Fraction calculator
Fractions and mixed numbers, with every step shown
Type two fractions such as 3/4 or 1 1/2, and choose what to do. The example adds 1/2 and 1/3.
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- As a mixed number
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- As a decimal
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Working, step by step
How fractions are worked out
A mixed number such as 1 1/2 is turned into a top-heavy fraction first: 1 × 2 + 1 = 3, so 1 1/2 is 3/2. A decimal such as 0.75 becomes 75/100, which simplifies to 3/4.
Adding and subtracting
The bottom numbers (denominators) must match before the tops can be added. The page uses the lowest common denominator, the smallest number both bottoms divide into. For 1/2 + 1/3 that is 6: 1/2 = 3/6 and 1/3 = 2/6, so the total is 5/6.
Multiplying
Multiply the tops together and the bottoms together: 2/3 × 3/4 = 6/12, which simplifies to 1/2.
Dividing
Turn the second fraction upside down and multiply: 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2. Dividing by zero has no answer, so the page refuses it.
Simplifying
Every answer is reduced to lowest terms by dividing the top and bottom by their greatest common factor: 6/12 becomes 1/2 because 6 divides both. The answer is also shown as a mixed number and as a decimal. If the decimal repeats forever, such as 5/6 = 0.8333…, the repeating digits are named.
Negative fractions
Put the minus sign at the front: −3/4, or −1 1/2 for minus one and a half.
Formula and sources
- Adding and subtracting with unlike denominators by equivalent fractions: Common Core 5.NF.A.1. Multiplying fractions: 5.NF.B.4. Dividing fractions: 6.NS.A.1.
- Lowest terms by the greatest common factor, found with Euclid's algorithm (Euclid, Elements, Book VII, Propositions 1 and 2).
- Checked in test_maths.js: 1/2 + 1/3 = 5/6; 3/4 − 1/6 = 7/12; 2/3 × 3/4 = 1/2; 1/2 ÷ 1/4 = 2; 1 1/2 + 2 2/3 = 4 1/6; 6/8 simplifies to 3/4; 5/6 = 0.8(3).