Understanding Percentages

Understanding the concept

Percentages describe parts of a whole using 100 as the reference. The symbol % means “per hundred”. For example, 25% means 25 out of 100, which is one quarter.

This lesson uses simple, fixed examples to explain the method. Identify the quantities, choose the correct formula, and check that the units in your answer make sense.

Percentage of an amount

Percentage amount = total × percentage ÷ 100. To find what percentage one amount is of another, divide the part by the total and multiply by 100.

Write down the original values before substituting numbers. Keep full precision during the calculation and round only when presenting the final result.

Worked example

Question: What is 18% of $250?

1. Write 18% as 0.18.
2. Multiply 250 × 0.18.
3. The result is $45.

Check the answer against the original question. An answer should include the appropriate unit or percentage where relevant.

Key points to remember

• 25% = 25/100 = 0.25.
• 50% is half; 10% is one tenth.
• A percentage greater than 100% can describe a quantity larger than the original whole.

Common mistakes

Mixing up “18% of 250” with “250 as a percentage of 18”; the starting quantity matters.

To avoid this, label each number, identify the starting amount and use a quick estimate to see whether the final answer is reasonable.

Try it yourself

What is 12% of 150?

Percentage conversions and quick checks

Use this table as a quick reference. Check which quantities and units each method requires before calculating.

More worked examples

Work through each calculation and notice how the method changes with the question.

Example 1: Find 15% of $80

Method: 80 × 0.15 = 12.

Example 2: What percentage is 18 of 60?

Method: 18 ÷ 60 × 100 = 30.

Example 3: A class has 12 students out of 30 wearing hats. What percentage?

Method: 12 ÷ 30 × 100 = 40.

Using this in everyday life

Use percentages for marks, discounts, surveys and comparing portions. Always identify the whole: 20 out of 50 is 40%, but 20 out of 100 is 20%.

Before you begin: Identify what the question asks, write down the given information, use matching units, then estimate the result to catch mistakes.

Extra practice questions

Try these independently before expanding the answer. Show your working, not just the final number.