What is $10 as a percentage of $40 ?
The Correct Answer and Explanation is :
To determine what percentage $10 is of $40, you can use the formula for calculating percentages:
[
\text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100
]
In this case, the “part” is $10, and the “whole” is $40. Plugging these values into the formula gives:
[
\text{Percentage} = \left( \frac{10}{40} \right) \times 100
]
Calculating the fraction:
[
\frac{10}{40} = 0.25
]
Now, multiplying by 100 to convert it to a percentage:
[
0.25 \times 100 = 25
]
Thus, $10 is 25% of $40.
Explanation
Understanding percentages is essential in various real-life situations, from budgeting and finance to statistics and data analysis. A percentage represents a fraction of 100. When you say “X is Y% of Z,” you’re essentially asking how much of Z is represented by X in terms of parts per hundred.
In this example, we are assessing how much $10 is in relation to $40. This can be thought of in terms of proportion. To find out the percentage, we first express the part ($10) as a fraction of the whole ($40). This fraction (0.25) tells us that $10 constitutes one-quarter of $40.
Converting this fraction into a percentage involves multiplying by 100, transforming the decimal representation into a more relatable format—specifically, a part out of 100. This step is crucial for comprehension since most people are accustomed to interpreting values in percentage terms rather than fractions or decimals.
This calculation can also have practical applications. For example, if you’re looking at discounts during shopping, knowing how much a discount ($10) is relative to the original price ($40) can help you make informed decisions. Overall, the concept of percentage is a vital tool for evaluating proportions and making comparisons across various contexts.