Rewrite this fraction problem as a percent problem.
Find $\frac{3}{5}$ of 250.
Find □ % of 250.
To rewrite the fraction problem "Find \(\frac{3}{5}\) of 250" as a percentage problem, we need to convert the fraction \(\frac{3}{5}\) into a percentage equivalent. A percentage represents a part of 100, where \(x\%\) is equivalent to the ratio \(\frac{x}{100}\). Our objective is to find the value of \(x\) such that \(\frac{3}{5} = \frac{x}{100}\).
To convert any fraction \(\frac{a}{b}\) into a percentage, we multiply the fraction by 100%. This is based on the relationship:
\[\text{Percentage} = \left( \frac{a}{b} \right) \times 100\%\]
Applying this to our fraction \(\frac{3}{5}\), we calculate:
\[\frac{3}{5} \times 100\% = 3 \times \left( \frac{100\%}{5} \right) = 3 \times 20\% = 60\%\]
This confirms that 60% is equivalent to the fraction \(\frac{3}{5}\).
We can verify this result by calculating the value of both expressions.
First, for the original fraction:
\[\frac{3}{5} \times 250 = 3 \times \frac{250}{5} = 3 \times 50 = 150\]
Second, for our calculated percentage:
\[60\% \text{ of } 250 = \frac{60}{100} \times 250 = 0.6 \times 250 = 150\]
Since both calculations yield 150, the fraction \(\frac{3}{5}\) is indeed equivalent to 60%. Therefore, the problem "Find \(\frac{3}{5}\) of 250" can be rewritten as "Find \(\boxed{60}\)% of 250".
Percentages are used extensively in everyday life, such as when calculating shopping discounts. For example, if a store offers a 60% discount on a item priced at \$250, you can determine the savings by calculating 60% of \$250. Converting fractions to percentages helps you quickly understand the proportion of a whole, making it easier to manage finances, compare data, or analyze growth. Understanding this relationship allows for faster mental math and clearer decision-making in commercial situations.