Everyday maths 1 (Wales)
Everyday maths 1 (Wales)

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Everyday maths 1 (Wales)

3.2 Drawing fractions

Example: Drawing the fractions

If you need to compare one fraction with another, it can be useful to draw the fractional parts.

Look at the mixed numbers below. (A mixed number combines a whole number and a fraction.) Say you wanted to put these amounts in order of size, with the smallest first:

2 one divided by two, 3 one divided by four, 1 one divided by three

Method

To answer this you could look at the whole numbers first and then the fractional parts. If you were to draw these, they could look like this:

Described image
Figure 16 Drawing the fractions

So the correct order would be:

1 one divided by three, 2 one divided by two, 3 one divided by four

Use the example above to help you with the following activity. Remember to check your answers once you have completed the questions.

Activity 20: Putting fractions in order

  1. Put these fractions in order of size, smallest first:
  • 5 one divided by four, 6 one divided by five, 2 one divided by two
  1. Put these fractions in order of size, smallest first:
  • 2 two divided by five, 1 nine divided by 10, 2 one divided by two

Answer

  1. The correct order would be:
  • 2 one divided by two, 5 one divided by four, 6 one divided by five
  • In this case, even though one divided by two is bigger than one divided by four and one divided by four is bigger than one divided by five, you need to look at the whole numbers first and then the fractions. The diagram illustrates this more clearly:
Described image
Figure 17 Drawing the fractions
  1. The correct order would be:
  • 1 nine divided by 10, 2 two divided by five, 2 one divided by two
  • Looking at the whole numbers, 1 nine divided by 10 would be the smallest because the other two mixed numbers are both greater than 2. To see which is bigger out of 2 two divided by five or 2 one divided by two, you need to compare the fraction part. Which is bigger: two divided by five or one divided by two?
  • To work this out, you could draw images as above, or you could use the method we looked at earlier where you change to equivalent fractions – the bottom numbers of the fractions are 5 and 2, and the lowest common multiple of 5 and 2 is 10:
  • 5 × 2 = 10
  • 2 × 5 = 10
  • Whatever you do to the bottom, do to the top:
  • If you mulitiply the top and bottom numbers in two divided by five by 2, you make four divided by 10.
  • If you mulitiply the top and bottom numbers in one divided by two by 5, you make five divided by 10.
  • four divided by 10 (two divided by five) is smaller than five divided by 10 (one divided by two), so 2two divided by five is smaller than 2one divided by two.
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