### EQUIVALENT FRACTIONS

__Understanding equivalent fractions__

Here I will explain equivalent fractions, so you'll know the importance of
understanding equivalent fractions.
Equivalent fractions don't look the same. They have a different
numerator and a different denominator. But they value is the same.
A few big pieces of a cake can be the same as many small pieces.
Why are they the same? Because when you multiply or divide
both the top and bottom by the same number, the fraction
keeps its value.
You only multiply or divide, never add or subtract, to get an equivalent fraction.

__Check equivalent fractions__

A simple way to check for **equivalent fractions** is
**cross-multiply**, which means multiple the numerator
of one fraction by the denominator of the other fraction.
Then do the same multiply in reverse. Now compare the
answers to check if they are equal. If they are equal, then you have
equivalent fractions.
So you can see 1/2 is not an equivalent fraction of 2/3.
If you remember the cross-multiply method, you can always
verify equivalent fractions.

__Simplifying fractions__

Simplifying or reducing fractions means to make the fraction
as simple as possible. Why say 4/8 when you really mean
1/2. Simplifying fractions is easy now you know everything about
equivalent fractions.
Try finding an equivalent fraction by dividing both the top and
bottom of the fraction until you can't go any further.
You use the knowledge of equivalent fractions to simplify fractions.
So you look for the **greatest common factor**.

__Adding and subtracting fractions__

Before you can add or subtract fractions you have to make
sure that the bottom numbers (the denominators) are the same.
Use your knowledge about equivalent fractions to change one or
both fractions so they both have the same denominator.

__Common Denominator__

What is a Common Denominator?
Common Denominator means that the denominators in two
(or more) fractions are common. They are the same.
Before you can add or subtract fractions, the fractions need to have a common denominator.
Multiply both parts of each fraction by the denominator of the other.
So 1/3 + 2/5 give you 5/15 + 6/15 = 11/15.
This always works, but you will often need to simplify the fraction afterwards.

__Least Common Denominator__

The Least Common Denominator is the Least Common Multiple of the denominators.
List the multiples of both denominator.
The first, smallest number that is the same is the Least Common Denominator.
So for 1/3 + 2/6 you do'nt use 18 but 6 as the common denominator.
That give you 2/6 + 2/6 = 4/6.