Simplifying Fractions

When a fraction's numerator and/or denominator can be divided by other factors other than the number 1 and itself, the fraction may still be simplified. This type of numbers are known as composite numbers.

Examples of composite numbers are 4, 6, 8, 9, 12, etc.

For instance,

^{2}/

_{4},

^{5}/

_{15} and

^{4}/

_{20} can be simplified into

^{1}/

_{2},

^{1}/

_{3} and

^{1}/

_{5}, respectively.

An easy way to simplify a fraction is to find a common factor that would divide both numerator and denominator. Then, divide both numbers by the common factor. Do this again until the fraction can no longer be simplified.

Here's an example:

### ^{8}/_{40} > ^{4}/_{20} > ^{2}/_{10} > ^{1}/_{5}

In the example above, both 8 and 40 were divided by 2, so we came up with 4 and 20, which was again divided by 2 to come up with 2 and 10. Then, 2 and 10 were each divided into 2 again, so we ended up with 1 and 5, which can no longer be simplified.

Another method of simplifying fractions is finding the greatest common factor (GCF) and dividing both numerator and denominator by that number. The GCF is the largest number or factor by which both numerator and denominator can be evenly divided.

Let's use this method on our earlier example. The greatest common factor of the numbers 8 and 40 of

^{8}/_{40} is the number

**8**. Both numbers can be evenly divided by

**8**, and the resulting fraction is its simplest form.

8 divided by 8 = 1

40 divded by 8 = 5

This gives us

^{8}/_{40} =

^{1}/_{5}.