## Percentages

 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) To write a number as a percentage you have to know how many hundredths it contains:

 Examples Answers 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 third onehalf 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: x100 × (the quantity)

 Example Answer Find 40% of 500 Write 40% as a fraction OR as a decimal and then multiply it by 500. Either 500 × 0.40 = 200OR500 × 40/100 = 200

One quantity as a percentage of another quantity:

To find a out of b as a percentage. Calculate: ab × 1001

 Example Answer 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. Applications
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
= 100 − 52 − 42
= 6%

 Fiction 9000 × 0.52 =4680 Non-fiction 9000 × 0.42 =3780 Reference 9000 × 0.06 = 540
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

### 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. Topic 6 Harder Number Work Includes percentage increase and decrease, profit and loss and discounts. Topic 47