Fraction Calculator

Fraction calculator with mixed numbers

Use the arithmetic mode to add, subtract, multiply, or divide proper fractions, improper fractions, whole numbers, and mixed numbers. Enter a negative sign on the whole-number field to make the entire mixed number negative. If the whole number is zero, put the negative sign on the numerator.

Adding and subtracting fractions

Fractions need a common denominator before their numerators can be combined. This calculator shows the least common denominator and the equivalent fractions used in the operation, then reduces the answer to lowest terms.

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

a/b - c/d = (a x d - c x b) / (b x d)

Multiplying and dividing fractions

To multiply fractions, multiply the numerators and denominators. To divide, multiply the first fraction by the reciprocal of the second. Division is undefined when the second fraction equals zero.

a/b x c/d = (a x c) / (b x d)

a/b divide c/d = (a x d) / (b x c)

Mixed numbers and improper fractions

A mixed number combines a whole number and a proper fraction. Before calculating, the tool converts each mixed number to an improper fraction. For example, 1 1/2 becomes 3/2 because 1 x 2 + 1 = 3.

Simplify a fraction

Select Simplify a fraction to divide the numerator and denominator by their greatest common divisor. For example, the greatest common divisor of 42 and 56 is 14, so 42/56 reduces to 3/4.

Convert a decimal to a fraction

Select Convert a decimal to a fraction to express a terminating decimal as an exact fraction based on the entered decimal places. For example, 0.375 becomes 375/1000 and reduces to 3/8.

Decimal and percentage equivalents

Every valid result includes a decimal and percentage equivalent. The decimal is the numerator divided by the denominator; the percentage is that decimal multiplied by 100.

Fractions from ratios

A ratio of 2 red counters to 3 blue counters gives two different fractions depending on the question. Red compared with blue is 2/3, but red as a share of all five counters is 2/5. Enter 2 over 5 here to get 0.4 and 40%; entering 2 over 3 answers the first comparison instead.

Use the ratio calculator to simplify ratios or split a total into proportional shares. For a direct part-and-whole question such as 2 is what percent of 5, use the percentage calculator. Keep the compared quantities in the same units before reducing their ratio.

Frequently asked questions

Can the denominator be zero?

No. A fraction with a denominator of zero is undefined, so the calculator displays an error instead of a numerical result.

How do I enter a whole number?

Enter the number in the Whole field and use 0 as the numerator. You can also enter the whole number as a numerator over 1.

Does the calculator reduce answers automatically?

Yes. It divides the numerator and denominator by their greatest common divisor and keeps the denominator positive.