MathQuick

Fraction Calculator

Type fractions like 3/4, mixed numbers like 1 1/2 (whole number, space, fraction), whole numbers or decimals. The answer comes back simplified, as a mixed number when it is bigger than 1, with every step written out the way a teacher expects to see it.

Answer

11/12

≈ 0.916667 as a decimal

Step by step

  1. Find a common denominator: the least common multiple of 3 and 4 is 12.
  2. Rewrite each fraction over 12: 2/3 = 8/12 and 1/4 = 3/12.
  3. Add the numerators and keep the denominator: 8 + 3 = 11, giving 11/12.
  4. 11/12 is already in simplest form (the top and bottom share no factor other than 1).

Answer: 11/12

Still stuck? Ask the tutor about these steps
0/800

How it works

Add / subtracta/b ± c/d = (a·d ± c·b) / (b·d), then simplify
Multiplya/b × c/d = (a·c) / (b·d)
Dividea/b ÷ c/d = a/b × d/c

Adding and subtracting need a common denominator: you can only add pieces that are the same size. The calculator uses the least common multiple so the numbers stay small.

Multiplying is the easy one — top times top, bottom times bottom.

Dividing: keep the first fraction, change ÷ to ×, flip the second fraction (“keep, change, flip”), then multiply.

Mixed numbers are turned into improper fractions first: 2 1/3 = (2 × 3 + 1)/3 = 7/3.

Want to see why it works? How to add fractions — see the common denominator happen.

Worked example

Work out 2/3 + 1/4.

  1. LCM of 3 and 4 is 12
  2. 2/3 = 8/12, 1/4 = 3/12
  3. 8/12 + 3/12 = 11/12

Frequently asked questions

How do I enter a mixed number?

Type the whole number, a space, then the fraction: 2 1/2 for two and a half. Negative mixed numbers work too: -1 3/4.

Why does the calculator use the least common denominator?

Any common denominator works, but the least one keeps the numbers small and means less simplifying at the end.

How do you divide fractions?

Multiply the first fraction by the reciprocal of the second. 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 1 1/2.

Does it simplify the answer?

Yes. Every answer is reduced to lowest terms by dividing the top and bottom by their greatest common factor, and improper fractions are also shown as mixed numbers.