Lesson 11: Percents

New Concept

This course builds your mathematical foundation, showing how numbers can be represented as fractions, decimals, and percents to solve a variety of problems.

What’s next

To begin, we'll explore a key connection: percents. You’ll see worked examples on converting fractions to percents and applying them to word problems.

Property

The word percent means per hundred. The denominator 100 is indicated by the word percent or by the symbol %. One hundred percent equals one whole, so $50\%$ means $\frac{50}{100}$.

Examples

• Twenty-five percent is just a quarter in disguise: $25\% = \frac{25}{100} = \frac{1}{4}$.
• A perfect score is one whole thing: $100\% = \frac{100}{100} = 1$.
• A tiny slice of the pie: $5\% = \frac{5}{100} = \frac{1}{20}$.

Explanation

Think of a percent as a secret identity for a fraction whose denominator is always 100. It's like a superhero's code name! Instead of saying you ate $\frac{1}{2}$ the pizza, you can sound fancier by saying you ate 50% of it. It’s all about showing parts of a whole, but with style.

Property

To convert a fraction to a percent, multiply the fraction by 100%. For example, $\frac{1}{3} \cdot 100\% = \frac{100\%}{3} = 33\frac{1}{3}\%$.

Examples

• The easy way with a friendly denominator: $\frac{3}{4} = \frac{3 \cdot 25}{4 \cdot 25} = \frac{75}{100} = 75\%$.
• The universal method for any fraction: $\frac{5}{8} \cdot 100\% = \frac{500\%}{8} = 62\frac{1}{2}\%$.
• For repeating decimals, keep the fraction: $\frac{2}{3} \cdot 100\% = \frac{200\%}{3} = 66\frac{2}{3}\%$.

Explanation

Ready to give a plain old fraction a flashy promotion? Just multiply it by 100%! This simple trick instantly transforms it into its percent equivalent. If the fraction’s denominator is a factor of 100 (like 4, 5, or 20), you can also create an equivalent fraction over 100 for a quick conversion.

Property

To perform calculations with percents, we first convert the percent to a fraction. For example, $40\% = \frac{40}{100} = \frac{2}{5}$.

Examples

• A simple conversion: $70\% = \frac{70}{100} = \frac{7}{10}$.
• With a mixed number percent: $37\frac{1}{2}\% = \frac{37.5}{100} = \frac{375}{1000} = \frac{3}{8}$.
• For a small percentage: $4\% = \frac{4}{100} = \frac{1}{25}$.

Explanation

To change a percent back into a familiar fraction, just take the number, drop the % symbol, and place it over 100. That’s it! The percent has revealed its true fractional form. Don’t forget to simplify the fraction to its most handsome, reduced self, because nobody likes a clunky, unsimplified fraction at the dinner table.