Lesson 3-1: Connect Percentages and Proportional Reasoning

Property

A percent is a part-to-whole ratio where the whole is always 100. The symbol % means "per hundred."

Examples

• $45\%$ represents the ratio of 45 to 100, which is written as the fraction $\frac{45}{100}$.
• $150\%$ represents the ratio of 150 to 100, written as the fraction $\frac{150}{100}$.
• $0.5\%$ represents the ratio of 0.5 to 100, written as the fraction $\frac{0.5}{100}$.

Explanation

Understanding a percent as a ratio helps to see it as a comparison between a "part" and a "whole" of 100. This relationship is the foundation for converting percents into fractions and decimals. By writing a percent as a fraction with a denominator of 100, you can easily simplify it or perform calculations. This concept is useful for solving problems like finding a "percent of" a number.

Property

To solve real-world percent problems, identify the known and unknown values (the part, the whole, or the percent) and set up a percent proportion or equation: