RATIO AND PROPORTION

Ratio Of Parts To Whole

Learn the reliable method for ratio of parts to whole, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

A part-to-part ratio must be converted before it can describe a fraction of the whole.

Picture itCompare each group in the same order
Bowls, fruit, scales and a measuring jug showing ratio and measurement in baking
2 · THE METHOD

Follow these steps

  1. Add all ratio parts to find the whole number of shares.
  2. Use the required part as the numerator.
  3. Simplify the resulting fraction if possible.
one share = total ÷ sum of ratio parts
3 · WORKED EXAMPLES

See the method in action

Example 1

The ratio of red to blue counters is 3:5. What fraction of all the counters are red?

  1. There are 3 + 5 = 8 total parts, of which 3 are red, so the fraction is 3/8.
Answer: 3/8
Example 2

Yellow and green beads are in the ratio 4:6, with 100 beads altogether. What percentage are yellow, and how many yellow beads are there?

  1. Yellow is 4/10 = 40%.
  2. Each ratio part represents 10 beads, so yellow beads = 4 × 10 = 40.
Answer: 40%; 40 beads
4 · ELEVENSPRINT TIP

A useful shortcut

Simplify the resulting fraction if possible.

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.