Page 289 - Math Smart - 7

Finding a quantity given a percentage of the quantity

Example
15% of the fish in an aquarium are goldfish. There are 3 goldfish.
The total number of fish in the aquarium is 20.

Check: 15% of 20 = x 20 = 3

Finding the percentage of one quantity of another quantity

To express Quantity A as a percentage of Quantity B, write Quantity A as a fraction of Quantity B.
Then express the fraction as a percentage by multiplying by 100%.

Examples
a) There are 60 basketball players and 75 football players in Stage 7. Percentage of basketball players
expressed as a percentage of the number of football players in Stage 7 = ^ x 100%
= 80%

b) 13 g expressed as a percentage of 1 kg = x 100% = 1.3%
(The quantities have to be expressed in the same units.)

Mathematics Connect
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Percentages work for you
Whilst doing research work, you may come across data in the form of tables, imsnuuiiHiB- a, i 1
graphs or reports. This can be difficult to read and compare if the data is recorded
in different formats.
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For example, a bookstore owner may be researching book sales figures. The
following table shows the sales of different genres of books of a bookstore in
2017 and 2018.

Year Horror Non-fiction Romance Crime
2017 2.4 46.2 159.7 78.3
2018 2.5 36.6 158.8 87.0
We can convert the number of books sold over the years to percentages to
make it easier to compare the sales across different companies or platforms. For
example, the table below shows that in 2017, 16.1% of the books sold were non-
fiction books, but in 2018, this quantity had fallen to 12.8%.

Year Horror Non-fiction Romance Crime
2017 0.8% 16.1% 55.7% 27.4%
2018 0.9% 12.8% 55.7% 30.6%
The bookstore owner may use this information to decide what books to purchase
or whether to mark up the price of future bestsellers by a percentage.
Percentages are useful for comparing information where the sample sizes or
totals are different. By converting different data to percentages, you can readily
compare them.