Percentage explained | Primary Maths

01 Out of a hundred, always

45% means 45 out of every 100. As a fraction that is 45/100, and as a decimal 0.45. They are three ways of writing one number, and a question may hand you any of them.

Fixing the denominator at 100 is what makes percentages useful: 17/25 and 33/50 are hard to compare at a glance, but 68% and 66% are not.

100% is the whole thing. More than 100% is more than you started with, which is perfectly possible when something grows.

02 Finding a percentage of an amount

Two routes, and which is quicker depends on the numbers.

Ten per cent first, then build the answer out of it.

Through 1%. Divide by 100 to get 1%, then multiply. 45% of 240: one per cent is 2.4, so 45 × 2.4 = 108.
Through the fraction. 45% is 45/100, which simplifies to 9/20. Then 240 ÷ 20 × 9 = 108.
Through the easy ones. 50% is half, 25% is a quarter, 10% is a tenth. 45% is 50% − 5%, and 5% is half of 10%. Often the fastest route in an exam.

03 Increase and decrease, and the trap in them

A price rising by 20% becomes 120% of what it was. Falling by 20% makes it 80%. Work with the new percentage rather than finding the change and adding it separately — fewer steps, fewer slips.

Here is the trap, and papers use it deliberately: a 20% rise followed by a 20% fall does not bring you back to the start. $100 rises to $120, then falls by 20% of $120, which is $24, leaving $96.

The reason is that the two percentages are of different wholes. Whenever a question mentions a percentage, ask what it is a percentage of before doing anything.

04 Working backwards

The harder P6 questions give you the part and want the whole. The move is the same as any unit problem: get to 1%, then to 100%.

After a 20% discount a bag costs $96. What was the original price? The $96 is 80%, so 1% is 96 ÷ 80 = $1.20, and 100% is $120.

Dividing $96 by 100 here would be answering a different question — $96 is not the whole.

05 How to say them

These are words most children have never said out loud, and a word you cannot say is a word you avoid using. Capitals mark the syllable you lean on. Tap the speaker to hear it.

percentagesaypuh-SEN-tijmore than onepercentages
A number of parts per hundred, written with a % sign.
per cent, written %saypuh SENT
Out of a hundred. 45% is 45 out of every 100.
discountsayDIS-kowntmore than onediscounts
An amount taken off a price, usually given as a percentage of the original price.
interestsayIN-truhst
Money added to a savings amount, given as a percentage of it. A year at 2% on $500 adds $10.
GSTsaygee ess TEE
Goods and Services Tax, a percentage added to a price in Singapore. Questions give the rate to use.

06 What each level is tested on

The same topic, asked differently as it goes up. The percentage is the share of papers at that level in which it appears.

P5
Writing a percentage as a fraction and a decimal, and finding a simple percentage of a quantity.
Practise P5 Percentage — 10 questions →
51% of P5 papers
P6
Discounts, GST and interest, percentage increase and decrease, and working backwards from a changed amount to the original.
Practise P6 Percentage — 10 questions →
94% of P6 papers

07 Mistakes worth knowing about

Each of these is wrong. Decide why before you open it.

“It went up 20% then down 20%, so it is back where it started.”
It is not. $100 → $120 → $96, because the 20% fall is of $120, not of $100. Two percentages of different wholes never cancel.
“After a 20% discount it costs $96, so the original was 96 + 20% = $115.20.”
The $96 is 80% of the original. 1% is $1.20, so 100% is $120. Adding 20% to the discounted price uses the wrong whole.
“50% of 80 is 40, so 50% of 200 is also 40.”
A percentage is always a percentage of something. Half of 200 is 100. The same percentage of a different whole is a different amount.
“120% is impossible — you cannot have more than everything.”
You can have more than you started with. A price rising by 20% becomes 120% of the old price.
“45% as a decimal is 4.5.”
0.45. Per cent means divide by 100, so the digits move two places, not one.

Now try it

20 questions across 2 levels, marked as you go with the working shown.

P510 questions P610 questions