FRACTIONS, DECIMALS AND PERCENTAGES

Comparing Fractions

Learn the reliable method for comparing fractions, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

Compare fractions by making the part sizes equal.

Picture itCount equal parts of one whole
Bowls, fruit, scales and a measuring jug showing ratio and measurement in baking
2 · THE METHOD

Follow these steps

  1. Find a common denominator or convert each fraction to a decimal.
  2. Compare the resulting values.
  3. Keep each original fraction attached to its converted value when ordering.
3 · WORKED EXAMPLES

See the method in action

Example 1

Five cards show the fraction of a design shaded: 2/5, 8/9, 2/17, 2/11, 2/3. Which fraction is the second least?

  1. Compare the fractions using common denominators or cross-products.
  2. In order they are 2/17, 2/11, 2/5, 2/3, 8/9, so the second least is 2/11.
Answer: 2/11
Example 2

Five cards show fractions of the same tank filled: 1/5, 3/10, 2/3, 13/18, 13/16. Find the greatest and least, then calculate their exact difference.

  1. In increasing order the fractions are 1/5, 3/10, 2/3, 13/18, 13/16.
  2. Therefore the required difference is 13/16 − 1/5 = 49/80.
Answer: 49/80
4 · ELEVENSPRINT TIP

A useful shortcut

Keep each original fraction attached to its converted value when ordering.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.