 close   ## Working with fractions  Audio for slide 1 (mp3 |6|KB)
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.  Audio for slide 2 (mp3 |6|KB)
For example, if there are two pieces in the whole, each piece is one half.

That is, each piece represents 1/2.  Audio for slide 3 (mp3 |6|KB)
If there are 8 pieces, each will be an eighth, or 1/8.  Audio for slide 4 (mp3 |6|KB)

### 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.  Audio for slide 5 (mp3 |6|KB)
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.  Audio for slide 6 (mp3 |6|KB)
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?  Audio for slide 7 (mp3 |6|KB)
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  Audio for slide 8 (mp3 |6|KB)
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  ### Learning activity

Audio 9 (mp3 |6|KB)

Here are some fraction exercises. Enter your answers in the cell beside each question. When you've finished them all, click 'Check your answers' to see how you went. What are they?  