Lesson 3: The Percent Proportion

Property

In percent word problems, identify three key components:

• Part: The portion or amount being compared
• Whole: The total amount (often follows the word "of")
• Percent: The rate per 100 (includes % symbol or words like "percent")

Examples

Property

Visual models like the bar (tape) model help illustrate percent problems. A bar is divided into equal parts representing friendly percentages (like $10\%$ or $25\%$). Each section of the bar represents both a portion of the whole quantity and its corresponding percentage, making it easier to visualize the relationship between parts, wholes, and percents.

Examples

Property

Percent problems involve three components: the part ($A$), the whole ($B$), and the percent ($P$). Given any two of these components, the third can be found using the relationship $\frac{A}{B} = \frac{P}{100}$.

1. Find the Part: $A = (\frac{P}{100}) \times B$
2. Find the Percent: $P = (\frac{A}{B}) \times 100$
3. Find the Whole: $B = A \div (\frac{P}{100})$

Examples

• Find the part: A 50 dollar shirt is on sale for $20\%$ off. The discount is $0.20 \times 50 = 10$ dollars.
• Find the percent: You answered 24 out of 30 questions correctly on a test. Your score is $\frac{24}{30} = 0.8$, which is $80\%$.
• Find the whole: 9 students, which is $30\%$ of the class, have brown hair. The total number of students in the class is $9 \div 0.30 = 30$.

Explanation

Every percent problem has three key pieces: the part, the whole, and the percent. If you know any two, you can always find the third. It's like a math detective game where you use the formula to find the missing clue.