Percentages (I) · Ages 12–13
Percentage increase and decrease
A percentage change is always of the original.
How to do it
Method
A percentage change is always of the original
120 up 20%: 120 × 20% = 24, 120 + 24 = 144
Another way
One multiplication
120 × (1 + 20%) = 120 × 1.2 = 144
In full
A percentage change is always taken on the original value: change = original × rate. 120 up by 20%: one way, find the increase first, 120 × 20% = 24, so the new value is 120 + 24 = 144. Another, in one step: up 20% means it becomes 120% of the original, 120 × 1.2 = 144. Down 20% means it becomes 80%: 120 × 0.8 = 96. The other way round, the percentage change = the change ÷ the original × 100%. From 80 up to 100 is 20 ÷ 80 × 100% = 25% up; from 100 down to 80 is 20 ÷ 100 × 100% = 20% down. The same gap of 20, on a different base, makes a different percentage.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Each box in the picture stands for the same amount, and the top row is 20. The bottom row is % more than the top, and it is .
Fill in each blank
Show the answer and working
Answer: 100, 40
The top has 4 boxes and the bottom 8, 4 more: 4 ÷ 4 × 100% = 100%. A box is 20 ÷ 4 = 5, so the bottom row is 8 × 5 = 40.
Example 2
From 300 down to 180: what is the percentage decrease?
- A. 40%
- B. 60%
- C. 66.7%
- D. 120%
Choose the right answer
Show the answer and working
Answer: A. 40%
It fell by 300 − 180 = 120, and 120 ÷ 300 × 100% = 40%.
Example 3
A price goes up from $200 to $239. By what percentage did it increase?
Show the answer and working
Answer: 19.5%
It went up by 239 − 200 = 39, and 39 ÷ 200 × 100% = 19.5%. A percentage can be a decimal.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.290 decreased by 40%: the new value =
Answer:
2.60 increased by 30% is 78.
True or false?
Answer:
3.From 200 down to 150: what is the percentage decrease?
- A. 75%
- B. 33.3%
- C. 25%
- D. 50%
Choose the right answer
Answer:
4.From 40 up to 52: the percentage increase = %
Answer:
5.From 160 up to 400 is a 150% increase. From 400 down to 160, what is the percentage decrease?
- A. 150%
- B. 60%
- C. 40%
- D. 240%
Choose the right answer
Answer:
All the answers
- 1. 174
- 2. True
- 3. C. 25%
- 4. 30
- 5. B. 60%
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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