Step-by-step worked examples and graded practice questions on percentages — finding a percentage of an amount, percentage increase and decrease, reverse percentages and compound interest.
📚 Foundation & Higher✅ 15 Practice Questions🔍 Full Worked Examples⚠️ Common Mistakes
Struggling with percentages?
Alamin diagnoses exactly which skills are missing and builds a structured plan to fix them — backed by AI-powered practice between sessions.
"Per cent" means "out of 100" — a percentage is a fraction with a denominator of 100. To use a percentage in a calculation, it's usually easiest to convert it to a decimal first by dividing by 100 (see the Decimals page): 15% = 0.15, and 8% = 0.08.
Finding a percentage of an amount
Worked Example 1
Find 15% of £240.
1
Convert 15% to a decimal: 15% = 0.15
2
Multiply: 0.15 × 240 = 36
Answer£36
The shaded 15% strip represents £36 out of the whole £240 bar.
Percentage increase and decrease
The quickest method is a multiplier: to increase by a percentage, add it to 100% first; to decrease, subtract it from 100%. Then convert to a decimal and multiply.
Worked Example 2
(a) Increase £80 by 20%. (b) Decrease £150 by 30%.
A reverse percentage question gives you the amount after a percentage change and asks for the original amount. Divide by the multiplier — never subtract or add the percentage directly.
Worked Example 3
A coat's sale price is £68 after a 15% reduction. Find the original price.
1
A 15% reduction gives a multiplier of 0.85 (100% − 15%)
2
The sale price is 0.85 × original, so: original = 68 ÷ 0.85
3
68 ÷ 0.85 = £80
Answer£80
Common trap: you cannot find £80 by adding 15% of £68 to £68 — that gives the wrong answer, because 15% of the original price is not the same as 15% of the reduced price.
Compound interest and repeated percentage change
Compound interest applies the percentage change repeatedly, each time to the new amount — not the original. Use the multiplier raised to the power of the number of time periods.
Worked Example 4
£2000 is invested at 3% compound interest per year. Find the value after 4 years.
Solving reverse percentage questions by adding or subtracting instead of dividing
If £68 is the price after a 15% reduction, you cannot add 15% of £68 back on — the 15% was taken off a different (larger) starting amount. Always divide by the multiplier instead.
Common Mistake 2
Treating compound interest like simple interest
Compound interest is calculated on the new total each year, not the original amount every time. Using "original × rate × years" instead of "original × multiplier^years" gives the wrong answer for any period beyond the first year.
Common Mistake 3
Using the wrong multiplier for a decrease
A 15% decrease uses the multiplier 0.85 (100% − 15%), not 0.15. Confusing "the percentage removed" with "the multiplier to apply" is one of the most common errors in this topic.
Common Mistake 4
Rounding money too early
Keep full decimal accuracy through every step of a multi-year compound interest calculation, and round to the nearest penny only at the very end.
Exam tips
💡 Exam Tip 1
Always find the multiplier first
Before doing any calculation, write down the multiplier: 100% ± the percentage change, converted to a decimal. This turns almost any percentage question into a single multiplication.
💡 Exam Tip 2
Spot reverse percentage language
Phrases like "after a reduction", "including VAT", or "after depreciation" signal that you're given the final amount and need to divide to find the original — never the other way round.
💡 Exam Tip 3
Use powers for repeated percentage change
Any "per year for n years" question uses multiplier^n. Write this out explicitly (e.g. 1.03⁴) before calculating, so you don't lose track of how many times the multiplier should be applied.
💡 Exam Tip 4
Estimate to sanity-check your answer
Before finalising an answer, check it's a sensible size — an "increase" should always be bigger than the original, and a "decrease" should always be smaller.
Want to improve your grade faster?
If percentages are still causing problems, Alamin's diagnostic approach identifies exactly which skills are missing and builds a targeted plan to address them — with AI-powered practice between sessions.