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CALCULATOR · SHOWS THE WORKING

Fraction calculator

Add, subtract, multiply, divide and simplify fractions and mixed numbers. Every step is written out.

Add, subtract, multiply or divide fractions

Try:

1/2 + 1/3 = 5/6

  • Decimal: ≈ 0.833333

The working

  1. Find a common denominator. The lowest common multiple of 2 and 3 is 6.
  2. Rewrite both fractions over 6: 1/2 = 3/6 and 1/3 = 2/6.
  3. Add the numerators: 3 + 2 = 5. That gives 5/6.
  4. 5/6 is already in its simplest form: 5 and 6 share no factor larger than 1.

Simplify a fraction

Try:

18/24 = 3/4

  • Decimal: 0.75

The working

  1. Simplify by dividing the top and bottom by 6, the largest number that divides both: 18 ÷ 6 = 3 and 24 ÷ 6 = 4. So 18/24 = 3/4.

How it works

How to type fractions

Type a fraction with a slash, as in 3/4. For a mixed number, put a space between the whole number and the fraction, as in 1 1/2. Whole numbers and decimals such as 5 or 0.75 work too, and a minus sign in front makes any of them negative.

Adding and subtracting need a common denominator

You can only add or subtract fractions that are cut into the same size pieces. For 1/2 + 1/3, the lowest common multiple of 2 and 3 is 6, so the fractions become 3/6 and 2/6, and together they make 5/6. The calculator always uses the lowest common denominator, which keeps the numbers small.

Multiplying and dividing do not

To multiply, multiply the tops and multiply the bottoms. To divide, turn the second fraction upside down and multiply. 5/8 ÷ 3/4 becomes 5/8 × 4/3, which is 20/24, or 5/6 once simplified.

Simplifying

A fraction is in its simplest form when the top and bottom share no factor larger than 1. Divide both by their greatest common factor: 18/24 becomes 3/4 after dividing by 6. Answers larger than 1 are also shown as mixed numbers and as decimals.

Worked examples

Add 2/3 and 3/4

2/3 + 3/4 = 17/12

  • Mixed number: 1 5/12
  • Decimal: ≈ 1.416667
  1. Find a common denominator. The lowest common multiple of 3 and 4 is 12.
  2. Rewrite both fractions over 12: 2/3 = 8/12 and 3/4 = 9/12.
  3. Add the numerators: 8 + 9 = 17. That gives 17/12.
  4. 17/12 is already in its simplest form: 17 and 12 share no factor larger than 1.
  5. As a mixed number: 12 goes into 17 once with 5 left over, so 17/12 = 1 5/12.

Subtract 1 3/4 from 3 1/2

3 1/2 − 1 3/4 = 7/4

  • Mixed number: 1 3/4
  • Decimal: 1.75
  1. Turn the mixed number into an improper fraction: 3 1/2 = (3 × 2 + 1)/2 = 7/2.
  2. Turn the mixed number into an improper fraction: 1 3/4 = (1 × 4 + 3)/4 = 7/4.
  3. Find a common denominator. The lowest common multiple of 2 and 4 is 4.
  4. Rewrite both fractions over 4: 7/2 = 14/4 and 7/4 = 7/4.
  5. Subtract the numerators: 14 − 7 = 7. That gives 7/4.
  6. 7/4 is already in its simplest form: 7 and 4 share no factor larger than 1.
  7. As a mixed number: 4 goes into 7 once with 3 left over, so 7/4 = 1 3/4.

Divide 5/8 by 3/4

5/8 ÷ 3/4 = 5/6

  • Decimal: ≈ 0.833333
  1. Dividing by a fraction is the same as multiplying by it turned upside down: 5/8 ÷ 3/4 becomes 5/8 × 4/3.
  2. Multiply the tops: 5 × 4 = 20. Multiply the bottoms: 8 × 3 = 24. That gives 20/24.
  3. Simplify by dividing the top and bottom by 4, the largest number that divides both: 20 ÷ 4 = 5 and 24 ÷ 4 = 6. So 20/24 = 5/6.

Simplify 42/56

42/56 = 3/4

  • Decimal: 0.75
  1. Simplify by dividing the top and bottom by 14, the largest number that divides both: 42 ÷ 14 = 3 and 56 ÷ 14 = 4. So 42/56 = 3/4.

Common questions

How do you add fractions with different denominators?

Rewrite both fractions over a common denominator, then add the tops. For 1/4 + 1/6 the common denominator is 12, giving 3/12 + 2/12 = 5/12.

How do you turn an improper fraction into a mixed number?

Divide the top by the bottom. The whole-number part of the answer is the whole number, and the remainder goes over the original bottom number. 7/4 is 1 with 3 left over, so it is 1 3/4.

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