LESSON 8
PERCENTAGES
Parts Per Hundred
What is a Percentage?
A percentage is a way of expressing a number as a fraction of 100. The word 'percent' comes from the Latin 'per centum', meaning 'out of one hundred'. The symbol for percent is %.
Percentages are used everywhere in daily life — sales discounts, test scores, interest rates, statistics, and nutrition labels all use percentages. Understanding them is one of the most practical math skills you can develop.
Converting Between Fractions, Decimals, and Percents
Fractions, decimals, and percentages are three ways to express the same value. To convert a fraction to a percent, divide the numerator by the denominator and multiply by 100. To convert a decimal to a percent, multiply by 100. To convert a percent to a decimal, divide by 100.
Finding a Percent of a Number
To find a percentage of a number, convert the percent to a decimal and multiply. For example, to find 30% of 80, convert 30% to 0.30 and multiply: 0.30 × 80 = 24. A quick mental trick: 10% of any number is just that number divided by 10.
Percent Increase and Decrease
Percent change tells us how much something has grown or shrunk relative to its original value. To find percent change, subtract the original from the new value, divide by the original, and multiply by 100. A positive result is an increase; a negative result is a decrease.
Finding the Whole from a Percent
Sometimes you know the percent and the part, and need to find the whole. Divide the part by the percent (written as a decimal). This is the reverse of finding a percent of a number and is useful for working backwards from a sale price or a test score.
Key Facts
100% means the whole thing. 50% means half. 200% means twice as much as the original.
The percent symbol (%) evolved from the Italian 'per cento', which was abbreviated over centuries into the modern % sign.
A 20% tip on a $35 bill is easy to calculate: 10% = $3.50, so 20% = $7.00.
Interest rates on loans and savings accounts are expressed as percentages — understanding them can save or earn you thousands of dollars over a lifetime.