Converting Fraction to Percentage

Two Steps to Convert a Fraction to a Percent

Use division to convert the fraction to a decimal: 1/4 = 1 ÷ 4 = 0.25
Multiply by 100 to get percent value: 0.25 × 100 = 25%

Convert the fraction to a decimal number

The fraction bar between the top number (numerator) and the bottom number (denominator) means "divided by." So converting a fraction such as 1/4 to a decimal means you need to solve the math: 1 divided by 4. 1 ÷ 4 = 0.25

Multiply by 100 to convert decimal number to percent

0.25 × 100 = 25%

You can reduce a fraction before converting to a decimal but it's not necessary because the answer will be the same. If you need to do the conversion by long division, reducing might make the math easier.

For example, 6/12 = 6 ÷ 12 = 0.50. If you solve this with a calculator then it is easy to get the answer. However, if you solve this by hand or in your head reducing 6/12 = 1/2 may make the problem easier and you may even recognize that 1/2 = 0.50.

Multiplying 0.50 by 100 means that 6/12 = 50%.

Example

Converting Fractions to Percentages

Converting a fraction to a percentage means expressing the fraction as a value out of 100. This is useful for understanding proportions in everyday scenarios such as test scores, discounts, and probability.

The general approach to converting a fraction to a percentage includes:

Dividing the numerator by the denominator to get a decimal.
Multiplying the decimal by 100 to express it as a percentage.

Converting a Proper Fraction

A proper fraction has a numerator smaller than its denominator.

Example:

If the fraction is \( \frac{3}{5} \), the conversion is:

Step 1: Divide \( 3 \div 5 = 0.6 \).
Step 2: Multiply by 100: \( 0.6 \times 100 = 60\% \).

Converting an Improper Fraction

An improper fraction has a numerator larger than or equal to its denominator.

Example:

If the fraction is \( \frac{7}{4} \), the conversion is:

Step 1: Divide \( 7 \div 4 = 1.75 \).
Step 2: Multiply by 100: \( 1.75 \times 100 = 175\% \).

Converting a Mixed Number

A mixed number consists of a whole number and a fraction.

Example:

If the mixed number is \( 2\frac{1}{4} \), the conversion is:

Step 1: Convert to an improper fraction: \( 2\frac{1}{4} = \frac{9}{4} \).
Step 2: Divide \( 9 \div 4 = 2.25 \).
Step 3: Multiply by 100: \( 2.25 \times 100 = 225\% \).

Real-life Applications of Fraction to Percent Conversion

Converting fractions to percentages has many practical applications, such as:

Determining the percentage of test scores (e.g., scoring **18 out of 20** is \( \frac{18}{20} = 90\% \)).
Calculating discounts in shopping (e.g., a product originally priced at **R200**, with a **25% discount**, means a discount of \( \frac{25}{100} \times 200 = R50 \)).
Understanding probability (e.g., rolling a die and getting a **4 or higher** occurs in **\(\frac{3}{6} = 50\%\)** of cases).

Common Fraction to Percentage Conversions

\(\frac{1}{2} = 50\%\)

\(\frac{1}{4} = 25\%\)

\(\frac{3}{4} = 75\%\)

\(\frac{2}{5} = 40\%\)

Quick Tip: If the fraction's denominator is **100**, the numerator is already the percentage (e.g., \( \frac{45}{100} = 45\% \)).

Fraction to Percent Calculator Examples Table
Fraction Type	Description	Steps to Convert	Example
Proper Fraction	A fraction where the numerator is smaller than the denominator.	Divide the numerator by the denominator. Multiply the result by 100 to convert to a percentage.	For \( \frac{3}{5} \), divide \( 3 \div 5 = 0.6 \), then multiply by 100 to get 60%.
Improper Fraction	A fraction where the numerator is greater than or equal to the denominator.	Divide the numerator by the denominator. Multiply by 100 to get the percentage.	For \( \frac{7}{4} \), divide \( 7 \div 4 = 1.75 \), then multiply by 100 to get 175%.
Mixed Number	A number that consists of a whole number and a fraction.	Convert the mixed number into an improper fraction. Divide the numerator by the denominator and multiply by 100.	For \( 2\frac{1}{4} \), convert to \( \frac{9}{4} \), divide \( 9 \div 4 = 2.25 \), then multiply by 100 to get 225%.
Real-life Applications	Using fractions to percentages in everyday scenarios.	Convert test scores to percentages. Find percentage discounts when shopping.	If a student scores 18 out of 20, convert \( \frac{18}{20} \) to a percentage: \( 18 \div 20 = 0.9 \), then multiply by 100 to get 90%.