What percent of 284 is 71 ?
The Correct Answer and Explanation is :
To find what percent 71 is of 284, we use the following formula for percentage calculation:
[
\text{Percent} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100
]
In this case:
- The part is 71.
- The whole is 284.
Step-by-Step Calculation:
- Divide the part by the whole:
[
\frac{71}{284} = 0.25
] - Multiply the result by 100 to convert it into a percentage:
[
0.25 \times 100 = 25
]
So, 71 is 25% of 284.
Explanation of the Formula:
The formula (\text{Percent} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100) is derived from the basic concept of finding a fraction of a number. Here’s why it works:
- Part represents the quantity you’re comparing (71 in this case).
- Whole represents the total quantity (284 in this case).
- The ratio (\frac{\text{Part}}{\text{Whole}}) gives you the fraction of the whole that the part represents. Multiplying by 100 converts that fraction into a percentage.
For example:
- If you were asked “What percent is 71 of 284?” you’re essentially determining how much of 284 is represented by 71 as a fraction of the whole.
- If the part is equal to the whole, the result would be 100%, meaning the part is 100% of the whole.
Real-Life Application:
Knowing how to find percentages is useful in everyday situations, such as:
- Understanding discounts (e.g., 25% off of an item priced at $284 is $71 off).
- Calculating scores or grades in exams (e.g., if a student scored 71 out of 284 points, their score is 25%).
- Financial calculations like interest rates, tax rates, or even when dealing with tips in restaurants.
This process helps break down complex numbers into understandable, actionable information, which can be used in numerous fields such as business, education, and finance.