Number
Grade 2-4Percentages of Amounts
Percentages show up everywhere from discounts to exam grades, and questions on them split neatly into two types: non-calculator questions that expect you to build up an answer from 10% and 5%, and calculator questions where a single multiplication does the job. This lesson covers both, along with converting a percentage to a decimal or fraction.
Written by Asad, Co-Founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Converting a percentage to a decimal
"Per cent" means "out of 100", so any percentage converts to a decimal by dividing by 100, which moves the decimal point two places to the left.
35% ÷ 100 = 0.35, and 8% ÷ 100 = 0.08. Watch out for percentages above 100%, such as 120%, which becomes 1.2.
Converting a percentage to a fraction
Write the percentage over a denominator of 100, then simplify the fraction fully by dividing the numerator and denominator by their highest common factor.
40% becomes 40/100, and dividing both by 20 gives 2/5. 15% becomes 15/100, and dividing both by 5 gives 3/20.
Finding a percentage without a calculator
Build the percentage you need from 10% and 5%, since 10% of an amount is found by dividing by 10, and 5% is half of that. Other percentages can then be added or subtracted from these building blocks.
To find 15% of £80: 10% of £80 is £8, and 5% is half of £8, which is £4. Adding these gives 15% = £8 + £4 = £12.
Finding a percentage with a calculator
Convert the percentage to a decimal and multiply it directly by the amount, which is much faster than building up from 10% once a calculator is allowed.
To find 23% of £350: convert 23% to 0.23, then multiply 0.23 × 350 = £80.50.
Worked Examples
Three exam-style questions, fully solved.
Write 35% as a decimal.
Easy- 1.Divide 35 by 100, moving the decimal point two places to the left
Answer: 0.35
Work out 15% of £80.
Medium- 1.Find 10% of £80 by dividing by 10: £8
- 2.Find 5% of £80 by halving the 10% value: £8 ÷ 2 = £4
- 3.Add the two building blocks together: £8 + £4 = £12
Answer: £12
A charity raised £2400. 45% of the money was spent on equipment. How much money was spent on equipment?
Hard- 1.Convert 45% to a decimal: 45 ÷ 100 = 0.45
- 2.Multiply the decimal by the total amount: 0.45 × 2400
Answer: £1080
Avoid These
The most common mistakes students make.
Dividing by 10 instead of 100 when converting a percentage to a decimal, for example writing 35% as 3.5 instead of 0.35.
When using the 10%/5% building-block method, recalculating 5% from scratch instead of simply halving the 10% value already found.
Converting a percentage to a fraction and forgetting to simplify it fully, leaving an answer like 40/100 instead of 2/5.
Leaving the units off a worded answer, for example writing 1080 instead of £1080 when the question is about money.
Using the percentage-of-an-amount method on a question that is actually asking for a percentage increase or decrease, and forgetting to add or subtract from the original amount.
FAQ
Questions parents and students ask.
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