Fractions are made up of two parts.

The top part is called the numerator and tells you how many pieces you've got.

The bottom part is called the denominator and tells you how many pieces make up the whole.

For example, if there are two pieces in the whole, each piece is one half.

That is, each piece represents 1/2.

If there are 8 pieces, each will be an eighth, or 1/8.

Equivalent fractions

When you divide the same whole into different numbers of pieces, you can write the same proportion in different ways.

For example, this whole is divided into 4 pieces, and 3 of them are shaded blue. In other words, we've shaded 3 quarters of the whole, or 3/4.

But if we divide the same whole into 8 pieces but still shade the same amount, we've now shaded 6 eighths of the whole, or 6/8.

This means that 3/4 is equivalent to 6/8.

If we divide the original whole into 12 pieces, we'll have shaded 9 pieces.

Therefore: 3/4 = 6/8 = 9/12

So if you were presented with the fraction 9/12, how would you know it was really the same proportion as 3/4?

All you need to do is divide the top and bottom of the fraction by the same number.

In this case, we know that 3 will divide evenly into both 9 and 12.

That is:

       9  ÷ 3 =  3 
      12 ÷ 3 =  4   

We can also run the calculation in reverse by multiplying both halves of the fraction by the same number.

That is:

       3  x 3 =  9 
       4  x 3 = 12