$Rules and Definitions$

Reducing Fractions Through Factorization

Reducing fractions is another way of saying, "finding the lowest equivalent fraction." That's because you are normally trying to reduce a proper fraction to its simplest term.

Note: The term "reduce" refers to proper fractions (the numerator is smaller than the denominator). Whereas, the term "simplify" generally refers to improper fractions (the numerator is larger than the denominator).

When reducing a proper fraction, follow these steps:

Factor the numerator.

Factor the denominator.

Cancel-out fraction mixes that have a value of 1.

Re-write your answer as the reduced fraction.

Example:

To reduce 24/56 we factor the Numerator (24 = 2 x 2 x 2 x 3) and then factor the Denominator (56 = 2 x 2 x 2 x 7).

In this example all of the 2s are eliminated because there are an equal number of 2s in both the numerator and denominator. They cancel-out one-for-one. That's what we mean by a fraction mix that has the value of "1".

The correct answer for the example above is a reduced fraction that's equal to 3/7.

Here's another way to look at reducing 24/56.

You already know that 2/2 = 1, so...

is the same as which is equal to 1 x 1 x 1 x 3/7