FRACTIONS, DECIMALS AND PERCENTAGES

Percentage Of An Amount

Learn the reliable method for percentage of an amount, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

A percentage is a number of parts out of 100. Fractions, decimals and percentages are different ways to show the same proportion.

Picture itCount equal parts of one whole
Stationery and UK money arranged as a real-life shopping problem
2 · THE METHOD

Follow these steps

  1. Find 10%, 1% or another useful unit percentage.
  2. Scale that value to the percentage required.
  3. Check whether the answer should be smaller or larger than the starting amount.
percentage = amount ÷ 100 × rate
3 · WORKED EXAMPLES

See the method in action

Example 1

Asha scores 72 out of 80; Ben scores 16 out of 40. By how many percentage points is Asha's score higher?

  1. Convert 72/80 and 16/40 to percentages.
  2. Subtract the second percentage from the first.
  3. Therefore the answer is 50 percentage points.
Answer: 50 percentage points
Example 2

At a sports event, 50% of 160 juniors and 20% of 100 seniors choose athletics. How many more juniors than seniors choose athletics?

  1. Find 50% of 160.
  2. Find 20% of 100, then compare the numbers.
  3. Therefore the answer is 60 people.
Answer: 60 people
4 · ELEVENSPRINT TIP

A useful shortcut

For reverse percentages, divide by the percentage represented—not the percentage change.

5 · COMMON MISTAKES

Watch out for these

Using the final value as 100%

In a reverse problem, the final value represents the percentage left.

6 · TRY IT YOURSELF

Three fresh questions

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