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Fraction calculator with steps

  

Exact fraction arithmetic. The answer is reduced to lowest terms.

Operation

3/4 + 5/6

19/12

Mixed number 1 7/12, decimal 1.583333

How we got this

  1. Common denominator: LCM(4, 6) = 12.
  2. Rewrite: 3/4 = 9/12 and 5/6 = 10/12.
  3. Add the tops: 9 + 10 = 19, so 19/12.
  4. 19/12 is already in lowest terms.

The steps teachers want to see

To add or subtract, the pieces must be the same size, so rewrite both fractions over a common denominator, then add the tops. To multiply, multiply straight across. To divide, multiply by the reciprocal. In every case, finish by dividing top and bottom by their greatest common divisor.

Ratios are fractions written another way; the ratio and proportion calculator simplifies them and solves for a missing value. A fraction times 100 is a percent, which the percentage calculator handles, and powers and roots of fractions are in square roots and exponents.

Sources

What this calculator does not account for

  • Mixed operations in one expression beyond the ones shown.
  • Irrational numbers, which cannot be written as an exact fraction.

How this is calculated

Formula: Fraction rules

a/b + c/d =(ad + bc)/bd; a/b × c/d =ac/bd; a/b ÷ c/d =ad/bc

What the symbols mean

  • LCMThe least common multiple of the bottoms, used as the common denominator.
  • GCDThe greatest common divisor, used to simplify.

Good to know

  • Using the LCM keeps the numbers small; any common multiple gives the same simplified answer.

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Worked examples

Each example is worked out by the same code as the calculator above.

3/4 + 5/6

LCM 12. 3/4 = 9/12, 5/6 = 10/12. 19/12 = 1 7/12 ≈ 1.5833.

2/3 × 9/10

18/30. GCD 6: 3/5 = 0.6.

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Questions

What is 3/4 + 5/6?

The LCM of 4 and 6 is 12: 9/12 + 10/12 = 19/12, or 1 7/12.

How do I divide fractions?

Flip the second fraction and multiply: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.

How do I enter a mixed number?

Convert it first: 2 1/3 is (2 × 3 + 1)/3 = 7/3.