Fraction Calculator

What does the fraction calculator do?

It carries out the four operations on fractions step by step and gives the result in three forms: a reduced fraction, a mixed number and a decimal. You can work with two or three fractions, reduce a fraction to lowest terms, turn a decimal into a fraction or a fraction into a decimal, and put up to four fractions in order. All arithmetic uses whole numbers, so nothing is rounded.

How to type

• Fraction: 3/4
• Negative fraction: -3/4
• Mixed number: 2 1/3 (a space between the whole part and the fraction)
• Decimal: 0.75
• Repeating decimal: put the repeating digits in brackets, 0.1(6) means 0.1666…

Rules

• Adding and subtracting: bring the fractions to a common denominator (the least common multiple of the denominators) and add or subtract the numerators.
• Multiplying: multiply the numerators together and the denominators together.
• Dividing: flip the divisor and multiply.
• Simplifying: divide the numerator and the denominator by their greatest common divisor.
• With three fractions, multiplication and division are done before addition and subtraction.

Example

For 2 1/3 + 3/4 the mixed number is first turned into an improper fraction: 2 1/3 = 7/3. The denominators are 3 and 4, so the common denominator is 12. Since 7/3 = 28/12 and 3/4 = 9/12 the sum is 37/12, which is 3 1/12 as a mixed number.

Repeating decimals

A fraction whose reduced denominator has only 2 and 5 as prime factors has a decimal expansion that ends: 3/8 = 0.375. Any other prime factor makes the digits repeat: 1/6 = 0.1666… The tool finds the repeating block and shows it in brackets: 0.1(6). Going the other way, to turn a repeating decimal into a fraction let x = 0.1666…, write 100x and 10x and subtract so that the repeating part cancels: 90x = 15, so x = 1/6.

Limits

Numbers can have at most 120 digits. When the repeating block is longer than 400 digits only the first digits are shown and the tool says so. The tool works with numbers only: for fractions that contain letters see the expression simplifier.