Increase $80 by 35% (two-step)
- 35% as a decimal: 0.35 × 80 = 28
- Add to original: 80 + 28 = $108
- Works, but takes two steps
Year 9 maths lesson · Percentages
Percentage Increase and Decrease
Increase or decrease an amount by a percentage using a single multiplier. Increase by p% means multiply by (1 + p÷100); decrease by p% means multiply by (1 − p÷100).
- About 6–9 minutes
- 7 quick questions as you go
- Then about 6 minutes of practice
- Have a calculator ready
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Worked examples
Multiplier shortcut: increase $80 by 50%
- 1.5 means 1 whole lot + half a lot
- 1.5 × 80 = $120 — same answer, one step
Increase $200 by 30%
- Multiplier: 1 + 0.30 = 1.3
- 1.3 × 200 = $260
Decrease $150 by 20%
- Take off 20% → keep 80%
- Multiplier: 1 − 0.20 = 0.8
- 0.8 × 150 = $120
Increase $80 by 35% (one step)
- Multiplier: 1 + 0.35 = 1.35
- 1.35 × 80 = $108
Before this lesson
It helps to be comfortable with:
- Percentage of an amount
- Decimals
Lesson transcript
Everything the lesson says, word for word
Teacher: Hey Jamie, here’s a question for you — a jacket costs $80, and the store increases the price by 35%. What’s the new price?
Student: OK, 35% as a decimal is 0.35… times 80…
Student: That’s 28. So 80 plus 28…
Student: $108!
Teacher: That’s great! That method works perfectly. Today I want to show you a slightly faster way though.
Teacher: Let me start with something simpler. Increase $80 by 50%.
Student: Well, 50% of 80 is 40… then I add that to the original… 80 plus 40… that’s $120!
Teacher: That’s right! But there’s a quicker way. We can just multiply by 1.5.
Student: 1.5 times 80? Why 1.5?
Teacher: Think about it — 1.5 means 1 whole lot plus half a lot. So 1.5 times 80 is the original 80, plus an extra 50%. Let’s check.
Student: $120! Same answer, but just one step!
Teacher: Nice. Now try this one — increase $200 by 30%.
Student: I need to multiply by 1.3! That’s 1 lot plus an extra 30% of a lot. So 1.3 times 200…
Student: $260!
Teacher: Great! Try this one. Increase $450 by 12%.
Student: Multiply by 1.12!
Student: $504!
Teacher: See the pattern? We just take the percentage as a decimal and add 1. So 12% is 0.12 — add 1 and you get 1.12. That’s our multiplier.
Teacher: Now here’s a tricky one — increase $270 by 150%.
Student: 150%? That’s more than 100%! But… 1.5 plus 1 is 2.5. So I multiply by 2.5!
Student: $675!
Teacher: Excellent! Now let’s look at percentage decreases. Decrease $150 by 20%.
Student: OK, I’d find 20% of 150, that’s 30… then subtract it off… 150 minus 30 is $120.
Teacher: That works! But here’s a faster way. If we take off 20%, we’re left with 80% of the original. So instead of subtracting, we can just multiply by 0.8. Let’s check.
Student: $120! Same answer!
Teacher: Nice. Try this one — decrease $360 by 15%.
Student: 100% minus 15% is 85%… so I multiply by 0.85!
Student: $306!
Teacher: And one more — decrease $520 by 8%.
Student: 100% minus 8% is 92%… so 0.92 times 520…
Student: $478.40!
Teacher: So here’s the pattern. To increase by a percentage, add the decimal to 1 and multiply. To decrease, subtract the decimal from 1 and multiply.
Teacher: Now let’s go back to our original question — increase $80 by 35%.
Student: 1.35 times 80!
Student: $108!
More Percentages lessons
- Fractions, Decimals and PercentagesConvert fluently between fractions, decimals, and percentages.
- Percentage of an AmountCalculate percentages of amounts using mental and written methods.
- Reverse PercentagesIf you know a percentage of an amount, work backwards to find the whole.
- Expressing a Quantity as a PercentageExpress a quantity as a fraction, then use the calculator to find the decimal and percentage.
- Percentage Change Year 10Find the percentage change between two values using the multiplier method.
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