Lesson 4: Percentages

Property

The word percent comes from the Latin phrase, per centium, literally “of one hundred.” Percents are a special type of fraction with a denominator of 100. Percents represent fractions or decimals and means, “per hundred.” The symbol “%” is used to represent percent. For example, 25% means 25 per hundred, $\frac{25}{100}$, or $0.25$.

Examples

• 45% means 45 out of 100. As a fraction, it is $\frac{45}{100}$ (or $\frac{9}{20}$ simplified), and as a decimal, it is $0.45$.
• A score of 18 out of 20 on a quiz is equivalent to $\frac{18}{20} = \frac{90}{100}$, which is 90%.
• 200% represents 200 per 100, or $\frac{200}{100} = 2$. It means two times the original amount.

Explanation

Percent is just a special way of talking about fractions that means “out of one hundred.” Using a common denominator of 100 makes it super easy to compare different parts of a whole, like comparing test scores or discounts.

Property

To estimate the percent of a number, round the percent to a nearby benchmark percent that is easy to calculate mentally. Common benchmark percents include $10\% = \frac{1}{10}$, $25\% = \frac{1}{4}$, $50\% = \frac{1}{2}$, and $75\% = \frac{3}{4}$.

Examples

Property

When given a part and its corresponding percent, use the percent proportion $\frac{\text{part}}{\text{whole}} = \frac{\text{percent}}{100}$ and solve for the whole by rearranging to $\text{whole} = \frac{\text{part} \cdot 100}{\text{percent}}$.

Examples