Question

1. find the error a student used equivalent ratios to find what percent 15 is of 300. find the student’s mistake and correct it. \\(\frac{45}{300} = \frac{15}{100}\\) 15 is 45% of 300.

Explanation:

Step1: Recall percent proportion formula

The correct proportion to find what percent \( a \) is of \( b \) is \( \frac{a}{b}=\frac{p}{100} \), where \( p \) is the percentage. Here, \( a = 15 \), \( b=300 \), so the proportion should be \( \frac{15}{300}=\frac{p}{100} \), not \( \frac{45}{300}=\frac{15}{100} \). The student incorrectly set up the numerator of the first fraction (used 45 instead of 15) and the denominator of the second fraction (used 100 as denominator for 15 instead of for percentage).

Step2: Solve the correct proportion

From \( \frac{15}{300}=\frac{p}{100} \), cross - multiply: \( 300p=15\times100 \).
\( 300p = 1500 \).
Divide both sides by 300: \( p=\frac{1500}{300}=5 \).

Answer:

The student's mistake was in the setup of the equivalent ratios. The correct proportion is \( \frac{15}{300}=\frac{p}{100} \), and solving it gives that 15 is \( 5\% \) of 300.