FRACTIONS, DECIMALS AND PERCENTAGES

Ordering Fractions

Learn the reliable method for ordering 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

Four pupils completed these fractions of the same activity: 8/9, 6/17, 8/15, 2/17. Which option orders their progress from least to greatest?

  1. Compare using equivalent fractions or cross-products: 2/17, 6/17, 8/15, 8/9.
Answer: 2/17, 6/17, 8/15, 8/9
Example 2

Order 3/10, 1/3, 7/20, 2/5, 5/8 from least to greatest. Then subtract the middle fraction from the greatest fraction. What is the exact difference?

  1. Comparing with common denominators or cross-products gives 3/10 < 1/3 < 7/20 < 2/5 < 5/8.
  2. The greatest is 5/8 and the middle value is 7/20; subtracting gives 11/40.
Answer: 11/40
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.