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Fraction Calculator

Math

Choose an operation and enter one or two fractions, with a whole number part for mixed numbers such as 2 1/3. You get the answer in lowest terms, as a mixed number and as a decimal, with every step shown.

Operation

Only for mixed numbers like 2 1/3; otherwise leave 0. A minus sign goes here, not in the numerator.

The top number. Without a whole number part it can be negative.

The bottom number, at least 1.

Only for mixed numbers; otherwise leave 0.

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Result: Answer in lowest terms

5/6

1/2 + 1/3 = 5/6. As a mixed number: 5/6; as a decimal: 0.833333.

  • As a decimal (rounded to 6 places): 0.833333

Step by step

1/2 + 1/3 = 3/6 + 2/6 = 5/6

  1. Write each number as a fraction without a whole part; mixed numbers become improper fractions: 1/2 and 1/3.
  2. Common denominator: the least common multiple of 2 and 3 is 6.
  3. Rewrite both fractions with that denominator: 1/2 becomes 3/6, 1/3 becomes 2/6.
  4. Add the numerators and keep the denominator: 3/6 + 2/6 = 5/6.
  5. Simplify: the greatest common factor of the numerator and the denominator is 1 (if it is 1, the fraction is already in lowest terms). Reduced, it is 5/6.
  6. As a mixed number the result is 5/6 (a proper fraction or a whole number stays as it is). As a decimal it is 0.833333.

Formula

a/b + c/d = (a × (n ÷ b) + c × (n ÷ d)) / n
a, c
numerators
b, d
denominators
n
least common denominator (least common multiple of b and d)

How it works

To add or subtract fractions, they need a common denominator. The calculator uses the least common denominator, the least common multiple of the two denominators. For 1/4 + 1/6 that is 12: 1/4 becomes 3/12 and 1/6 becomes 2/12, so the sum is 5/12. Then the numerators are added or subtracted and the denominator stays the same.

To multiply, multiply the numerators together and the denominators together: 2/3 × 3/4 = 6/12 = 1/2. To divide, flip the second fraction (its reciprocal) and multiply: 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9. Mixed numbers are first turned into improper fractions, so 2 1/3 becomes 7/3 because 2 × 3 + 1 = 7.

Every answer is reduced to lowest terms by dividing the numerator and the denominator by their greatest common factor. An answer larger than 1 is also shown as a mixed number (23/6 = 3 5/6), and every answer as a decimal. The math is exact with whole numbers, so even large fractions come out right. For percentages of a number, use the percentage calculator.

The formula

A mixed number w a/b is the improper fraction (w × b + a) / b. With a minus sign the whole mixed number is negative: -2 1/3 is -(2 + 1/3) = -7/3, which is why the sign goes in the whole number field.

Any common denominator works, for example b × d, but the least one keeps the numbers small. Dividing by a fraction equal to zero is not possible, so the calculator stops with a message.

Example

What is 2 1/3 + 1 1/2?

  1. Turn the mixed numbers into fractions: 2 1/3 is 7/3 and 1 1/2 is 3/2.
  2. Common denominator: the least common multiple of 3 and 2 is 6.
  3. Rewrite: 7/3 becomes 14/6 and 3/2 becomes 9/6.
  4. Add: 14/6 + 9/6 = 23/6. The greatest common factor is 1, so nothing to reduce.
  5. Answer: 23/6, which is 3 5/6 as a mixed number and 3.833333 as a decimal.

2 1/3 + 1 1/2 = 23/6. As a mixed number: 3 5/6; as a decimal: 3.833333.

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Frequently asked questions

How do you add fractions with different denominators?

Find a common denominator, rewrite both fractions with it, then add the numerators. 2/3 + 1/4: the least common denominator is 12, so 8/12 + 3/12 = 11/12. Reduce the answer if the numerator and denominator share a factor.

How do you divide fractions?

Keep the first fraction, change division to multiplication and flip the second fraction. 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2, or 1 1/2. People remember it as keep, change, flip.

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

Multiply the whole number by the denominator and add the numerator; the denominator stays. 3 2/5 becomes (3 × 5 + 2) / 5 = 17/5. The other way, divide: 17 ÷ 5 = 3 remainder 2, so 3 2/5.

How do I simplify a fraction?

Divide the numerator and the denominator by their greatest common factor. For 18/24 that factor is 6, so 18/24 = 3/4. If the greatest common factor is 1, the fraction is already in lowest terms.

How do I enter a negative fraction?

For a mixed number, put the minus sign on the whole number: -2 1/3 is entered as -2, 1 and 3. For a plain fraction, leave the whole number at 0 and make the numerator negative, such as -3/4.

How do I convert a decimal to a fraction?

Write the decimal over a power of ten and reduce. 0.375 is 375/1000; the greatest common factor is 125, so 0.375 = 3/8. In the same way 0.75 = 75/100 = 3/4, 0.2 = 1/5 and 1.25 = 1 1/4. A repeating decimal such as 0.333... stands for 1/3. Enter the fraction in the calculator to add it to or multiply it with another one.

How do I add three fractions?

Do it in two steps: add the first two, then add the third to the result. 1/2 + 1/3 + 1/4: 1/2 + 1/3 = 5/6, then 5/6 + 1/4 = 10/12 + 3/12 = 13/12, which is 1 1/12. Enter the first answer as the first fraction and the third fraction as the second one.

Last updated: Responsible editor: Jared Alan
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