Percentage

Percentages are everywhere — a test scored 80 percent, a sale with 20 percent off, a phone battery at 45 percent. The word percent simply means "out of 100", so a percentage is just a special fraction with a bottom of 100. Once you know that, every percentage question turns into a fraction question you already know how to do. Let's master it.

Parents: let your child predict before they reveal each step. The blue dotted words are tappable definitions, and the "Method tip" boxes name exactly what a PSLE marker rewards in the working — not just the final number.

By the end you'll be able to find a percentage of a quantity, write one quantity as a percentage of another, and convert between percentage, fraction and decimal. Here we go.

Finding a percentage of a quantity

A percentage means "out of 100". To find a percentage of an amount, change it to a fraction over 100 and multiply. To find 20 percent of 50, work 20 over 100 × 50 = (50 ÷ 100) × 20 = 10.

A faster route is to find 10 percent first by dividing by 10, then scale. 10 percent of 50 is 5, so 20 percent is double that, which is 10. Finding 10 percent first is a handy trick for mental working.

One quantity as a percentage of another

Sometimes you have two amounts and must say what percentage one is of the other. Write the part over the whole as a fraction, then multiply by 100. If 15 out of 20 questions are correct, the fraction is 15 over 20, and 15 over 20 × 100 = 75 percent.

The key is to get the right number on the bottom — the whole, the total you are comparing against. The part goes on top, the whole goes underneath.

Converting percentage, fraction and decimal

These three are the same value in different clothes. To turn a percentage into a fraction, write it over 100 and simplify: 40 percent is 40 over 100, which simplifies to two fifths. To turn a percentage into a decimal, divide by 100: 40 percent is 0.4.

Going the other way, a decimal becomes a percentage by multiplying by 100, so 0.35 is 35 percent. Some are worth memorising: one half is 50 percent, one quarter is 25 percent, three quarters is 75 percent, and one fifth is 20 percent.

Watch out — these are easily mixed up

Quick recap

🎯 Mastery check

Answer all 6 — your progress is saved on this device.

1. What is 10 percent of 250?

   251050

2. What is 40 percent of 60?

   242040

3. A pupil gets 12 out of 16 marks. What percentage is this?

   75 percent60 percent80 percent

4. What is 0.25 written as a percentage?

   2.5 percent25 percent250 percent

5. What is 30 percent written as a fraction in simplest form?

   Three tenthsThirty hundredths onlyOne third

6. A jacket costs $80. A 15 percent deposit is paid. How much is the deposit?

   $12$15$8

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