Fractions, decimals & percentages
Understanding Percentages: Fractions, Decimals & Percentages
Year 5 · Year 6
- ✓By the end of this lesson students will be able to understand that 'per cent' means 'out of 100'.
- ✓By the end of this lesson students will be able to recognise and write percentages as fractions with a denominator of 100, and as decimals.
- ✓By the end of this lesson students will be able to recall common fraction, decimal, and percentage equivalences.
- ✓By the end of this lesson students will be able to calculate simple percentages of amounts, such as 10%, 25%, 50%, and 75%.
Key concepts
A percentage is a way of expressing a number as a fraction of 100. The word 'per cent' comes from the Latin 'per centum', meaning 'out of 100'. We use the symbol '%' to show a percentage. For example, 50% means 50 out of 100. Imagine a grid of 100 squares; if 50 of them are coloured in, then 50% of the grid is coloured.
Fractions, decimals, and percentages are all different ways to represent parts of a whole. They can be converted into each other. For example, 1/2, 0.5, and 50% all represent the same amount – half of something. To convert a fraction to a percentage, you can make its denominator 100. To convert a decimal to a percentage, you multiply by 100. To convert a percentage to a decimal, you divide by 100.
To find a percentage of an amount, you can use different methods. One common method is to convert the percentage to a fraction or a decimal first. For example, to find 50% of an amount, you can find 1/2 of that amount. To find 10% of an amount, you can find 1/10 of that amount (divide by 10). To find 1% of an amount, you can find 1/100 of that amount (divide by 100). You can also find 1% and then multiply by the percentage you need.
Key facts to remember
- 1The '%' symbol means 'per cent', which literally means 'out of 100'.
- 2100% represents the whole amount.
- 3To convert a percentage to a decimal, divide by 100 (e.g., 75% = 0.75).
- 4To convert a decimal to a percentage, multiply by 100 (e.g., 0.25 = 25%).
- 5To find 10% of an amount, divide the amount by 10.
- 6To find 1% of an amount, divide the amount by 100.
- 7Common equivalences: 1/2 = 0.5 = 50%; 1/4 = 0.25 = 25%; 3/4 = 0.75 = 75%; 1/10 = 0.1 = 10%; 1/5 = 0.2 = 20%.
Worked examples
Example 1
Convert 1/4 to a decimal and a percentage.
Answer
1/4 = 0.25 = 25%
Remember that 1/4 is a quarter, so 25% is a quarter of 100%.
Example 2
Find 50% of £60.
Answer
£30
Finding 50% of an amount is the same as finding half of that amount.
Example 3
Calculate 20% of 90 metres.
Answer
18 metres
Breaking down percentages into easier parts (like 10%) can make calculations simpler.
Common mistakes
- ✗Confusing the percentage value with the decimal value (e.g., thinking 25% is 25, instead of 0.25 or 25/100).
- ✗Incorrectly converting between fractions, decimals, and percentages, especially forgetting to divide or multiply by 100.
- ✗Trying to find a percentage of an amount by dividing by the percentage number instead of using 100 (e.g., for 20% of 50, doing 50 ÷ 20 instead of 50 ÷ 5 or 50 × 0.20).
- ✗Not simplifying fractions before converting to percentages, which can make calculations harder.
Exam tips
- ★Always remember that 'per cent' means 'out of 100'. This is key to all percentage calculations.
- ★Memorise common FDP equivalences (like 1/2, 1/4, 1/10) to quickly solve problems.
- ★When calculating a percentage of an amount, try to break it down into simpler percentages first (e.g., find 10% then multiply, or find 50% and 25% to make 75%).
- ★Check your answer: Does it make sense? If you're finding 25% of an amount, your answer should be smaller than the original amount.
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