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Level 7Grade 7skill: percent_of· 8 min read

How to Find a Percentage of a Number

In short: Turn the percent into a decimal (divide by 100) and multiply by the number. Mentally, build the answer from 10% (divide by 10), 5% (half of that) and 1% chunks. Two big exam traps: reverse percentages need division, not subtraction (£46 after a 15% charge means 46 / 1.15 = £40), and a percent of a percent multiplies, not adds (20% then 30% off is 44% off, not 50%).

The method: turn the percent into a multiplier

"Percent" just means "out of 100". So 30% of 50 is really thirty hundredths of 50. Write the percent as a decimal (divide by 100), then multiply. That single idea handles every percent-of-a-number question you will ever meet.

The multiplier for 30% is 0.30, so 30% of 50 = 0.30 × 50 = 15. No calculator? Build the answer from friendly chunks instead: 10% of a number is that number divided by 10, and once you have 10% you can reach almost anything by halving and adding.

For example, 45% of 60: 10% is 6, so 40% is 24, and 5% (half of 10%) is 3. Add them: 24 + 3 = 27. Same answer as 0.45 × 60, but you did it in your head.

  1. Read the percent as a number out of 100 and write it as a decimal (divide by 100): 30% becomes 0.30.
  2. Multiply that decimal by the base number: 0.30 x 50 = 15.
  3. Mental shortcut: find 10% by dividing by 10, then build the target from 10%, 5% (half of 10%) and 1% (divide by 100) chunks.
  4. Sanity-check the size: a percent under 100% must give an answer smaller than the base; over 100% must give a bigger one.

Why the 10% and 1% building blocks work Why it works

10% = one shift
To find 10%, divide by 10 (move the decimal one place left).

10% of 340 = 34; 10% of 8.5 = 0.85

1% = two shifts
To find 1%, divide by 100 (move the decimal two places left).

1% of 340 = 3.4; 1% of 8.5 = 0.085

Build any percent
Combine 10% chunks, 5% (half of 10%) and 1% chunks to assemble the percent you actually want.

35% = 10% + 10% + 10% + 5% = 17 + 17 + 17 + 8.5 = 59.5 for a base of 170

Swap trick
"A% of B" always equals "B% of A", because both are (A x B) / 100 - so flip to whichever is easier.

18% of 50 is awkward, but 50% of 18 is just half of 18 = 9

That last row hides the payoff most students never cash in: because percent-of is commutative, you get to choose the friendlier order. When you see something like 8% of 25, don't reach for 0.08 × 25 - flip it to 25% of 8, which is a quarter of 8 = 2. Strong candidates win time in exams by spotting which of the two orders lands on rounder numbers.

Worked examples (with the traps flagged)

Find 35% of 80. = 28
  1. 10% of 80 = 8, so 30% = 3 x 8 = 24.
  2. 5% is half of 10%, so 5% = 4.
  3. Add the chunks: 24 + 4 = 28.
A coat costs £150. It is reduced by 20%, then a further 30% is taken off the reduced price. What is the final price? = £84
  1. The tempting move is to add the discounts to 50% off - that is wrong, because the second discount is taken on a smaller price.
  2. After 20% off: 150 x 0.80 = 120.
  3. After a further 30% off: 120 x 0.70 = 84.
  4. So the true single discount is only 44%, not 50%.
After a 15% service charge is added, a restaurant bill comes to £46. What was the bill before the charge? = £40
  1. Do NOT subtract 15% of 46 - the 15% was taken on the original, not on £46.
  2. The £46 represents 115% of the original, i.e. the original x 1.15.
  3. So original = 46 / 1.15 = 40.
  4. Check: 40 x 1.15 = 46. Correct.
In a school, 60% of pupils play a sport, and 25% of those sporty pupils play tennis. What percentage of the whole school plays tennis, and how many is that out of 240 pupils? = 15%, which is 36 pupils
  1. "Percent of a percent" means multiply the multipliers: 0.60 x 0.25 = 0.15.
  2. So 15% of the whole school plays tennis.
  3. Of 240 pupils: 0.15 x 240 = 36.
A shop buys a lamp for £40 and sells it for £50. What is the percentage profit? = 25%
  1. Profit percentage is always measured against the COST, not the selling price.
  2. Profit = 50 - 40 = 10.
  3. As a percent of cost: 10 / 40 = 0.25 = 25%.
  4. (Dividing by 50 would give 20% - that is the classic wrong base.)

Five mistakes that cost marks

Writing the percent number down as the answer

✗ 30

Faced with "30% of 50", it is tempting to just copy the 30. But 30% is a fraction of 50, not the number 30. Percent means "out of 100", so you still have to take that share of the base.

Fix: Turn 30% into 0.30, then multiply: 0.30 x 50 = 15. Notice 15 is smaller than 50, which is exactly what a percentage under 100% should give.

percent_as_whole

Putting the decimal in the wrong place

✗ 90

For "15% of 60", writing 15% as 1.5 instead of 0.15 shifts the decimal one place and gives 1.5 x 60 = 90 - bigger than the base, which is impossible for 15%.

Fix: 15% = 15/100 = 0.15 (two decimal places, because you divide by 100). Then 0.15 x 60 = 9. Always ask: is my answer smaller than the base? It must be for any percent below 100%.

decimal_point_shift

Adding two discounts instead of multiplying

✗ £75

On a £150 coat with 20% off then 30% off, adding the discounts to 50% gives 150 x 0.50 = 75. But the second discount applies to the already-reduced price, so you must multiply the multipliers, not add the percents.

Fix: Chain the multipliers: 150 x 0.80 x 0.70 = £84. The real discount is 44%, not 50%. Two successive percentage changes always multiply.

wrong_operation

Stopping one step too early

✗ 144

For "60% play a sport, 25% of those play tennis, out of 240 pupils", 60% of 240 = 144 is only the number who play any sport. That is a correct intermediate value - but it is not the tennis answer the question asked for.

Fix: Take the second percentage of that result: 25% of 144 = 36. Or multiply straight through: 0.60 x 0.25 x 240 = 36. Re-read the question and finish the last step.

partial_computation

Taking the percentage of the wrong base

✗ 20%

Buying at £40 and selling at £50 gives £10 profit. Dividing by the selling price, 10 / 50 = 20%, uses the wrong base - profit percentage is measured against what you paid.

Fix: Divide the profit by the cost: 10 / 40 = 25%. Whenever a question says "profit/loss percent", the base is the cost price unless it explicitly says otherwise.

base_confusion

Practise it

Now try a mixed set. Watch for the reverse-percentage questions (divide, don't subtract) and the percent-of-a-percent chains (multiply, don't add). Aim to spot the commutative swap whenever it makes the numbers friendlier.

Before and after this skill

First, make sure of

Frequently asked questions

What is the quickest way to find a percentage of a number without a calculator?

Build it from friendly chunks. Find 10% by dividing by 10, then combine: 5% is half of 10%, and 1% is a hundredth of the number. For 45% of 60, that is 40% (24) plus 5% (3) = 27. Faster than reaching for 0.45 x 60.

How do I find the original amount before a percentage was added or removed?

Divide, don't subtract. If a 15% charge brings a bill to £46, that £46 is 115% of the original, so the original is 46 / 1.15 = £40. For a decrease of 15%, you would divide by 0.85 instead.

Do a 20% discount and a 30% discount combine to 50% off?

No. Successive discounts multiply rather than add. 20% off then 30% off is 0.80 x 0.70 = 0.56, so you pay 56% of the price - a true discount of 44%, not 50%.

Is 15% of 40 the same as 40% of 15?

Yes. "A% of B" always equals "B% of A" because both equal (A x B) / 100. Use it to flip an awkward calculation into an easy one: 40% of 15 is just 6, which is far quicker than 0.15 x 40.

When a question asks for percentage profit, do I divide by the cost or the selling price?

By the cost price, unless the question explicitly says otherwise. Buying at £40 and selling at £50 is a £10 profit on a £40 cost, which is 25% - not the 20% you would get by wrongly dividing by the £50 selling price.