Understand percentages
Objective. Interpret a percentage as parts per hundred.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
A percentage expresses a quantity as parts per hundred, so 1% means 1 out of every 100. Writing a percentage as a fraction out of 100 or as a decimal makes it easy to use in calculations: 40% equals 40/100, which simplifies to 2/5, or equivalently 0.4. Percentages let you compare proportions easily even when the totals being compared are different sizes. For example, 30 out of 50 is the same proportion as 60%, since 30/50=60/100.
Worked example
Write 18 out of 40 as a percentage.
- 1Write the proportion as a fraction: 18/40.
- 2Scale to a denominator of 100 by multiplying by 2.5: 18×2.5=45, 40×2.5=100.
- 3The fraction becomes 45/100.
- 4Write as a percentage: 45%.
Answer: 45%
Concept mastery
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Practice
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Start practisingCommon mistake. Pupils often think a percentage can be directly compared to a raw count without considering the total, assuming 40 out of 200 is more than 30%. Always convert to a percentage first before comparing.
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