a. 160 is what percentage of 40?
b. 40 is 160% of what number?
c. What number is 40% of 160?
The Correct Answer and Explanation is:
To solve the problems presented, we will break each one down step by step.
a. 160 is what percentage of 40?
To find out what percentage 160 is of 40, we can use the formula:
[
\text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100
]
Here, the “Part” is 160, and the “Whole” is 40:
[
\text{Percentage} = \left( \frac{160}{40} \right) \times 100 = 4 \times 100 = 400\%
]
So, 160 is 400% of 40.
b. 40 is 160% of what number?
To find the number of which 40 is 160%, we can rearrange the percentage formula:
[
\text{Part} = \text{Percentage} \times \text{Whole}
]
Here, the “Part” is 40, and the “Percentage” is 160% (or 1.6 in decimal form):
[
40 = 1.6 \times \text{Whole}
]
To find the “Whole”, we can rearrange the equation:
[
\text{Whole} = \frac{40}{1.6} = 25
]
So, 40 is 160% of 25.
c. What number is 40% of 160?
To find 40% of 160, we will again use the percentage formula:
[
\text{Part} = \text{Percentage} \times \text{Whole}
]
Here, the “Percentage” is 40% (or 0.4 in decimal form) and the “Whole” is 160:
[
\text{Part} = 0.4 \times 160 = 64
]
So, 40% of 160 is 64.
Explanation
Understanding percentages is crucial in mathematics and everyday applications. Percentages express a number as a fraction of 100, providing a straightforward way to compare ratios. In the first problem, we determined how much larger 160 is compared to 40 by calculating that it is 400% of it, meaning it is four times the value of 40.
In the second problem, we rearranged the percentage formula to find the original number (25) from which 40 is 160%. This demonstrates how percentages can help us understand proportions and conversions between values.
Lastly, the calculation of 40% of 160 illustrates the application of percentages in finding parts of a whole, which is especially useful in various contexts, such as finance, statistics, and data analysis. Percentages help quantify changes, comparisons, and relationships, making them a fundamental concept in both mathematical theory and practical usage. Understanding these concepts equips individuals with the tools to interpret information critically and make informed decisions in real-life situations.