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Adding Fractions Calculator

The adding fractions calculator rewrites 3/4 and 5/6 over their least common denominator, 12, adds the numerators to get 19/12, and gives the mixed number 1 7/12.

When rewriting over a denominator, the denominator to rewrite the first fraction over.

Answer19/12

As a mixed number
1 7/12
As a decimal The digits in brackets repeat forever. A decimal cannot write this fraction exactly, which is why the fraction is the better answer.
1.58(3)
The problem
3/4 + 5/6 = 19/12
Common denominator The least common multiple of 4 and 6. Multiplying the denominators together would give 24, which also works but needs reducing afterward.
12
Rewritten over it
9/12 + 10/12 = 19/12
Reduced
already in lowest terms
As a percentage
158.3333%
Comparison Compared by cross-multiplying rather than by converting to decimals, so the answer is exact even when the decimals are not.
3/4 is smaller than 5/6
  • Every answer is exact and in lowest terms. No step converts to a decimal, which is what lets 1/3 + 1/6 come out as exactly 1/2.
  • A mixed number's sign applies to the whole quantity: -2 1/3 means -(2 + 1/3), which is -7/3.

How the Fraction Calculator works

Fractions can only be added when they count pieces of the same size, which means the same denominator. Adding fractions with different denominators is a matter of making them the same first.

Same denominator. Add the numerators and keep the denominator: 1/8 + 3/8 = 4/8, which simplifies to 1/2. Adding the denominators as well (to get 4/16) is the classic mistake; the pieces are still eighths.

Different denominators. Take 3/4 + 5/6.

1. Find the least common denominator, the smallest number both denominators divide into. For 4 and 6 it is 12.

2. Rewrite each fraction over 12. 3/4 = 9/12 (times 3 top and bottom) and 5/6 = 10/12 (times 2).

3. Add the numerators: 9/12 + 10/12 = 19/12.

4. Simplify if possible. 19 and 12 share no factor, so 19/12 is already in lowest terms, which is 1 7/12 as a mixed number.

Multiplying the denominators together (4 x 6 = 24) also gives a common denominator, just a larger one: 18/24 + 20/24 = 38/24, which then has to be reduced to 19/12. The least common denominator saves that last step. When the two denominators share no factor, as 3 and 4 do not, their product is the least common denominator anyway.

More than two fractions. Add two at a time, or find one denominator that all of them divide into. For 1/2 + 1/3 + 1/4 that is 12: 6/12 + 4/12 + 3/12 = 13/12.

Why not use decimals? 1/3 + 1/6 is exactly 1/2, but in decimals it is 0.333... + 0.1666..., and a computer working in floating point gets 0.49999999999999994. Every step here is done in whole numbers, so the answer is exact.

Fraction Calculator FAQ

How do you add fractions with different denominators?

Rewrite both over a common denominator, then add the numerators. 3/4 + 5/6 = 9/12 + 10/12 = 19/12, or 1 7/12.

Do you add the denominators when adding fractions?

No. The denominator says the size of the pieces, and adding does not change it. 1/8 + 3/8 = 4/8, not 4/16.

What is the least common denominator of 4 and 6?

12, the smallest number both 4 and 6 divide into. Using 24, their product, also works but leaves a fraction to reduce at the end.

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