4 P4: Percents
Working with Percents
Introduction
Percents are another way to represent parts of a whole — similar to fractions and decimals.
The word percent means per hundred. For example, 40% means 40 out of every 100, or [latex]\dfrac{40}{100}[/latex].
Procedural fluency with percents includes the ability to:
- Find a percent of a number.
- Determine what percent one number is of another.
- Find the whole when given a part and a percent.
- Apply percents in real-world contexts (discounts, tax, and tips).
Understanding the Percent Equation
The relationship among part, whole, and percent can be expressed as:
[latex]\text{part} = \text{percent} \times \text{whole}[/latex]
You can solve for any missing value by rearranging the equation.
| Form | Equation |
|---|---|
| Finding a part | [latex]\text{part} = \text{percent} \times \text{whole}[/latex] |
| Finding a percent | [latex]\text{percent} = \dfrac{\text{part}}{\text{whole}}[/latex] |
| Finding a whole | [latex]\text{whole} = \dfrac{\text{part}}{\text{percent}}[/latex] |
Finding a Percent of a Number
To find a percent of a number, convert the percent to a decimal and multiply.
Example 1
What is 16% of 80?
[latex]0.16 \times 80 = 12.8[/latex]
Answer: 12.80
Example 2
What is 40% of 250?
[latex]0.40 \times 250 = 100[/latex]
Answer: 100
Finding What Percent One Number Is of Another
To find what percent one number is of another, divide the part by the whole and multiply by 100.
Example 3
What percent of 90 is 18?
[latex]\dfrac{18}{90} \times 100 = 20%[/latex]
Answer: 20%
Example 4
Tracey paid $150 for an item originally priced at $330.
[latex]\dfrac{150}{330} \times 100 = 45.5%[/latex]
Answer: Tracey paid 45.5% of the original price.
Finding the Whole Given a Part and a Percent
To find the whole when given the part and percent, divide the part by the percent (in decimal form).
Example 5
27 is 30% of what number?
[latex]\dfrac{27}{0.30} = 90[/latex]
Answer: 90
Example 6
Joyce paid $220, which was 50% of the original price.
[latex]\dfrac{220}{0.50} = 440[/latex]
Answer: The original price was $440.
Applying Percents to Real-World Problems
Example 7 — Tip
At a restaurant, the bill is $80, and you leave a 16% tip.
[latex]0.16 \times 80 = 12.80[/latex]
Tip: $12.80
Example 8 — Discount
A shirt costs $70 and is 30% off.
[latex]0.30 \times 70 = 21[/latex]
Discount = $21
Price after discount: [latex]70 - 21 = 49[/latex]
You pay: $49
Converting Between Fractions, Decimals, and Percents
| Fraction | Decimal | Percent |
|---|---|---|
| [latex]\dfrac{1}{2}[/latex] | 0.5 | 50% |
| [latex]\dfrac{1}{4}[/latex] | 0.25 | 25% |
| [latex]\dfrac{3}{5}[/latex] | 0.6 | 60% |
| [latex]\dfrac{7}{10}[/latex] | 0.7 | 70% |
| [latex]\dfrac{9}{20}[/latex] | 0.45 | 45% |
To convert:
- Percent → Decimal: move the decimal point 2 places left (e.g., 25% → 0.25).
- Decimal → Percent: move the decimal point 2 places right (e.g., 0.6 → 60%).
Common Student Errors and Corrections
| Error | Example | Correction Strategy |
|---|---|---|
| Forgetting to convert percent to decimal | Using 25 instead of 0.25 | Divide by 100 before multiplying. |
| Mixing up part and whole | “What is 30% of 90?” solved as 90 ÷ 0.3 | Emphasize structure: of means multiply. |
| Rounding too early | 45.4545% → 45% | Wait until final answer before rounding. |
| Using incorrect base when finding discount | 30% off of $49 instead of $70 | Always apply percent to the original amount. |
H5P Practice Activities
H5P 1: Fill-in-the-Blank — Find a Percent of a Number
Prompt: Convert percent to decimal, multiply, and simplify.
H5P Placeholder:
Examples
- 16% of 80 →
12.8 - 40% of 250 →
100 - 75% of 180 →
135
H5P 2: Fill-in-the-Blank — Find the Percent
Prompt: Divide part by whole, then multiply by 100.
H5P Placeholder:
Examples
- What percent of 90 is 18? →
20% - 150 is what percent of 330? →
45.5% - 30 is what percent of 99? →
30.3%
H5P 3: Fill-in-the-Blank — Find the Whole
Prompt: Divide the part by the percent (in decimal form).
H5P Placeholder:
Examples
- 27 is 30% of what number? →
90 - 220 is 50% of what number? →
440 - 99 is 25% of what number? →
396
H5P 4: Word Problems — Real-World Applications
Prompt: Read each problem carefully and compute your answer.
H5P Placeholder:
Examples
- A restaurant bill is $80. Leave a 16% tip. →
\$12.80 - A shirt costs $70 and is 30% off. →
\$49 - Joyce paid $220, which was 50% of the original price. →
\$440
Reflection for Pre-Service Teachers
- How can percent problems be connected to fraction and decimal understanding?
- What misconceptions do students often have about “percent increase” vs “percent decrease”?
- What strategies can make percent estimation (like tips or discounts) intuitive?
- How can real-life examples make percent problems more meaningful in elementary classrooms?
Summary
Procedural fluency with percents builds on understanding of fractions and decimals.
Pre-service teachers should help students:
- Recognize the part–whole–percent relationship.
- Accurately convert between forms (fraction, decimal, percent).
- Apply percents to real-world contexts such as tax, tips, and sales.
- Check results for reasonableness through estimation.
By practicing systematically, students develop confidence and efficiency when working with percents.