Verified Answer :

  • Identify the part (5) and the whole (15).
  • Create the ratio \(\frac{5}{15}\) and simplify it to \(\frac{1}{3}\).
  • Convert the fraction to a percentage by multiplying by 100: \(\frac{1}{3} \times 100 \approx 33.33\%\).
  • The correct option is \(\boxed{33.33\%}\).

Explanation

  1. Understanding the Percentage Problem

To determine what percent 5 is of 15, we identify the part and the whole. Here, the 'part' is 5 and the 'whole' is 15. The formula to calculate the percentage is:
\[\text{Percentage} = \left( \frac{\text{part}}{\text{whole}} \right) \times 100\]
Substituting our values:
\[\text{Percentage} = \left( \frac{5}{15} \right) \times 100\]

  1. Simplifying and Converting to Percentage

We simplify the fraction \(\frac{5}{15}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 5:
\[\frac{5 \div 5}{15 \div 5} = \frac{1}{3}\]
Now, we multiply by 100 to convert the fraction into a percentage:
\[\frac{1}{3} \times 100 = 33.333...\%\]
Rounding to the two decimal places as shown in the options, we get approximately 33.33%.

  1. Conclusion

Comparing our result of 33.33% to the given options (10%, 20%, 33.33%, 30%), it matches the third option perfectly. Therefore, 5 out of 15 is 33.33%. The final answer is \(\boxed{33.33\%}\).

Examples

Percentages are used everywhere in daily life, such as calculating discounts during a sale or determining the grade on an assignment. For instance, if you answer 5 questions correctly out of a 15-question quiz, you can use the same method to find your score: \(\frac{5}{15} \times 100 \approx 33.33\%\). Understanding this helps you quickly grasp proportions and relative values in various real-world situations.

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