Understanding Percentages

A percentage is a way of expressing a number as a fraction of 100 (per cent meaning “per hundred” in Latin).
It is often denoted using the percent sign (%).
Percentages are used to express a proportion of a whole.
For example, 45% means 45 out of 100.

Calculating Percentages

To find a percentage of a number or an amount, you multiply that number by the percentage, then divide by 100.
For example, to find 20% of 50, multiply 50 by 20 and then divide by 100.
Alternatively, you can express the percentage as a decimal (20% = 0.20) or a fraction (20% = 20/100 = 1/5), and multiply by the number directly.

To convert a percentage to a decimal, divide by 100. E.g. 20% = 20 / 100 = 0.20.
To convert a decimal to a percentage, multiply by 100. E.g. 0.20 = 0.20 * 100 = 20%.
To convert a fraction to a percentage, divide the numerator (top number) by the denominator (bottom number), then multiply the result by 100. E.g. 1/5 = 1 ÷ 5 = 0.20, and 0.20 * 100 = 20%.
To convert a percentage to a fraction, write the percentage as the numerator of a fraction with 100 as the denominator, then simplify if possible. E.g. 20% = 20 / 100 = 1/5.

To increase a number by a percentage, add that percentage of the number to the original number. For example, to increase 50 by 20%, find 20% of 50, then add it to 50.
To decrease a number by a percentage, subtract that percentage of the number from the original number. For example, to decrease 50 by 20%, find 20% of 50, then subtract it from 50.

A percentage increase or decrease measures the relative change in an amount.
The formula for calculating percentage change is: (new amount - original amount) ÷ original amount * 100.
For example, if a quantity changes from 50 to 60, the percentage change is: (60 - 50) ÷ 50 * 100 = 20%.

Be prepared to use percentages in the context of a word problem or real-life situation. This might involve calculating the tip on a restaurant bill, working out a reduction in a sale, or determining the impact of an increase in population.