| A percentage is a way of writing a fraction with a denominator of 100. Percentage means "out of 100" or "parts per hundred" Calculations involving percentages often require multiplication or division by 100. x percent, written x%, means x⁄100 (or x parts out of 100) |
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To write a number as a percentage you have to know how many hundredths it contains:
| Write 34 hundredths as a percentage | 34 hundredths = 34% |
| Write 3 tenths as a percentage | 3 tenths = 30 hundredths = 30% |
|
Write the fraction 7⁄10 as a percentage |
7⁄10 = 70 hundredths = 70% |
You should remember these often used percentages:
| Percentage |
0%
|
10%
|
25%
|
33%
(approx.) |
50%
|
67%
(approx.) |
75%
|
100%
|
| Fraction | nothing |
one
tenth |
one
quarter |
one |
one |
two
thirds |
three quarters
|
one whole
(everything!) |
Percentage Calculations
Below are some of the types of problem that use percentages.
Percentage of a quantity:
To find x percent of a quantity. Calculate: x⁄100 × (the quantity)
|
Find 40% of 500 |
Write 40% as a fraction OR as a decimal and then multiply it by 500. Either 500 × 0.40 = 200 |
One quantity as a percentage of another quantity:
To find a out of b as a percentage. Calculate: a⁄b × 100⁄1
|
Write 16 out of 25 as a percentage |
Write 16 out of 25 as a fraction and then multiply it by 100. 16⁄25 × 100⁄1 = 64% OR Write 16 out of 25 as a fraction and then find the equivalent fraction with a denominator of 100.
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Applications
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| a | In a library, 52% of the books are fiction, 42% are non-fiction and the rest are reference books. If the library has 9000 books how many of each type does it have? |
The percentage of reference books
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| b |
A man has a total weight of 80 kg. His muscles weigh 32 kg. What percentage of his weight is muscle? |
Percentage of muscle = 32/ 80 = 40% | |||||||
|
c
|
A sausage weighs 96 grams and 15% of the sausage is fat. How many grams of fat are there in the sausage?
|
 |
Weight of fat = 96 × 0.15 = 14.4 grams
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Further Work on Percentages
There are several other types of calculations that use percentages and these are covered in other topics:
| Conversions | Fractions <--> Decimals <--> Percentages. | |
| Harder Number Work | Includes percentage increase and decrease, profit and loss and discounts. |
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