Percentages (II) · Ages 13–14
Changes in the parts
Parts multiplied: multiply the factors. Parts divided: divide them.
How to do it
Method
Parts multiplied: multiply the factors. Parts divided: divide them
1.2 × 0.9 = 1.08: the area is up 8%
Another way
Put numbers in
12 × 9 = 108, 108 ÷ 100 = 1.08
In full
Some quantities are made by multiplying or dividing others: area = length × width, takings = price × number sold, speed = distance ÷ time. When the parts change by percentages, multiply or divide their factors. Length up 20% and width down 10%: one way, multiply the factors, 1.2 × 0.9 = 1.08, so the area is up 8%, not 20% − 10% = 10%; another, put numbers in: say the length and the width are both 10, then the new area is 12 × 9 = 108, 8% more than 100. Dividing works alike: distance up 20% and time up 50% make the speed 1.2 ÷ 1.5 = 0.8 times as much, 20% down. Where the parts are added (all the people = men + women), each part's change counts by its size; the percentages don't simply add.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The price rises 10% and the number sold rises 20%: the takings rise %
Show the answer and working
Answer: 32
Takings = price × sales: (1 + 10%) × (1 + 20%) = 1 + 32%. The factors multiply, a little more than 10% + 20%.
Example 2
An item's price goes up 10% and its sales fall 40%. Its takings (price × number sold) become what percentage of before?
- A. 70%
- B. 154%
- C. 60%
- D. 66%
Choose the right answer
Show the answer and working
Answer: D. 66%
(1 + 10%) × (1 − 40%), that is 66% of before.
Example 3
The distance grows 50% and the time taken falls 60%: the speed becomes times as much, % more.
Fill in each blank
Show the answer and working
Answer: 3.75, 275
Speed = distance ÷ time, so the factors divide: (1 + 50%) ÷ (1 − 60%) = 3.75, 275% more.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.A triangle's base grows 50% and its height shrinks 25%: its area becomes times as much, % more.
Fill in each blank
Answer:
2.An item's price goes up 50% and its sales fall 10%. Its takings (price × number sold) become what percentage of before?
- A. 135%
- B. 140%
- C. 90%
- D. 165%
Choose the right answer
Answer:
3.Over the same distance, a speed 300% higher cuts the time by 300%.
True or false?
Answer:
4.Takings = price × number sold. The price falls 36%. By what percentage must sales rise to keep the takings the same?
- A. 36%
- B. 56.25%
- C. 64%
- D. 156.25%
Choose the right answer
Answer:
5.A club has 600 men and 600 women. This year the men grow by 15% and the women fall by 10%: the membership grows by %
Answer:
All the answers
- 1. 1.125, 12.5
- 2. A. 135%
- 3. False
- 4. B. 56.25%
- 5. 2.5
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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