CornerTools

Fraction Calculator

Add, subtract, multiply and divide fractions and mixed numbers, simplified, with the steps.

Fractions as 3/4, mixed numbers as 2 1/3. Use + − * ^ and brackets; to divide, type ÷ or a / with a space on each side.

Result

54

Mixed number
1 1/4
Decimal
1.25
Percentage
125%

Type a calculation with fractions, mixed numbers, whole numbers or decimals, such as 1/2 + 3/4, and the answer appears as you type: 5/4 in lowest terms, 1 1/4 as a mixed number, 1.25 as a decimal and 125% as a percentage. The working shows one step for each operation, in the order it is done.

How to type a calculation

  • A fraction is two whole numbers with a slash and no spaces: 3/4.
  • A mixed number is a whole number, a space, then a proper fraction: 2 1/3. A fraction of 1 or more after the space is refused (“Mixed numbers take a proper fraction: 2 3/2”); for a product, write 2 * 3/2.
  • Add with +, subtract with -, multiply with * or ×.
  • Divide with ÷, or with a slash that has a space on each side: 1/2 / 3/4.
  • Raise to a whole power with ^, negative powers included: (1/2)^-2 is read as (1/2)^−2 and gives 4.
  • Group with brackets: (1/2 + 1/3) ÷ 5/6 is read as (1/2 + 1/3) ÷ 5/6 and gives 1.

When the tool groups a calculation in a way the typed text does not show, or reads a slash as a division, Read as appears under the box and draws the calculation as it was understood, with every grouping written out, so a power or a division can be checked before trusting the answer. A calculation takes up to 10 numbers of up to 100 digits each.

Simplify swaps the box for a numerator and a denominator, and reduces that one fraction, naming the greatest common divisor it divides by. Everything runs in your browser.

The rules it follows

Arithmetic is exact, on whole-number numerators and denominators of any size, so no answer is a rounded decimal turned back into a fraction. Every result is reduced by the greatest common divisor of its two parts. A decimal that repeats is written with the repeating digits in brackets: 0.1(6) is 0.1666….

Powers come first, then multiplication and division from left to right, then addition and subtraction. A fraction typed with an unspaced slash is one number, as it is on paper, so 3/4^2 is read as (3/4)^2 and gives 9/16. Most calculators, the Scientific Calculator among them, treat every slash as a division and work out the power first: with spaces, 3 / 4^2 is read as 3 ÷ 4^2 and gives 3/16. A leading minus applies after the power: -3/4^2 is read as −(3/4)^2 and gives −9/16.

Two unspaced slashes in a row have no single reading, so 1/2/3 is refused with the two ways to write it (“Write 1/2 ÷ 3 or 1 ÷ 2/3”).

a/b + c/d = (a × d + c × b) ÷ (b × d), then simplified
a/b − c/d = (a × d − c × b) ÷ (b × d), then simplified
a/b × c/d = (a × c) ÷ (b × d)
a/b ÷ c/d = a/b × d/c
(a/b)ⁿ = aⁿ/bⁿ

Examples

Adding fractions with different denominators

2/3 + 5/8 gives 31/24, or 1 7/24 as a mixed number.

  1. The lowest common denominator of 3 and 8 is 24. Write both over it, then add the numerators. 2/3 + 5/8 = 16/24 + 15/24 = 31/24
  2. As a mixed number: divide the numerator by the denominator, and keep the remainder over it. 31/24 = 1 7/24

A mixed number times a fraction

2 1/3 * 3/5 gives 7/5, or 1 2/5.

  1. Write the mixed number as an improper fraction. 2 1/3 = (2 × 3 + 1)/3 = 7/3
  2. Multiply the numerators together and the denominators together. 7/3 × 3/5 = 21/15 = 7/5
  3. As a mixed number: divide the numerator by the denominator, and keep the remainder over it. 7/5 = 1 2/5

Dividing by a fraction

3/4 ÷ 2/5 gives 15/8, which is 1.875 as a decimal.

  1. To divide by a fraction, multiply by its reciprocal. 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8
  2. As a mixed number: divide the numerator by the denominator, and keep the remainder over it. 15/8 = 1 7/8

Simplifying 84/126

With Simplify chosen, a numerator of 84 and a denominator of 126 give 2/3.

  1. The greatest common divisor of 84 and 126 is 42.
  2. Divide the numerator and the denominator by it. 84 ÷ 42 = 2, 126 ÷ 42 = 3
  3. The fraction in lowest terms. 84/126 = 2/3

Frequently asked questions

A fraction is in simplest form, or lowest terms, when its numerator and denominator share no factor other than 1. Dividing both by their greatest common divisor gets there in one step: 18/24 = 3/4.
They are two ways of writing the same value above 1. An improper fraction has a numerator larger than its denominator; a mixed number splits off the whole part. 7/4 = 1 3/4. The tool shows both.
The minus sign applies to the whole number and the fraction together: -1 1/2 is read as −1 1/2 and gives −3/2, not −1 + 1/2.

See also