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Year 7AC9M7N09

Percentage Increase and Decrease

Use mathematical modelling to solve practical problems, involving rational numbers and percentages, including financial contexts; formulate problems, choosing representations and efficient calculation strategies; interpret and communicate solutions in terms of the situation.

Discounts, mark-ups, tips and price rises are all the same calculation. There is a slow way and a one-step way, and the one-step way is worth learning properly.

Builds onYr 7 · Finding a Percentage of a Quantity

Method

Two-step method
find the change, then add or subtract it\text{find the change, then add or subtract it}
Always works. Slower, but hard to get wrong.
One-step multiplier: increase
+15% ⇒ ×1,15+15\% \ \Rightarrow\ \times 1{,}15
The original 100% plus the extra 15% makes 115%.
One-step multiplier: decrease
−20% ⇒ ×0,80-20\% \ \Rightarrow\ \times 0{,}80
You keep 80% of what you started with.
A rise then an equal fall does not return you to the start
100→110→99100 \to 110 \to 99
The percentages are taken of different amounts.

Worked example

e.g. A jacket costs 90 and is reduced by 20%. Find the sale price.\text{A jacket costs } 90 \text{ and is reduced by } 20\%. \text{ Find the sale price.}
  1. Two-step method. Find the discount first.20% of 90=1820\% \text{ of } 90 = 18
  2. Subtract it from the original price.90−18=7290 - 18 = 72
  3. One-step method. Work out what fraction you keep.100%−20%=80%100\% - 20\% = 80\%
  4. Write that as a decimal multiplier.80%=0,8080\% = 0{,}80
  5. Multiply once.90×0,80=7290 \times 0{,}80 = 72
  6. Check the answer is smaller than the original, since it was a decrease.72<90✓72 < 90 \quad\checkmark

Practice

Use the multiplier method, then check with the two-step method.

1
Increase 200 by 15%\text{Increase } 200 \text{ by } 15\%
Answer200×1,15=230200 \times 1{,}15 = 230
2
Decrease 60 by 25%\text{Decrease } 60 \text{ by } 25\%
Answer60×0,75=4560 \times 0{,}75 = 45
3
A price of 48 rises by 10%\text{A price of } 48 \text{ rises by } 10\%
Answer52,8052{,}80
4
What multiplier increases by 8%?\text{What multiplier increases by } 8\%?
Answer1,081{,}08
5
What multiplier decreases by 5%?\text{What multiplier decreases by } 5\%?
Answer0,950{,}95
6
A price rises 10% then falls 10%. Is it back to the start?\text{A price rises } 10\% \text{ then falls } 10\%. \text{ Is it back to the start?}
AnswerNo. 100→110→99 — the fall is taken from a larger amount.\text{No. } 100 \to 110 \to 99 \text{ — the fall is taken from a larger amount.}
Next step
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