160 is what percent of 40? Please explain.
The Correct Answer and Explanation is:
To determine what percent 160 is of 40, use the following formula: Percentage=(PartWhole)×100\text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100Percentage=(WholePart)×100
In this case, the part is 160 and the whole is 40: Percentage=(16040)×100=4×100=400%\text{Percentage} = \left( \frac{160}{40} \right) \times 100 = 4 \times 100 = 400\%Percentage=(40160)×100=4×100=400%
Explanation
To understand what it means to find what percent one number is of another, consider the general concept of percentages. A percentage represents a ratio or a fraction out of 100. When expressing one number as a percentage of another, the idea is to determine how many times the second number fits into the first, and then express that relationship on a scale from 0 to 100 (or more, if it exceeds the base).
In this case, the goal is to find what percent 160 is of 40. Begin by recognizing that the word “of” in mathematics typically indicates multiplication or comparison to a whole. Here, 40 serves as the reference or base value, and the task is to determine how large 160 is in comparison to 40.
To solve this, divide 160 by 40, which gives the value 4. This result indicates that 160 is four times as large as 40. Since percentages are based on 100, multiply this result by 100 to convert it to a percentage. This gives 4 × 100 = 400%.
The interpretation is that 160 is 400% of 40. This means 160 is not only equal to 40, but is four times greater than it. Any time the result exceeds 100%, it indicates that the part being considered is more than the whole. A 100% result would indicate that both values are equal, while anything less than 100% would indicate the part is smaller than the whole.
This concept is foundational in arithmetic and applied across financial analysis, statistics, and everyday problem-solving.
