Lesson 1: 6-1 Understand Percent

Property

A percent is a ratio that compares a number to 100.
The symbol % means "per hundred," so any percent can be written as a fraction with a denominator of 100.

Property

A percent is a ratio that compares a number to 100. To write a fraction as a percent, create an equivalent fraction with a denominator of 100. The numerator of this new fraction is the percent.

Examples

Property

$100\% = 1$ (the complete whole)
This means that 100% represents the entire quantity or the complete amount of something.

Examples

Property

Visual models like the bar (tape) model and the double number line help illustrate percent problems. A bar is divided into equal parts representing friendly percentages (like $10\%$ or $25\%$). A double number line draws a correspondence between the percent scale (from $0\%$ to $100\%$) and the quantity scale (from 0 to the whole amount), allowing for visual calculation.

Examples

• To find $40\%$ of 30, draw a bar model with 10 sections. The whole bar is 30, so each section is $30 \div 10 = 3$. Shading 4 sections for $40\%$ gives $4 \times 3 = 12$.
• A recipe needs 2 cups of sugar, which is $25\%$ of the total ingredients. Using a bar model with 4 sections (each $25\%$), one section is 2 cups. The total is $4 \times 2 = 8$ cups.
• On a double number line, 15 minutes corresponds to $20\%$. To find how long it takes to reach $100\%$, you can see that $100\%$ is $5 \times 20\%$. So the total time is $5 \times 15 = 75$ minutes.

Explanation

Models like bar diagrams and double number lines turn tricky percent problems into pictures. They help you visually connect the part, the whole, and the percent, making it much easier to see the relationship and find the answer.