KS3 · Maths

Finding a percentage of an amount (with a multiplier)

A 250 g block of cheese is 37% water. How many grams is that? You can't weigh the water — but you can work it out in one line.

Maths · Percentages

Line 100% up with the whole

Percentage: 8/20. Percentage 40%. Of 600 240. Of 240 96. Of 800 320

Percentage40%Of 600240Of 24096Of 800320

The whole bar is 100%. Each small part is 5%, so two parts make 10% — a tenth of the whole. Drag along the bar and watch three different wholes keep pace: 10% of 600 is 60, 40% of 600 is 240, and 100% always lands on the whole amount.

Maths · Percentages

How do you find 5% of 240?

You need 5% of 240. Three learners each have a plan.

Which plan is closest to what you would do?

It's 5%, so divide by 5. 240 ÷ 5 = 48.5% is a small part, so divide by 50. 240 ÷ 50 = 4.8.Find 10% first by dividing by 10: 24. 5% is half of that: 12.

How sure are you?

I'm sureI think soI'm guessing

It's 5%, so divide by 5. 240 ÷ 5 = 48.

This is a common misconception

Dividing by 5 splits 240 into five equal parts and gives you ONE of them: one fifth. One fifth is 20%, not 5%. You can see it's too big: 10% of 240 is only 24, so 5% has to be less than 24, and 48 is double that.

5% is a small part, so divide by 50. 240 ÷ 50 = 4.8.

This is a common misconception

Dividing by 50 splits 240 into fifty equal parts. Share 100% into fifty parts and each part is 2%, so 4.8 is 2% of 240. (And the other way round: 50% isn't ÷ 50 — 50% is half, so it's ÷ 2.)

Find 10% first by dividing by 10: 24. 5% is half of that: 12.

This matches the evidence

Spot on. 10% is one tenth, so 240 ÷ 10 = 24. 5% is half of 10%, so half of 24 = 12. Keep going and you get the third building block too: 1% is 10% divided by 10, so 24 ÷ 10 = 2.4.

For 240: 10% = 24, 5% = 12, 1% = 2.4. Divide by 10 for 10%, halve it for 5%, divide by 10 again for 1%. Never divide by the percentage number itself.

Maths · Percentages

Build it from the building blocks

Build each percentage from 10%, 5% and 1%. At each gap, choose the step that finishes the job.

35% of 24. 10% is 24 ÷ 10 = 2.4, so 30% is 3 × 2.4 = 7.2, and 5% is half of 2.4 = 1.2.
missing step

Which line is step 2?

35% = 24 ÷ 35 ≈ 0.6935% = 30% + 5% = 7.2 + 1.2 = 8.435% = 30% + 5% = 7.2 + 12 = 19.2

The multiplier route

Problem

A 250 g block of cheese is 37% water. How many grams of water are in it? First, see the route on two simpler amounts: 45% of 20 and 68% of 430.

Maths · Percentages

Spot the slip

Find 3% of 812 using a multiplier.

A student's answer — which line goes wrong?

3% of 812 means 3% × 812.
3% = 0.3
0.3 × 812 = 243.6
So 3% of 812 = 243.6

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

Line 100% up with the whole, build from 10%, 5% and 1%, and let 'of' mean multiply.

What you need to know

Per cent comes from the Latin per centum, 'by the hundred'. 1% is one part in every hundred, or 1/100. On a hundred square, the whole square is 100% and each small square is 1%.
The whole amount is 100%. On a bar model or a double number line, 100% lines up with the whole amount, and both lines start at zero.
10% means divide by 10. 5% is half of 10%. 1% is 10% divided by 10 (the whole divided by 100).
Build other percentages by adding or subtracting: 35% = 30% + 5%, 72% = 70% + 2%, 29% = 30% − 1%, 99% = 100% − 1%.
A percentage is a fraction out of 100, so 45% of 20 = 45/100 × 20 = 9. Other fractions can be scaled up to hundredths: 17/20 = 85/100 = 85%.
The decimal multiplier is the percentage divided by 100: 68% = 0.68, 3% = 0.03. Then multiply: 68% of 430 = 0.68 × 430 = 292.4.

The big picture

Per cent means 'out of a hundred', so the whole amount is always 100%. Split the whole into ten equal parts and each part is 10% (divide by 10). Halve 10% to get 5%, and divide 10% by 10 to get 1%. Add or subtract those building blocks to make any percentage. Or divide the percentage by 100 to get a decimal multiplier (68% = 0.68, 3% = 0.03) and multiply, because 'of' means multiply.

Key points

1A percentage is a number of parts per hundred, so 'percentage of' an amount is a multiplication.

2Never divide by the percentage number: ÷ 5 finds 20%, ÷ 50 finds 2%, and 50% is ÷ 2.

3A single-digit percentage needs a zero after the point as a multiplier: 3% = 0.03, not 0.3.

4There is more than one route, so pick the one with fewest steps: 75% is 50% + 25%, or 100% − 25%.

5Sense-check with 10%: 3% of an amount must be smaller than 10% of it.

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Worked example

Problem

Find 35% of 460 without a calculator.

⚠ Watch out

Dividing by the percentage number. 5% of 80 is not 80 ÷ 5 = 16 — that's one fifth, which is 20%. Find 10% first (8) and halve it: 5% of 80 is 4. The decimal version of the same slip is writing 6% as 0.6, which finds 60%.

🧠

Memory hook

Ten, five, one: divide by ten, halve it, divide by ten again. And 'of' means times.

✓

Check yourself

Find 15% of 40 using the building blocks, then check it with a multiplier. (10% = 4 and 5% = 2, so 15% = 6. Check: 0.15 × 40 = 6.)

Flashcards

(15)

What does 'per cent' mean?

Out of a hundred — from the Latin per centum, 'by the hundred'. 1% is 1/100.

On a bar model or double number line, what does 100% line up with?

The whole amount. Both lines start at zero.

How do you find 10% of an amount?

Divide by 10 — it is one tenth. 10% of 350 is 35.

How do you find 5% of an amount?

Find 10%, then halve it. For 60: 10% is 6, so 5% is 3.

How do you find 1% of an amount?

Divide the whole by 100. 1% of 900 is 9.

What does dividing an amount by 5 actually find?

One fifth of it, which is 20% — not 5%.

What does dividing by 50 find? How do you find 50%?

÷ 50 finds 2%. 50% is half, so divide by 2.

Quick way to find 99% of 200?

100% − 1%: 200 − 2 = 198.

Give three ways to find 75% of an amount.

50% + 25%, or 100% − 25%, or 3 × 25%. Never ÷ 75.

What is a decimal multiplier?

The percentage divided by 100: 26% = 0.26, 5.8% = 0.058.

Write 3% and 30% as multipliers.

3% = 0.03 and 30% = 0.3. A single-digit percentage needs a zero straight after the point.

What does 'of' mean in '68% of 430'?

Multiply: 0.68 × 430 = 292.4.

How can you work out 0.24 × 182 without a calculator?

Do 24 × 182 = 4368, then × 0.01 = 43.68. Grouping a multiplication differently doesn't change the answer.

Use a fraction out of 100 to find 42% of 25.

42/100 × 25 = 1050/100 = 10.5.

Write 8/25 as a percentage.

Multiply top and bottom by 4: 32/100 = 32%.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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How do you find 5% of 240?

Build it from the building blocks

Spot the slip

More KS3 Maths topics