Fraction to Percent Conversion

In daily life, we quite often compare two quantities. Fractions and percents 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 Rosy passed 5 out of 6 subjects while John passed 6 out of 8 subjects. So, can you determine who has the better pass percentage? For that, we need to calculate their pass percentage first. So, we need to convert the given fractions to percentages. We have two different methods for converting a fraction into a percent. 

But before learning about the conversion of fractions to percent, let us learn the definitions of fractions and percentages.

What is a Fraction?

In mathematics, a fraction is referred to as a numerical value that expresses a part of a whole. A fraction is a portion of any quantity taken from a whole, whereas the whole can be any number, a thing, or a certain value. For example, if a square is divided into four equal parts and we have to express a selected part of the square, we can express it as 1/4, which means one in four equal parts. It can also be written as “one-fourth” or “1 by 4.” A fraction has two parts called the numerator and the denominator that are separated by a fractional bar, where the numerator is the upper part of the fraction and represents the sections of the fraction, while the denominator is the lower part of the fraction and represents the total number of parts into which the fraction is divided.

What is a Percent?

In mathematics, the percent refers to “per hundred.” Percent can be said to be a number or a fraction with a denominator of 100. It is represented by the symbol “%.” It is a dimensionless number. For example, 26% of a number means 26 percent of its whole.

Fraction to Percent Formula

The following is the fraction to percent formula that helps in finding the share of a whole expressed in terms of 100.

p/q × 100 = x

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

(or)

Percentage = Fraction × 100

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%

Conversion of Fractions to Percentage

To convert a fraction to a percent, multiply the given fraction by 100 and simplify it further. We have two different methods for converting a fraction into a percent. The first method is the conversion of a fraction to a decimal and then converting the obtained decimal to a percent. The second method is the conversion of a fraction to a percent using proportions.

Fraction to Percent Using Decimals

Follow the steps below to convert fractions to percents using decimals:

• First, divide the numerator by the denominator.
• Now, multiply the obtained result by 100.
• Add the percent symbol to the result obtained in the above step.

Example: Convert to 4/9 percent 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%

Fraction to Percent 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.

• Write the given fraction in proportion format.

a/b = x/100

• 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%

We have different methods to convert the given fraction to percent using proportions.

Method 1

Multiply the given fraction by 100, and then solve it further.

Example: Find the percent of 5/11

Solution:

5/11 

= (5/11 × 100) % 

= (500/11) % 

= 45.4545%

Method 2

Convert the given fraction into a decimal, and then multiply it by 100.

Example: Convert 5/11 to percentage

Solution:

5/11 

= 0.45454545

= 0.45454545 × 100% 

= 45.4545%

Method 3

Let x be the required percentage.

5/11 = x/100

x = (5/11) × 100 = 45.4545%

We can also convert mixed fractions into percentages using the above-mentioned methods. 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 Percent Chart

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

Fraction	Decimal	Percent
1/2	0.5	50%
1/3	0.3333333	33.3333%
2/3	0.6666666	66.6666%
1/4	0.25	25%
2/4	0.5	50%
3/4	0.75	75%
1/5	0.2	20%
2/5	0.4	40%
3/5	0.6	60%
4/5	0.8	80%
1/6	0.166666	16.6666%
2/6	0.3333333	33.3333%
3/6	0.5	50%
4/6	0.6666666	66.6666%
5/6	0.8333333	83.33333%

Read More,

• Whole Numbers
• Natural Numbers
• Real Numbers

Solved Examples on Fraction to Percent 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%

FAQs on Fraction and Percent

Q1: What is meant by a fraction?

Answer:

In mathematics, a fraction is referred to as a numerical value that expresses a part of a whole.

Q2: What is meant by a percentage?

Answer:

In mathematics, the percent refers to “per hundred.” Percent can be said to be a number or a fraction with a denominator of 100.

Q3: How to convert a fraction to a percent using decimals?

Answer:

Follow the steps below to convert a fraction to a percent using decimals:

• First, divide the numerator by the denominator.
• Now, multiply the obtained result by 100.
• Add the percent symbol to the result obtained in the above step.

Q4: How to convert a fraction to a percent using proportions?

Answer:

Follow the steps below to convert a fraction to a percent using proportions:

Step 1: First, we have to write the given fraction in proportion format.

Step 2: Now, let us solve the above proportion using the cross-multiplication method.

Step 3:  Simplify it further to obtain the required percent and finally add the percent symbol to the result.

Q5: How can we convert a mixed fraction to a percent?

Answer:

We can follow different methods to convert a mixed fraction to a percent. Follow the steps below to convert a mixed fraction to a mixed percent using decimals:

• First, convert the mixed fraction into an improper fraction. 
• Now, convert the improper fraction into a decimal, and divide the numerator by the denominator.
• Now, multiply the obtained result by 100.
• Finally add the percent symbol to the result obtained in the above step.