One difference between fractions and whole numbers is this. If two whole numbers look different, then you can be sure they are different. With fractions, though, it's more complicated; the fraction 14 ⁄ 21 is just another way of saying 2 ⁄ 3. Reducing a fraction means finding the simplest way to write it.

The basic idea is to look for common factors of the numerator (the first number) and the denominator (the second number). In the case of 14 ⁄ 21, say, 7 goes evenly into both 14 and 21. So, we can divide both 14 and 21 by 7, which gives us 2 ⁄ 3. Remember that you always divide the numerator and the denominator by the same number.

Here are some things to keep in mind:

• The number 1 goes evenly into everything. So we can always divide both the numerator and denominator by 1. That won't change anything, though, so why bother?
• You know you're done when the only number that goes evenly into both the numerator and denominator is 1. So, if your teacher asks you to reduce 2 ⁄ 3, you don't have to do any work; the answer is just 2 ⁄ 3 again.
• A whole number is the same thing as a fraction whose denominator is 1. So, if you have to reduce 9 ⁄ 3, you divide the numerator and denominator each by 3, getting 3 ⁄ 1, which you then write as 3. Similarly, if you're asked to reduce 3, just write 3.
• If there's a negative sign in front of a fraction you're asked to reduce, just leave it there.