A fraction represents a part of a whole or a ratio between two numbers. The top number is the numerator and the bottom number is the denominator.

How to Calculate Fractions: Formula, Examples & Easy Guide

Q: How do you add fractions?

To add fractions with the same denominator, add the numerators and keep the denominator. For different denominators, find a common denominator first.

Q: How do you divide fractions?

To divide fractions, multiply the first fraction by the reciprocal of the second fraction, then simplify the result.

Fractions are an important part of mathematics and are used to represent parts of a whole, ratios, measurements, percentages and many everyday quantities.

Learning how to calculate fractions helps you solve problems involving addition, subtraction, multiplication, division and comparisons. This guide explains fractions with simple formulas and step-by-step examples.

For quick calculations, you can also use our free Fraction Calculator .

Use the Fraction Calculator

What Is a Fraction?

A fraction represents a part of a whole or a relationship between two numbers.

A fraction has two main parts:

Numerator = top number

Denominator = bottom number

For example, in the fraction 3/4, 3 is the numerator and 4 is the denominator.

The fraction 3/4 means three parts out of four equal parts.

How to Calculate a Fraction

The calculation depends on what you want to do with the fractions. Common fraction operations include:

Adding fractions
Subtracting fractions
Multiplying fractions
Dividing fractions
Simplifying fractions
Converting fractions to decimals
Converting fractions to percentages

How to Add Fractions With the Same Denominator

When two fractions have the same denominator, adding them is simple. Add the numerators and keep the denominator unchanged.

a/c + b/c = (a + b)/c

Example

2/7 + 3/7

Add the numerators:

2 + 3 = 5

Keep the denominator 7.

2/7 + 3/7 = 5/7

How to Add Fractions With Different Denominators

When the denominators are different, you need to find a common denominator before adding the fractions.

Example: 1/2 + 1/3

The denominators are 2 and 3.

A common denominator is 6.

Convert the fractions:

1/2 = 3/6

1/3 = 2/6

Now add:

3/6 + 2/6 = 5/6

Answer = 5/6

How to Subtract Fractions

Fraction subtraction follows a method similar to addition. Fractions must have a common denominator before subtracting their numerators.

a/c − b/c = (a − b)/c

Example With the Same Denominator

7/9 − 2/9

7 − 2 = 5

7/9 − 2/9 = 5/9

Example With Different Denominators

3/4 − 1/2

Convert 1/2 to 2/4.

3/4 − 2/4 = 1/4

Answer = 1/4

How to Multiply Fractions

Multiplying fractions is usually straightforward. Multiply the numerators together and multiply the denominators together.

a/b × c/d = (a × c)/(b × d)

Example

2/3 × 4/5

Numerators:

2 × 4 = 8

Denominators:

3 × 5 = 15

Answer = 8/15

How to Divide Fractions

To divide one fraction by another, multiply the first fraction by the reciprocal of the second fraction.

a/b ÷ c/d = a/b × d/c

Example

2/3 ÷ 4/5

Change division to multiplication and flip the second fraction:

2/3 × 5/4

Multiply:

10/12

Simplify:

5/6

How to Simplify a Fraction

Simplifying a fraction means reducing it to its simplest equivalent form.

To simplify a fraction, divide both the numerator and denominator by their greatest common factor.

Example: Simplify 12/18

Numerator = 12

Denominator = 18

Greatest common factor = 6

12 ÷ 6 = 2

18 ÷ 6 = 3

12/18 = 2/3

How to Find the Greatest Common Factor

The greatest common factor, or GCF, is the largest positive number that divides two or more numbers without leaving a remainder.

Finding the GCF is useful when simplifying fractions.

Find the GCF of 24 and 36.

Common factors include 1, 2, 3, 4, 6 and 12.

The greatest common factor is 12.

Proper and Improper Fractions

Type	Description	Example
Proper Fraction	Numerator is smaller than denominator	3/5
Improper Fraction	Numerator is equal to or larger than denominator	7/4
Mixed Number	Whole number combined with a fraction	1 3/4

How to Convert an Improper Fraction to a Mixed Number

Divide the numerator by the denominator.

Example: Convert 7/3

7 ÷ 3 = 2 remainder 1

Therefore:

7/3 = 2 1/3

How to Convert a Mixed Number to an Improper Fraction

Multiply the whole number by the denominator, add the numerator and place the result over the original denominator.

Example: Convert 2 1/3

2 × 3 = 6

6 + 1 = 7

Therefore:

2 1/3 = 7/3

How to Convert a Fraction to a Decimal

To convert a fraction to a decimal, divide the numerator by the denominator.

3/4

3 ÷ 4 = 0.75

3/4 = 0.75

How to Convert a Fraction to a Percentage

To convert a fraction to a percentage, divide the numerator by the denominator and multiply the result by 100.

Percentage = (Numerator ÷ Denominator) × 100

Example

3/4 × 100

0.75 × 100 = 75

3/4 = 75%

Equivalent Fractions

Equivalent fractions have different numbers but represent the same value.

1/2

Multiply numerator and denominator by 2:

2/4

Multiply by 3:

3/6

Therefore:

1/2 = 2/4 = 3/6

How to Compare Fractions

Fractions can be compared by finding a common denominator, converting them to decimals or using cross multiplication.

Example: Compare 2/3 and 3/5

Cross multiply:

2 × 5 = 10

3 × 3 = 9

Since 10 is greater than 9:

2/3 is greater than 3/5

Common Mistakes When Calculating Fractions

Adding denominators directly when adding fractions.
Forgetting to find a common denominator.
Simplifying only the numerator or only the denominator.
Forgetting to flip the second fraction when dividing.
Making arithmetic errors when multiplying numerators and denominators.
Failing to simplify the final answer.

Fraction Formula Quick Reference

Operation	Formula
Addition	a/c + b/c = (a+b)/c
Subtraction	a/c − b/c = (a−b)/c
Multiplication	a/b × c/d = ac/bd
Division	a/b ÷ c/d = a/b × d/c
Percentage	(Numerator ÷ Denominator) × 100

How to Use a Fraction Calculator

When working with several fractions, a calculator can make the process faster and reduce manual calculation errors.

Open the Fraction Calculator.
Enter the fractions you want to calculate.
Select the required operation.
Calculate the result.
Simplify or review the final answer.

Our free Fraction Calculator can help you perform common fraction calculations quickly.

Calculate Fractions

Frequently Asked Questions

What is a fraction?

A fraction represents a part of a whole or a relationship between two numbers. The top number is the numerator and the bottom number is the denominator.

How do you add fractions?

For fractions with the same denominator, add the numerators and keep the denominator. For different denominators, first find a common denominator.

How do you multiply fractions?

Multiply the numerators together and multiply the denominators together. Then simplify the result if possible.

How do you divide fractions?

Multiply the first fraction by the reciprocal of the second fraction, then simplify the result.

How do you simplify a fraction?

Divide the numerator and denominator by their greatest common factor.

Related Math Calculators

You may also find these free calculators useful:

Final Thoughts

Fractions become much easier when you understand the basic rules for each operation. Addition and subtraction require common denominators when the denominators are different, while multiplication and division follow their own straightforward formulas.

Simplifying fractions is also important because it gives the result in its simplest equivalent form.

For quick and convenient calculations, use our free Fraction Calculator on Easy Online Tool.

Disclaimer: This article is provided for general educational and informational purposes. Always review mathematical calculations when accuracy is important.