Percentage Increase
When prices, populations and pay packets rise — two ways to find the new value quickly.
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A job pays $\$18$/hour and gives you a $12\%$ pay rise. How much will you earn now? Jot down your first reaction — then we'll see who's right.
A percentage increase ADDS a percentage of the original to itself. There are TWO equivalent methods — the add-the-increase method and the faster multiplier method.
A $12\%$ pay rise on $\$18$/hour. Method 1 (add): $12\%$ of $18$ is $\$2.16$; add to original $= \$20.16$. Method 2 (multiplier): the new wage is $112\%$ of the old, so $1.12 \times 18 = \$20.16$. Same answer. The multiplier is faster, especially with a calculator.
Know
- New value = original + (% of original)
- New value = original $\times (1 + \tfrac{P}{100})$
- $12\%$ increase $\to$ multiplier $1.12$
- $5\%$ increase $\to$ multiplier $1.05$
Understand
- Why $1 + \tfrac{P}{100}$ collapses the two steps into one
- How GST is a percentage increase
- The difference between an increase and the new total
Can Do
- Apply a percentage rise to any starting value
- Choose between the add and multiplier methods
- Use the multiplier method confidently on a calculator
Wrong: "$12\%$ rise on $\$18 = 18 + 12 = \$30$" — NO. You added 12 dollars, not 12 percent.
Right: $12\%$ of $18 = \$2.16$. New $= 18 + 2.16 = \$20.16$.
Wrong: "Multiplier for $12\%$ rise = $\times 0.12$" — NO. That gives the INCREASE, not the new total.
Right: Multiplier $= 1 + 0.12 = 1.12$. $1.12 \times 18 = \$20.16$.
A two-step approach: find the percentage as a quantity, then add it.
Take a $\$50$ jumper with a $20\%$ markup. Step 1: find $20\%$ of $\$50 = \$10$. Step 2: $\$50 + \$10 = \$60$. The intermediate step (the increase itself) is useful — it tells you HOW MUCH the price went up. But it's slower than the multiplier method.
A single multiplication. New value equals original times the multiplier.
A $15\%$ increase means the new value is $115\%$ of the old: a multiplier of $1.15$. So $\$200$ becomes $200 \times 1.15 = \$230$. A $7\%$ rise? Multiplier is $1.07$. The rule: $1 + \tfrac{P}{100}$.
Watch Me Solve It · 3 examples
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1Set up the multiplier$12\%$ rise $\to$ multiplier $= 1.12$$1 + 0.12 = 1.12$.
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2Multiply$18 \times 1.12$One calculator step.
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3Compute$18 \times 1.12 = \$20.16$New hourly rate.
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1Multiplier for $10\%$ rise$1 + 0.10 = 1.10$$10\%$ becomes $1.10$.
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2Multiply$45 \times 1.10$Apply to original.
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3Compute$45 \times 1.10 = \$49.50$Includes GST.
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1Add method: find the increase$4\%$ of $25\,000 = 0.04 \times 25\,000 = 1000$That's the number of new people.
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2Add to original$25\,000 + 1000 = 26\,000$New population.
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3Check with multiplier$25\,000 \times 1.04 = 26\,000$ ✓Same answer.
Common Pitfalls
Method 1: Add
- Increase $= \tfrac{P}{100} \times $ Original
- New $= $ Original $+$ Increase
- Two steps
Method 2: Multiplier
- Multiplier $= 1 + \tfrac{P}{100}$
- New $= $ Original $\times $ Multiplier
- One step
Common Multipliers
- $5\%$ rise: $\times 1.05$
- $10\%$ rise: $\times 1.10$
- $12.5\%$ rise: $\times 1.125$
GST
- GST = $10\%$
- Inc-GST price = $\times 1.10$
- Quick way to add GST
How are you completing this lesson?
Brain Trainer · 4 problems
Four drill problems to sharpen your skills. Work each, then reveal the answer.
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1 Increase $\$80$ by $25\%$.
$80 \times 1.25 = 100$.$\$100$ -
2 Increase $200$ kg by $15\%$.
$200 \times 1.15 = 230$.$230$ kg -
3 A $\$120$ jacket has GST added. What's the inc-GST price?
$120 \times 1.10 = 132$.$\$132$ -
4 A $\$50$ bill increases by $4\%$. New bill?
$50 \times 1.04 = 52$.$\$52$
Quick Check · 5 questions
Show Your Working · 3 questions
Q6. Increase each by the percentage shown using the multiplier method: (a) $\$340$ by $15\%$ (b) $80$ kg by $7.5\%$ (c) $\$1250$ by $4\%$
Q7. A streaming service charged $\$12/$month last year. Prices rose $8\%$ this year. What is the new price, and what was the increase in dollars?
Q8. A laptop is advertised at $\$1200$ exc-GST. The store also offers a $5\%$ "early-bird" markup on selected items. (a) Find the price after GST only. (b) Find the price after BOTH the early-bird markup and GST (apply markup first, then GST). (c) Is the order in which you apply the two increases important? Justify with calculation.
Quick Check
1. C — $200 \times 1.20 = \$240$.
2. C — $1 + 0.075 = 1.075$.
3. D — $160 \times 1.10 = \$176$.
4. C — $22 \times 1.05 = \$23.10$.
5. C — $4500 \times 1.12 = 5040$.
Show Your Working Model Answers
Q6 (3 marks): (a) $340 \times 1.15 = \$391$ [1]. (b) $80 \times 1.075 = 86$ kg [1]. (c) $1250 \times 1.04 = \$1300$ [1].
Q7 (2 marks): New: $12 \times 1.08 = \$12.96$ [1]. Increase: $12.96 - 12 = \$0.96$ [1].
Q8 (4 marks): (a) $1200 \times 1.10 = \$1320$ [1]. (b) Markup first: $1200 \times 1.05 = \$1260$. Then GST: $1260 \times 1.10 = \$1386$ [2]. (c) NO — order does not matter: $1200 \times 1.05 \times 1.10 = 1200 \times 1.10 \times 1.05 = \$1386$ (multiplication is commutative) [1].
The Doubling Salary
A worker earns $\$50\,000$/year. Their salary increases $7\%$ every year. (a) What is their salary after 1 year? After 5 years? (b) After how many full years has their salary more than doubled? (Hint: try multiplying the multiplier by itself repeatedly.)
Reveal solution
(a) Year 1: $\$53\,500$. Year 5: $50000 \times 1.07^5 = 50000 \times 1.4026 \approx \$70\,128$. (b) Need $1.07^n > 2$. $1.07^{10} \approx 1.967$ (not yet); $1.07^{11} \approx 2.105$ (yes!). So 11 years.
Add method
Find the increase, then add
Multiplier
$1 + \tfrac{P}{100}$
$10\%$ rise
$\times 1.10$
$5\%$ rise
$\times 1.05$
GST
A 10% increase
Always $> 1$
Multiplier for increase is bigger than 1
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