This question asks us to find the percentage that one quantity of time represents out of another quantity of time. To do this accurately, we need to ensure that both quantities are expressed in the same unit.

Understanding Percentage of Time

A percentage is a way to express a part of a whole as a fraction of 100. The formula for calculating percentage is:

$$ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100\% $$

In this problem, the "Part" is 15 seconds, and the "Whole" is 3 minutes. We need to convert the "Whole" into seconds to match the unit of the "Part".

Step-by-Step Calculation: Converting Minutes to Seconds

We know that:

• 1 minute = 60 seconds

So, to convert 3 minutes to seconds, we multiply the number of minutes by 60:

$$ 3 \text{ minutes} = 3 \times 60 \text{ seconds} $$

$$ 3 \text{ minutes} = 180 \text{ seconds} $$

Now we have both quantities in the same unit:

• Part = 15 seconds
• Whole = 180 seconds

Calculating the Percentage

Now we can use the percentage formula:

$$ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100\% $$

Substitute the values:

$$ \text{Percentage} = \left( \frac{15 \text{ seconds}}{180 \text{ seconds}} \right) \times 100\% $$

$$ \text{Percentage} = \left( \frac{15}{180} \right) \times 100\% $$

Simplify the fraction $\frac{15}{180}$. Both 15 and 180 are divisible by 15:

$$ \frac{15 \div 15}{180 \div 15} = \frac{1}{12} $$

So, the calculation becomes:

$$ \text{Percentage} = \frac{1}{12} \times 100\% $$

$$ \text{Percentage} = \frac{100}{12}\% $$

Simplify the fraction $\frac{100}{12}$ by dividing both numerator and denominator by their greatest common divisor, which is 4:

$$ \frac{100 \div 4}{12 \div 4} = \frac{25}{3} $$

So, the percentage is $\frac{25}{3}\%$.

Converting Improper Fraction to Mixed Number

The result $\frac{25}{3}\%$ is an improper fraction. To express it as a mixed number, we divide 25 by 3:

• 25 divided by 3 is 8 with a remainder of 1.

So, $\frac{25}{3}$ can be written as $8 \frac{1}{3}$.

Therefore, 15 seconds is $8 \frac{1}{3}\%$ of 3 minutes.

Summary of the Calculation

Here is a summary of the steps:

1. Convert 3 minutes to seconds: $3 \text{ minutes} = 3 \times 60 = 180 \text{ seconds}$.
2. Set up the percentage calculation: $\frac{\text{Part}}{\text{Whole}} \times 100\% = \frac{15}{180} \times 100\%$.
3. Simplify the fraction: $\frac{15}{180} = \frac{1}{12}$.
4. Calculate the percentage: $\frac{1}{12} \times 100\% = \frac{100}{12}\%$.
5. Simplify the resulting fraction: $\frac{100}{12}\% = \frac{25}{3}\%$.
6. Convert the improper fraction to a mixed number: $\frac{25}{3}\% = 8 \frac{1}{3}\%$.

Revision Table: Percentage Calculations and Time Units

Additional Information on Time Units and Percentages

Understanding how to convert between different units of time is crucial for solving many problems. The basic conversions are:

• 1 minute = 60 seconds
• 1 hour = 60 minutes
• 1 hour = 3600 seconds (60 minutes * 60 seconds/minute)
• 1 day = 24 hours

When calculating percentages involving different units, always convert to the smaller unit to avoid fractions in the initial values (e.g., converting minutes to seconds rather than seconds to minutes, which would give 15 seconds = 0.25 minutes).

Percentage calculations are widely used in various fields, including finance (interest rates), statistics, and everyday comparisons.