Fraction calculator

Add, subtract, multiply and divide fractions with an exact simplified result.

Add, subtract, multiply or divide two fractions and get an exact result in lowest terms.

Your inputs stay herePUFFINMINT

Set your data

First numerator

First denominator

Operation

Second numerator

Second denominator

Enter two fractions with integer numerators and denominators, then choose an operation. Each integer supports up to 30 digits.

Result

Enter your data and run the tool. Your result will appear here.

Fractions of the same whole

Compare the fractions and the result. For addition and subtraction you can switch to a common denominator.

The values you enter stay on this page. Reloading or closing it clears them.

We count which tools are used most, without including entered values or file contents in the statistics. Privacy

When a fraction calculator helps

Use it to check exercises or work with parts of a whole. Quantities must be compatible: adding a length to a weight does not produce a meaningful measurement.

Enter the two fractions

Compare the fractions and the result. For addition and subtraction you can switch to a common denominator.

Enter an integer numerator and denominator for each fraction.
Select addition, subtraction, multiplication or division, then calculate.
Read the reduced result and change the inputs to check another case.

Formulas and simplification

These formulas require nonzero b and d. Division also requires nonzero c. The engine uses BigInt integers and divides both parts by their greatest common divisor, without converting to a decimal.

Adding fractions

\frac{a}{b} + \frac{c}{d} = \frac{a \times d + b \times c}{b \times d}

Subtracting fractions

\frac{a}{b} - \frac{c}{d} = \frac{a \times d - b \times c}{b \times d}

Multiplying fractions

\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}

Dividing fractions

\frac{a}{b} \div \frac{c}{d} = \frac{a \times d}{b \times c}

Understand the reduced result

The numerator counts the parts; the denominator tells how many equal parts make the whole. A final denominator of 1 is omitted, so 6/3 becomes 2. A negative sign is placed on the numerator.

Worked examples: division and addition

Three-quarter portions

Input: $\frac{3}{4} \div \frac{1}{2}$
Result: $\frac{3}{2}$

Calculation steps

To divide, multiply by the reciprocal of the second fraction.
$\frac{3}{4} \div \frac{1}{2} = \frac{3}{4} \times \frac{2}{1}$
Multiply the numerators together and the denominators together.
$\frac{3 \times 2}{4 \times 1} = \frac{6}{4}$
Divide the numerator and denominator by 2 to reduce the fraction.
$\frac{6}{4} = \frac{6 \div 2}{4 \div 2} = \frac{3}{2}$

As a mixed number

\frac{3}{2} = 1 \frac{1}{2}

The result is one whole and one half. Each bar represents one unit of the result.

Dividing 3/4 by 1/2 asks how many halves fit into three quarters: one and a half. An improper fraction is a valid result.

Adding one half and one third

Input: $\frac{1}{2} + \frac{1}{3}$
Result: $\frac{5}{6}$

Calculation steps

Rewrite both fractions with the common denominator 6.
$\frac{1}{2} = \frac{3}{6}, \frac{1}{3} = \frac{2}{6}$
Add the numerators and keep the common denominator.
$\frac{3}{6} + \frac{2}{6} = \frac{3 + 2}{6} = \frac{5}{6}$

Adding one half and one third: 1/2 + 1/3 = 5/6.

The sum is five sixths: five of the six equal parts are highlighted. The calculator returns the reduced fraction; the mixed number in the previous example is an equivalent way to understand it.

Input limits and common mistakes

Each field accepts integers of up to 30 digits. Decimals and mixed numbers such as 1 1/2 are not accepted; enter 3 over 2 instead. A denominator cannot be zero, and the fraction you divide by cannot have a zero numerator.

Frequently asked questions

Can I add the denominators?

No. Addition requires a common denominator. For example, 1/2 + 1/3 = 5/6, not 2/5.

Why is the answer a fraction rather than a decimal?

A reduced fraction preserves the exact value, including values such as 1/3 that have no finite decimal representation. Inputs remain in this page and disappear when it reloads.

Fraction calculator

Set your data

Result

When a fraction calculator helps

Enter the two fractions

Formulas and simplification

Adding fractions

Subtracting fractions

Multiplying fractions

Dividing fractions

Understand the reduced result

Worked examples: division and addition

Three-quarter portions

Calculation steps

Adding one half and one third

Calculation steps

Input limits and common mistakes

Frequently asked questions

You might also need

Long division calculator with steps and remainders

Proportions and rule of three

Online calculator