 5/11 to percent using proportions.

Solution:

Step 1: First, we have to write the given fraction in proportion format.
5/11 = x/100

Step 2: Now, let us solve the above proportion using the cross-multiplication method.
x = (5/11) × 100

Step 3:  Simplify it further to obtain the required percent.
x = 45.4545%

Converting Mixed Fractions To Percentage

We can also convert mixed fractions into percentages using the above-mentioned method. But first, we have to convert the mixed fraction into an improper fraction. Then, we can follow any of the above-mentioned methods.

Example: Convert 1¾ into percent.

Solution:

First, convert the mixed fraction into an improper fraction. 
1¾ = 7/4

Now, convert 7/4 into a decimal, and divide the numerator by the denominator.
7/4 = 7 ÷ 4 = 1.75

Now, multiply the decimal by 100 to convert it to percent.
1.75 × 100 % = 175%

So, 7/4 = 175%

Fraction to Percentage Conversion Chart

The table given below is a fraction-to-percent chart that helps in solving numerical problems quickly.

Examples - Fraction to Percentage Conversion

Example 1: John passed 6 subjects out of 8 subjects. Calculate his pass percentage using the fraction to percent formula.

Solution:

Given data:
Number of subjects passed = 6
Total number of subjects = 8

So, the ratio of the number of subjects John passed out of the total number of subjects is 6 out of 8, i.e., 6/8.

The pass percentage of John = 6/8 × 100% = 75%
So, the pass percentage of John is 75%.

Example 2: Convert the following fractions to percentages by first converting them into decimal form. 

• 3/4
• 6/7
• 2/5

Solution:

a) To convert 3/4 into a decimal, divide the numerator by the denominator.
3 ÷ 4 = 0.75

Now, multiply the decimal by 100 to convert it to percent.0.75 × 100 % = 75%
So, 3/4 = 75%

b) To convert 6/7 into a decimal, divide the numerator by the denominator.
6 ÷ 7 ≈ 0.85714

Now, multiply the decimal by 100 to convert it to percent.
0.85714 × 100 % = 85.714%
So, 6/7 = 85.714%

c) To convert 2/5 into a decimal, divide the numerator by the denominator.
2 ÷ 5 = 0.4

Now, multiply the decimal by 100 to convert it to percent.
0.4 × 100 % = 40%

So, 2/5 = 40%

Example 3: Convert 5½ into percent.

Solution:

First, convert the mixed fraction into an improper fraction.
5½ = 11/2

Now, convert 7/4 into a decimal, and divide the numerator by the denominator.
11 = 11 ÷ 2 = 5.5

Now, multiply the decimal by 100 to convert it to percent.
5.5 × 100 % = 550%

So, 11/2 = 550%

Example 4: Convert 9/13 to percent using proportions.

Solution:

First, we have to write the given fraction in proportion format.
9/13 = x/100

Now, let us solve the above proportion using the cross-multiplication method.
x = (9/13) × 100

Simplify it further to obtain the required percentage.
x = 69.231%

Also Read:

• Fraction To Decimal Conversion
• Decimal Fraction