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Three students converted fractions to percents. Their results are in this table.
| Student | Fraction | Percent |
|---|---|---|
| Gavin | $2 / 5$ | $40 \%$ |
| Taylor | $21 / 4$ | $225 \%$ |
| Brent | $7 / 4$ | $17.5 \%$ |
Which statement is true?
A. Only Taylor has a correct answer.
B. Only Gavin has a correct answer.
C. Gavin and Brent have correct answers.
D. Gavin and Taylor have correct answers.
Answer (1)
Convert 5 2 to a percentage: 5 2 × 100% = 40% , which matches Gavin's answer.
Convert 4 21 to a percentage: 4 21 × 100% = 525% , which does not match Taylor's answer.
Convert 4 7 to a percentage: 4 7 × 100% = 175% , which does not match Brent's answer.
Only Gavin has a correct answer. $\boxed{Only Gavin has a correct answer.}
Explanation
Problem Analysis We need to check each student's conversion from fraction to percentage to determine who has a correct answer. To convert a fraction to a percentage, we multiply the fraction by 100%.
Checking Gavin's Answer Let's start with Gavin. Gavin converted 5 2 to 40% . To check this, we calculate 5 2 × 100% .
Gavin's Result 5 2 × 100% = 5 200 % = 40% Gavin's conversion is correct.
Checking Taylor's Answer Next, let's check Taylor. Taylor converted 4 21 to 225% . To check this, we calculate 4 21 × 100% .
Taylor's Result 4 21 × 100% = 4 2100 % = 525% Taylor's conversion is incorrect. 4 21 is equal to 525% , not 225% .
Checking Brent's Answer Now, let's check Brent. Brent converted 4 7 to 17.5% . To check this, we calculate 4 7 × 100% .
Brent's Result 4 7 × 100% = 4 700 % = 175% Brent's conversion is incorrect. 4 7 is equal to 175% , not 17.5% .
Conclusion Based on our calculations, only Gavin has a correct answer.
Examples
Understanding how to convert fractions to percentages is useful in many real-life situations. For example, when calculating discounts at a store, you might need to convert a fraction of the original price to a percentage to determine the amount of the discount. Another example is when calculating grades. If a student scores 45 out of 50 on a test, you can convert this fraction (45/50) to a percentage to find the student's grade (90%).
