Fraction Calculator: Add, Subtract, Multiply, Divide

Key facts

To add or subtract fractions, rewrite them over a common denominator first: 3/4 + 1/6 = 9/12 + 2/12 = 11/12.
To multiply, multiply the numerators and the denominators: 2/3 × 3/5 = 6/15 = 2/5.
To divide, multiply by the reciprocal of the second fraction: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8.
A fraction is in lowest terms when its numerator and denominator share no factor but 1, which their greatest common factor finds.

First fraction

Second fraction

1 1/2 + 2/3 =

2 1/6

1 1/2 + 2/3 = 2 1/6 (13/6), about 2.1667 as a decimal.

First1

Second

Sum2

Each whole is cut into 6 equal pieces, the common denominator.

As a fraction: 13/6
As a decimal: ≈ 2.166667
Repeating: 2.1(6)

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Worked example: 1 1/2 + 2/3How to add these fractions, step by step

Write the first number as an improper fraction: whole × denominator + numerator, over the same denominator.
1 1/2 = 1 × 2 + 1/2 = 3/2
Find a common denominator: the least common multiple of 2 and 3, which is their product because they share no factor = 6.
Rewrite each fraction over 6: multiply its top and bottom by the same number.
3 × 3/2 × 3 = 9/6, 2 × 2/3 × 2 = 4/6
Add the numerators.
9/6 + 4/6 = 9 + 4/6 = 13/6
As a mixed number: 13 ÷ 6 = 2 remainder 1.
13/6 = 2 1/6

Answer: 1 1/2 + 2/3 = 2 1/6 = 13/6.

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Frequently Asked Questions

How do I use the fraction calculator?

Type each fraction in its boxes: the numerator on top, the denominator underneath and, for a mixed number, the whole number to the left. Pick +, −, × or ÷ and the answer appears straight away, simplified, as a mixed number and as a decimal, with every step of the working below it.

Can it work with mixed numbers and negative fractions?

Yes. Put the whole number in the left box for a mixed number such as 2 1/3, and press ± to make a fraction negative. You can also type a decimal such as 0.75 in the whole-number box.

Are the answers exact?

Yes. The calculator keeps every number as an exact fraction of whole numbers, however large, and never rounds until it shows the decimal. 1/3 + 1/6 is exactly 1/2, not 0.49999.

Why do fractions need a common denominator to add, but not to multiply?

Adding counts pieces, and pieces can only be counted together when they are the same size, so both fractions are first cut into the same number of pieces. Multiplying takes a fraction of a fraction (a half of three quarters), which works with any piece sizes: multiply the tops and the bottoms.