Fraction Calculator

How to Use the Fraction Calculator

Choose Calculate to work with two fractions. Enter the numerator and denominator for each fraction, then select addition, subtraction, multiplication, or division.

The result is simplified automatically and shown as an exact fraction, mixed number where applicable, and decimal value.

Choose Convert when you want to change an improper fraction into a mixed number or convert a mixed number back into an improper fraction.

How to Add Fractions

Fractions need a common denominator before their numerators can be added. For example, 1/2 and 1/4 can be written as 2/4 and 1/4, giving 3/4.

When the denominators are different, the calculator performs the equivalent cross-multiplication and then reduces the final fraction to lowest terms.

How to Subtract Fractions

Subtraction follows the same common-denominator rule as addition. Rewrite both fractions with a shared denominator, subtract the numerators, and simplify the result.

For example, 3/4 − 1/2 becomes 3/4 − 2/4 = 1/4.

How to Multiply Fractions

Multiply the numerators together and multiply the denominators together, then simplify the result.

For example, 2/3 × 3/5 gives 6/15, which reduces to 2/5.

How to Divide Fractions

To divide by a fraction, multiply by its reciprocal. The reciprocal swaps the numerator and denominator of the second fraction.

For example, 2/3 ÷ 4/5 becomes 2/3 × 5/4 = 10/12, which reduces to 5/6.

Division by a zero-valued fraction is undefined, so the calculator reports an error when the second fraction has a numerator of zero.

How Fractions Are Simplified

A fraction is in lowest terms when its numerator and denominator have no common factor greater than 1.

The calculator finds the greatest common divisor of the numerator and denominator and divides both values by it. For example, 18/24 reduces to 3/4 because both numbers divide by 6.

The sign is normalized so a negative denominator is moved to the numerator. For example, 2/−4 is displayed as −1/2.

Improper Fractions and Mixed Numbers

An improper fraction has a numerator whose magnitude is at least as large as its denominator. For example, 7/3 is an improper fraction.

To convert 7/3 to a mixed number, divide 7 by 3. The quotient is 2 and the remainder is 1, giving 2 1/3.

To convert a mixed number back to an improper fraction, multiply the whole number by the denominator and combine it with the fractional numerator. For example, 2 1/3 becomes 7/3.

Fraction to Decimal

A fraction can be converted to decimal form by dividing its numerator by its denominator. For example, 3/4 equals 0.75.

Some fractions produce repeating decimals. One third, for example, is 0.3333… rather than a terminating decimal, so the decimal display is an approximation while the fraction remains exact.

Negative Fractions

A negative fraction can place the minus sign on the numerator, denominator, or in front of the entire fraction. These forms represent the same value.

For consistency, the calculator keeps the denominator positive and places a negative sign on the numerator.

Fraction Formulas

For fractions a/b and c/d, these are the standard arithmetic rules.

$a$

First numerator

$b$

First denominator

$c$

Second numerator

$d$

Second denominator

Examples

Frequently Asked Questions