College

Error Analysis

Raquel writes [tex]\frac{12}{25}[/tex] as the ratio 12:25. She incorrectly finds the equivalent percent to be 12%.

What percent is equivalent to [tex]\frac{12}{25}[/tex]? What is Raquel's error?

- 48% is equivalent to [tex]\frac{12}{25}[/tex].

Raquel's error was in calculating the percentage. She likely confused the numerator with the percent value. To find the correct percent, divide 12 by 25 and multiply by 100 to get 48%.

Answer :

To find the equivalent percent of the ratio [tex]\( \frac{12}{25} \)[/tex], we need to convert the fraction into a percentage.

1. Understanding the Fraction: The fraction [tex]\(\frac{12}{25}\)[/tex] means 12 parts out of a total of 25 parts.

2. Converting to Percent: To convert a fraction to a percent, you divide the numerator by the denominator and then multiply the result by 100. This is because a percent represents parts out of 100.

3. Calculation:
- Divide 12 by 25: [tex]\( \frac{12}{25} = 0.48 \)[/tex].
- Multiply 0.48 by 100 to convert it to a percent:
[tex]\[
0.48 \times 100 = 48\%
\][/tex]

Therefore, [tex]\(\frac{12}{25}\)[/tex] is equivalent to 48%.

Raquel's Error:
Raquel incorrectly found the percent to be 12%. Her mistake was assuming that the numerator, 12, directly represents the percent without considering the denominator. Raquel should have calculated by converting the whole fraction [tex]\(\frac{12}{25}\)[/tex] to a percent following the steps above.