What is a percentage?
A percent means per 100. To express
a percentage we use the symbol %.
Percentages are used to describe the proportion of a
quantity in relation to the number 100, i.e. 100% is the
whole amount and 50% is half of the amount.
Writing percentages
To find a number as a percentage of another
number, write it as a fraction and multiply by 100%.
Example:
Examples:
• 35% means “35 out of 100”.
• “11% of students walk to school” means “11 out of every 100 students walk to school”.
MATHS FLASHCARDS: percentages
Percentages greater
than 100%
MATHS FLASHCARDS: percentages
Percentages as decimals
Percentages are usually between 0 and 100, because
100% means a whole, but they can also be greater
than 100%.
To write a percentage as a decimal, divide it by 100.
Examples:
• 200% of an amount means double that amount.
• 300% of an amount means triple that amount.
• 150% of an amount means one and a half times that amount.
MATHS FLASHCARDS: percentages
Examples:
• 24% = 24 ÷ 100 = 0.24
• 6% = 6 ÷ 100 = 0.06
• 150% = 150 ÷ 100 = 1.5
MATHS FLASHCARDS: percentages
Percentages as fractions
To write a percentage as a fraction, first write
it over 100, then simplify it into its lowest terms by
cancelling the highest common factor of the numerator
and denominator.
Example:
MATHS FLASHCARDS: percentages
Percentage change
To find the percentage increase or decrease
between two amounts, use the formula:
Example:
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Percentages of amounts
To find a percentage of an amount, think of the “of” as
“×”.
Example:
10% of 30 means 10% × 30
Calculate this as: (10 ÷ 100) × 30 or 0.1 × 30
= 3
MATHS FLASHCARDS: percentages
Increasing by a percentage
To increase an amount by x%, multiply the
amount by (100 + x)%.
Example:
To increase 50 by 10%, calculate 50 × 110%,
i.e. 50 × 1.1 = 55.
MATHS FLASHCARDS: percentages
Decreasing by
a percentage
To decrease an amount by x%, multiply the amount by
(100 – x)%.
Example:
To decrease 50 by 10%, calculate 50 × 90%,
i.e. 50 × 0.9 = 45.
Compound percentages 1
A compound percentage is a percentage that
is applied repeatedly to an amount, for example
compound interest in banking.
The formula for finding the amount, A, after a
percentage r % is applied every t years to an original
(principal) amount P is:
A = P(1 + r/100)t
MATHS FLASHCARDS: percentages
MATHS FLASHCARDS: percentages
Compound percentages 2
An example of compound percentage:
$200 is invested for 5 years at an interest rate of 2%.
After these 5 years, the amount A is:
A = 200 (1 + 2/100)5 = 200 (1.02)5 = $220.82 MATHS FLASHCARDS: percentages
Finding the
original amount
To find the original amount after a percentage increase
or decrease, call the original amount “x” and write an
equation to solve for x.
Example:
An item costs $18 in a 20% off sale. To decrease an
amount by 20%, multiply the amount by (100 – 20)%.
x × (100 – 20)% = 18
x = 18 ÷ (100 – 20)%
x = 18 ÷ 80% = 18 ÷ 0.8 = $22.50
MATHS FLASHCARDS: percentages