Fraction Calculator

Add, subtract, multiply or divide two fractions — with the answer in lowest terms, as a mixed number and as a decimal, and every step shown.

Your details

Answer

5/6

In lowest terms.

As a mixed number
5/6
As a decimal
0.833333

Visual breakdown

  • 1/2
  • 1/3
  • = 5/6

  1. 1

    Find the lowest common denominator

    LCD = lcm(b, d)

    = lcm(2, 3)

    = 6

  2. 2

    Rewrite both fractions over it

    a/b = (a × LCD ÷ b)/LCD

    = 1/2 = 3/6, 1/3 = 2/6

    = 3/6 + 2/6

  3. 3

    Add the numerators

    (a′ + c′)/LCD

    = (3 + 2)/6

    = 5/6

  4. 4

    Reduce to lowest terms

    divide top and bottom by their greatest common divisor

    = gcd(5, 6) = 1

    = 5/6

  5. 5

    Write it as a decimal

    numerator ÷ denominator

    = 5 ÷ 6

    = 0.833333

What this calculates

Enter two fractions and choose to add, subtract, multiply or divide them, and this gives the answer in lowest terms, as a mixed number when it is more than one whole, and as a decimal — with each step of the working shown. Negative fractions work too.

The formula

Add and subtract

a/b ± c/d = (a × L÷b ± c × L÷d) / L, where L = lcm(b, d)

Multiply

a/b × c/d = (a × c) / (b × d)

Divide

a/b ÷ c/d = a/b × d/c

Lowest terms

divide the numerator and denominator by their greatest common divisor

L is the lowest common denominator — the smallest number both denominators divide into. The sign of a negative answer is carried on the numerator: −1/12, not 1/−12.

Worked example

Dividing works differently: 3/4 ÷ 1/2 flips the second fraction to 2/1, and 3/4 × 2/1 = 6/4 = 3/2, or 1 1/2.

When to use it, and the mistakes to avoid

Use it to check homework, to scale a recipe or a measurement, and to turn a fraction into a decimal or a mixed number.

The mistakes that cost the most:

  • Adding the tops and the bottoms. 1/2 + 1/3 is not 2/5. Put both over a common denominator first: 3/6 + 2/6 = 5/6.
  • Forgetting to flip when dividing. 3/4 ÷ 1/2 is not 3/8; flip the second fraction and multiply to get 3/2.
  • Not reducing the answer. 6/12 and 1/2 are the same number; lowest terms is the form anyone checking will expect.
  • Losing a minus sign. 3/4 − 5/6 is −1/12, a negative answer, because 5/6 is the larger fraction.
  • Using a zero denominator. It has no value at all, so the calculator refuses it.

FAQ

How do you add fractions with different denominators?

Rewrite both over a common denominator - the lowest common multiple of the two - then add the numerators. For 1/2 + 1/3 the lowest common denominator is 6: 1/2 is 3/6 and 1/3 is 2/6, so the sum is 5/6.

How do you multiply fractions?

Multiply the numerators together and the denominators together, then reduce. 2/3 × 3/4 = 6/12, which is 1/2 in lowest terms. No common denominator is needed.

How do you divide fractions?

Flip the second fraction and multiply. 3/4 ÷ 1/2 becomes 3/4 × 2/1 = 6/4, which is 3/2 - one and a half.

How do you simplify a fraction?

Divide the numerator and the denominator by their greatest common divisor. 15/30 has a greatest common divisor of 15, so it is 1/2 in lowest terms. The calculator reduces every answer this way.

What is a mixed number?

A whole number and a fraction together, for a value of more than one: 3/2 is 1 1/2, and 7/3 is 2 1/3. Divide the numerator by the denominator; the whole part is the quotient and the remainder goes over the denominator.

Why can't a denominator be zero?

Because the denominator is how many equal parts the whole is split into, and nothing can be split into zero parts - it would mean dividing by zero. For the same reason you cannot divide by a fraction worth zero.

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