Fraction Calculator
Add, subtract, multiply or divide fractions and mixed numbers, and get the answer in lowest terms, as a mixed number and as an exact decimal, with the working shown.
Type each number as a whole part and a fraction, pick add, subtract, multiply or divide, and the answer appears in lowest terms with the steps underneath. Adding 2 1/3 and 1 3/4 turns both into improper fractions, 7/3 and 7/4, rewrites them over the least common denominator 12 as 28/12 and 21/12, and adds the tops to get 49/12, which is the mixed number 4 1/12 and the decimal 4.08(3).
Answers are exact for the numbers entered; only a very long repeating decimal is shortened, and it is marked when that happens. For schoolwork, check which form your teacher wants, since lowest terms, mixed numbers and decimals are all correct answers to the same sum.
Leave the whole box empty for a plain fraction, or the top and bottom empty for a whole number. Put a minus sign in front of the whole number, or of the top when there is no whole number. Up to 12 digits per box.
Answer in lowest terms
49/12
- Mixed number
- 4 1/12
- Decimal
- 4.08(3)
- As fractions: 7/3 and 7/4
- Least common denominator: 12
- Rewrite over 12: 28/12 and 21/12
- Add the numerators: 49/12
- Already in lowest terms: 49/12
Digits in parentheses repeat forever.
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About the Fraction Calculator
Every number here is kept as an exact whole-number top and bottom, so nothing is rounded until the decimal is written out. To add or subtract, the calculator finds the least common denominator, the smallest number both bottoms divide into, rewrites each fraction over it and then adds or subtracts the tops: adding 1/6 and 1/3 means adding 1/6 and 2/6. To multiply it multiplies the tops together and the bottoms together, and to divide it flips the second fraction and multiplies, so dividing 3/4 by 1/8 means multiplying 3/4 by 8/1, which gives 6. The last step puts the answer in lowest terms by dividing the top and bottom by their greatest common divisor, found with Euclid's algorithm. A mixed number such as 2 1/3 is read as two plus one third, and a minus sign in front of the whole number makes the whole mixed number negative. The decimal comes from exact long division. When the digits start repeating, the repeating block is shown in parentheses, so in 4.08(3) the final 3 repeats forever; a decimal whose repeat is very long is cut after a fixed number of places and marked with an ellipsis.
Frequently asked questions
How do you add fractions with different denominators?+
Find a number both denominators divide into, ideally the smallest one, rewrite each fraction over it by multiplying its top and bottom by the same amount, then add the tops and keep the bottom. For 1/6 plus 1/3 the common denominator is 6, so you add 1/6 and 2/6 to get 3/6, which reduces to 1/2. The calculator shows each of these steps.
How do you divide fractions?+
Turn the second fraction upside down and multiply. Dividing 3/4 by 1/8 is the same as multiplying 3/4 by 8/1, which gives 24/4 and simplifies to 6: there are six eighths in three quarters. Dividing by zero has no answer, so the calculator asks for a different second number instead.
How do I enter a mixed number or a negative fraction?+
Put the whole part in the left box and the fraction in the top and bottom boxes, so two and one third goes in as a whole part of two with one over three. Leave the whole box empty for a plain fraction, or leave the top and bottom empty for a whole number. For a negative number, put the minus sign in front of the whole part, or in front of the top when there is no whole part.
What do the parentheses in the decimal mean?+
They mark digits that repeat without end. Every fraction is either a decimal that stops or one that falls into a repeating pattern, and the calculator finds the pattern by long division. So in 4.08(3) the 3 after the 8 repeats forever, while a fraction like 1/2 simply shows 0.5.
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