How to Use the Fraction Calculator

Enter the first fraction and second fraction, then choose whether you want to add, subtract, multiply or divide them.

For mixed numbers, enter the whole-number part separately.

The calculator shows:

• The simplified fraction;
• The improper fraction;
• The mixed-number result;
• The decimal equivalent;
• The percentage equivalent;
• The reciprocal; and
• A step-by-step calculation.

What Is a Fraction?

A fraction represents part of a whole and is normally written with a numerator above a denominator.

For example:

means three parts out of four equal parts.

How to Add Fractions

Fractions must have a common denominator before they can be added.

For example:

How to Subtract Fractions

For example:

3/4 − 1/2

Convert 1/2 to quarters:

1/2 = 2/4

Then:

3/4 − 2/4 = 1/4

How to Multiply Fractions

Multiply the numerators together and multiply the denominators together.

Example:

How to Divide Fractions

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

Example:

What Is a Mixed Number?

A mixed number contains a whole number and a proper fraction.

Example:

This means two whole units plus one third.

How to Convert a Mixed Number to an Improper Fraction

Multiply the whole number by the denominator and add the numerator.

What Is an Improper Fraction?

An improper fraction has a numerator that is greater than or equal to its denominator.

Examples include:

• 5/4;
• 7/3;
• 9/8; and
• 12/6.

How to Convert an Improper Fraction to a Mixed Number

Divide the numerator by the denominator.

For example:

Therefore:

How to Simplify Fractions

A fraction is simplified by dividing the numerator and denominator by their greatest common divisor.

For example:

The greatest common divisor of 8 and 12 is 4.

Therefore:

What Is the Greatest Common Divisor?

The greatest common divisor, or GCD, is the largest whole number that divides two numbers without leaving a remainder.

For example, the GCD of 18 and 24 is 6.

How to Convert a Fraction to a Decimal

Divide the numerator by the denominator.

For example:

How to Convert a Fraction to a Percentage

Convert the fraction to a decimal and multiply by 100.

For example:

Common Fraction to Decimal Conversions

• 1/2 = 0.5;
• 1/3 ≈ 0.3333;
• 1/4 = 0.25;
• 2/3 ≈ 0.6667;
• 3/4 = 0.75;
• 1/5 = 0.2;
• 1/8 = 0.125; and
• 7/8 = 0.875.

Common Fraction to Percentage Conversions

• 1/2 = 50%;
• 1/4 = 25%;
• 3/4 = 75%;
• 1/5 = 20%;
• 2/5 = 40%;
• 3/5 = 60%;
• 4/5 = 80%; and
• 1/10 = 10%.

What Is a Reciprocal?

The reciprocal of a non-zero fraction is found by swapping the numerator and denominator.

For example:

The reciprocal is especially important when dividing fractions.

Can the Fraction Calculator Handle Whole Numbers?

Yes. Enter the whole-number field and leave the fraction portion as zero if needed.

A whole number can also be represented as a fraction with denominator 1.

For example:

Can the Calculator Handle Negative Fractions?

Yes. Negative numerators or whole-number values are supported.

For example:

Why Can the Denominator Not Be Zero?

Division by zero is undefined in standard arithmetic.

Since a fraction represents numerator divided by denominator, a denominator of zero does not represent a valid finite number.

Fraction Calculator for Students

The calculator can be used to check fraction arithmetic and review the steps involved in:

• Adding fractions;
• subtracting fractions;
• multiplying fractions;
• dividing fractions;
• simplifying fractions;
• converting mixed numbers; and
• converting fractions to decimals and percentages.

Fraction Calculator Assumptions

This calculator assumes:

• Numerators and denominators are entered as whole integers;
• Denominators are not zero;
• Mixed-number whole parts are interpreted consistently with the fraction sign;
• Results are simplified using the greatest common divisor;
• Decimal results are rounded for display;
• Percentage results are calculated from the decimal value;
• Division by a zero fraction is not allowed; and
• Results are general mathematical calculations.

Related Maths Calculators