Calculating a Percentage of a Quantity

Find a percentage of an amount with a multiplier or from 10% and 5% blocks, find what is left, and handle questions where you must work out the amount first.

In the exam for Edexcel IGCSE Maths 4MA1, Cambridge IGCSE Maths 0580, Cambridge O Level Maths 4024 · 47 real past-paper questions below

اقرأ هذا الدرس مشروحاً بالعربي ←

What a Percentage of an Amount Is

Per cent means out of 100. So 35% of an amount means 35 out of every 100 parts of it.

Some percentages are easy fractions:

Percentage	Do this
50%	divide by 2
25%	divide by 4
10%	divide by 10
1%	divide by 100

Key idea

The word "of" means multiply. 35% of 260 means 35% times 260.

Key idea

Mental trick: $x %$ of $y$ is the same as $y %$ of $x$ . So 8% of 25 looks hard, but 25% of 8 is easy: 2. Try 4% of 75. (Answer: 75% of 4, which is 3.)

Using a Multiplier

The 2-mark question: work out 35% of 260. With a calculator, turn the percentage into a decimal and multiply.

Worked example

1
$35% = \frac{35}{100} = 0.35$ — Per cent means out of 100, so divide 35 by 100. This decimal is the multiplier.
2
$0.35 \times 260$ — “Of” means multiply, so multiply the multiplier by the whole amount. Write this line down: it earns a mark on its own.
3
$= 91$ — Work it out on the calculator. 91 is 35% of 260.

Common mistake

Writing 35% as 3.5. That gives 910, more than the whole 260. 35% is 0.35.

Key idea

Check the size: 35% is a bit more than a third, and a third of 260 is about 87. So 91 makes sense.

Key idea

Money answers need 2 decimal places. 17% of $38.25 is $6.5025, so write $6.50 (to the nearest cent), not $6.5.

Without a Calculator: Build It

The non-calculator question: work out 15% of 240. Build it from easy blocks.

Worked example

1
$10% of 240 = 240 \div 10 = 24$ — 10% is one tenth, so divide by 10. This is your easiest block.
2
$5% of 240 = 24 \div 2 = 12$ — 5% is half of 10%, so halve the 24.
3
$15% = 10% + 5%$ — Split 15% into the blocks you already have.
4
$15% = 24 + 12 = 36$ — Add the blocks. 15% of 240 is 36.

When the percentage does not end in 0 or 5, use 1% blocks too. Work out 12% of 65:

Worked example

1
$10% of 65 = 65 \div 10 = 6.5$ — Divide by 10 for 10%.
2
$1% of 65 = 65 \div 100 = 0.65$ — Divide by 100 for 1%. It is the 10% block divided by 10 again.
3
$2% = 2 \times 0.65 = 1.3$ — 12% is 10% and 2%, so double the 1% block.
4
$12% = 6.5 + 1.3 = 7.8$ — Add the blocks. 12% of 65 is 7.8.

Rule

Find 10% by dividing by 10 and 1% by dividing by 100. Halve, double or add these to make any percentage. Taking away can be quicker: 45% = 50% − 5%.

Common mistake

Finding 10% and then adding 5 for the 5%. You need 5% of 240, which is 12, not the number 5.

How Many Are Left?

The 3-mark question: 12% of 350 students fail a test. How many pass? The ones who pass are the rest.

Worked example

1
$100% - 12% = 88%$ — All the students are 100%. Take away the 12% who fail: the 88% who are left pass.
2
$88% = 0.88$ — Divide by 100 to get the multiplier.
3
$0.88 \times 350 = 308$ — Multiply by the whole group. 308 students pass.

You can also find 12% first, then take it away:

Worked example

1
$0.12 \times 350 = 42$ — 12% is 0.12. Multiply to find the 42 students who fail.
2
$350 - 42 = 308$ — Take the ones who fail away from everyone. Same answer, one more line.

Common mistake

Stopping at 42. The question asks how many pass, not how many fail.

A Percentage of What Is Left

Some questions take one part away, then a percentage or fraction of what remains. Read whether the next part is “of the total” or “of the remaining”.

Amir has $480. He spends 35% on rent and $\frac{1}{4}$ of the remaining money on food. How much is left?

Worked example

1
$0.35 \times 480 = 168$ — Rent is 35% of all the money, so use the whole $480. Rent is $168.
2
$480 - 168 = 312$ — Take the rent away. $312 is the remaining money, and the next part is a share of this.
3
$\frac{1}{4} \times 312 = 78$ — Food is a quarter of the remaining $312, not of $480. Food is $78.
4
$312 - 78 = 234$ — Take the food away too. $234 is left.

Common mistake

Taking a quarter of the whole $480. That gives $120 for food and the wrong answer $192. “Of the remaining” means of what is left, $312.

Key idea

If every part is “of the total”, work each part from the total. 600 tiles: 30% are red, $\frac{1}{3}$ are blue, the rest are green. Red is $0.3 \times 600 = 180$ , blue is $600 \div 3 = 200$ , so green is $600 - 180 - 200 = 220$ .

Find the Amount First

The 4 or 5-mark question: the amount is not given straight away. Work it out, then take the percentage.

300 students. There are 60 more boys than girls. 40% of the boys and 75% of the girls play a sport. How many play a sport?

Worked example

1
$300 - 60 = 240$ — Take away the extra 60 boys. What is left splits into two equal groups.
2
$240 \div 2 = 120$ — Halve it: there are 120 girls.
3
$120 + 60 = 180$ — There are 60 more boys than girls, so 180 boys. Check: 120 + 180 = 300.
4
$0.4 \times 180 = 72$ — 40% of the boys. 40% is 0.4, so 72 boys play.
5
$0.75 \times 120 = 90$ — 75% of the girls. 75% is 0.75, so 90 girls play.
6
$72 + 90 = 162$ — Add the two groups. 162 students play a sport.

Common mistake

Taking 40% and 75% of all 300. Each percentage belongs to its own group.

Key idea

Other ways the amount is hidden: cars per hour times hours, or a share of money in a ratio. See Dividing in a Given Ratio.

Deposits and Monthly Payments

On a payment plan you pay a deposit now (a percentage of the price), then the rest in equal monthly payments.

A laptop costs $840. You pay a 15% deposit, then monthly payments of $59.50. How many payments do you make?

Worked example

1
$0.15 \times 840 = 126$ — The deposit is 15% of the price. 15% is 0.15, so the deposit is $126.
2
$840 - 126 = 714$ — Take the deposit off the price. $714 is still to pay.
3
$714 \div 59.50 = 12$ — Each payment is $59.50. Dividing tells you how many payments cover the $714: 12.
4
$126 + 12 \times 59.50 = 840$ — Check: the deposit plus all the payments gives back the full price.

Common mistake

Dividing the full $840 by $59.50. Take the deposit off first: the monthly payments only cover the rest.

Key idea

Payment plans usually cost more. Total paid = deposit + number of payments × each payment. A $650 phone: the 20% deposit is $130, and 10 payments of $56 are $560. That is $690 in total, $40 more than paying all at once.

Which Method? Read the Question

Find the key words. They tell you which method to use.

You see	You do
work out 23% of 450	multiply by 0.23
no calculator	build from 10%, 5% and 1%
the rest, not faulty, remaining	100% take away, then multiply
per hour, more than, in a ratio	find the amount first
of the remaining, of the rest	take away first, then find the part of what is left
deposit, monthly payments	% of the price, then the rest ÷ each payment
which is larger	work out both and write both down
what percentage of	Expressing One Quantity as a Percentage
increase or decrease by 8%	Percentage Increases and Decreases
the price before the change	Reverse Percentages

Key idea

A percentage below 100% always gives less than the whole. If your answer is bigger, check the decimal. New to per cent? See Introduction to Percentages.

Key idea

Show every line. Most of the marks are for the working: a line like $0.35 \times 260$ earns a method mark even if the final answer slips.

Practise calculating a percentage of a quantity now

Interactive visual aids, then real past-paper questions marked on your working like the exam. Free to start.

Practise free on Lemmara

Real past-paper questions on calculating a percentage of a quantity

Each with a full worked solution.

All 47 questions on this topic →

Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education or Pearson Edexcel. The lessons and worked examples are Lemmara’s own.