Why do I need a common denominator?

You can't add 'apples' to 'oranges'. A denominator tells you the size of the slice. To add specific amounts, the slices must be the same size. 1/2 + 1/3 needs both to become /6 slices to be countable.

How do I divide fractions?

Use the 'Keep, Change, Flip' rule. Keep the first fraction, Change division to multiplication, and Flip the second fraction (find the reciprocal). Then multiply straight across.

What is a mixed number?

A mixed number combines a whole integer and a fraction, like 1 1/2. It is often easier to convert them to 'improper fractions' (like 3/2) before doing math with them.

Conquering the Fraction: A Student's Guide

Fractions are the most hated topic in elementary math. But once you know the secret of the "LCD," they become easy.

Check Your Work

Input your fractions to see the step-by-step solution.

Fraction Calculator

Step 1: The Golden Rule of Addition

The denominators (bottom numbers) MUST be the same.

Example: 1/4 + 1/2
You cannot add 4 and 2.
Change 1/2 into 2/4.
Now: 1/4 + 2/4 = 3/4.

Finding the LCD (Least Common Denominator)

If you have 1/3 + 1/5, look at the bottom numbers: 3 and 5.
Multiples of 3: 3, 6, 9, 12, 15...
Multiples of 5: 5, 10, 15...
The first match is 15. That is your LCD.

Multiplying is Easier!

You don't need a common denominator to multiply. Just multiply the tops (numerators) and multiply the bottoms (denominators).

2/3 x 4/5 = (2x4) / (3x5) = 8/15

Simplifying

The final step is to make the numbers as small as possible. If your answer is 4/8, realize that both divide by 4. 4/4 = 1. 8/4 = 2. The simplified answer is 1/2.