What is the percentage representation of 15 out of 75?
The Correct Answer and Explanation is:
To find the percentage representation of 15 out of 75, we can use the following formula:
[
\text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100
]
In this case:
- The part is 15 (the number we are interested in).
- The whole is 75 (the total or the maximum value).
So, we substitute these values into the formula:
[
\text{Percentage} = \left( \frac{15}{75} \right) \times 100
]
Now, we perform the division:
[
\frac{15}{75} = 0.2
]
Next, we multiply the result by 100 to convert it to a percentage:
[
0.2 \times 100 = 20
]
Thus, 15 out of 75 is 20%.
Explanation:
The concept of percentage represents a ratio as a fraction of 100. In the context of this problem, you are trying to determine what percentage 15 is of 75. The basic formula for calculating a percentage is to divide the part (15) by the whole (75) and then multiply by 100. This allows you to express the part as a portion of 100, which is the meaning of percentage.
To further explain, dividing 15 by 75 gives the decimal equivalent of how much of 75 is represented by 15, which is 0.2. Then, by multiplying this decimal by 100, you convert it into the percentage form, yielding 20%.
Understanding percentages is crucial because it helps in comparing parts to a whole in a way that is easy to grasp. For instance, knowing that 15 out of 75 is 20% helps convey that 15 is one-fifth of 75, since 20% is equivalent to 1/5.