Verified Answer :

  • Identify the part as \(5\) and the whole as \(15\).
  • Calculate the ratio \(\frac{5}{15}\) and simplify it to \(\frac{1}{3}\).
  • Convert the fraction to a percentage by multiplying by \(100\%\).
  • The result is \(\frac{100}{3}\% \approx 33.33\%\), which does not match the provided options.
  • The final answer is \(\boxed{33.33\%}\).

Explanation

  1. Identifying the Part and the Whole

To find what percentage \(5\) is of \(15\), we identify the 'part' as \(5\) and the 'whole' as \(15\). The ratio of a part to a whole is given by the fraction \(\frac{\text{part}}{\text{whole}}\). In this case, we have \(\frac{5}{15}\).

  1. Simplifying the Fraction

Next, we simplify the fraction \(\frac{5}{15}\). By dividing both the numerator and the denominator by their greatest common divisor, which is \(5\), we obtain:
\[\frac{5 \div 5}{15 \div 5} = \frac{1}{3}\]

  1. Converting to a Percentage

To convert the fraction \(\frac{1}{3}\) into a percentage, we multiply it by \(100\%\):
\[\frac{1}{3} \times 100\% = \frac{100}{3}\% \approx 33.33\%\]
Comparing this result to the provided options (a. 10%, b. 20%, c. 30%), we note that none of the choices perfectly matches the exact result of \(33.33\%\). However, the value calculated is the correct mathematical representation of the relationship.

Examples

Percentages are commonly used to describe parts of a whole in everyday life. For instance, if a bakery sells a box of 15 cookies and 5 of them are chocolate chip, you can determine that \(\frac{5}{15} \approx 33.33\%\) of the cookies in the box are chocolate chip. This helps in comparing proportions, such as understanding the composition of a product or analyzing survey results.

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