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Chapter 11: Problem 4

17 is what percent of \(85 ?\)

Short Answer

Expert verified
17 is 20% of 85.

Step by step solution

01

Understand the Problem

The question asks to find out what percent 17 is of 85. To find this, we need to use the formula for percentage: \[\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100\]. In this case, the part is 17 and the whole is 85.
02

Set Up the Formula

Plug the given values into the percentage formula: \[\text{Percentage} = \frac{17}{85} \times 100\].
03

Perform the Division

Divide 17 by 85: \[\frac{17}{85} = 0.2\].
04

Multiply by 100

Finally, multiply the result by 100 to convert it to a percentage: \[0.2 \times 100 = 20\].
05

Conclusion

So, 17 is 20% of 85.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

percentage formula
To calculate percentages, we use a basic formula that relates the part to the whole. The percentage formula is \[\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100\]. Here鈥檚 how it works:
- The 'Part' is the number you are trying to find the percentage for.
- The 'Whole' is the total or whole number around which you are calculating the percentage.
For example, in the exercise where 17 is what percent of 85, 17 is the 'Part,' and 85 is the 'Whole.'
By following the formula, you can solve for the percentage easily.
division
Division is a fundamental arithmetic operation where one number, the dividend, is divided by another, the divisor. The objective in division is to see how many times the divisor fits into the dividend.
In our exercise, we need to find out the fraction of 17 to 85, which involves division. To do this: \[ \frac{17}{85} = 0.2 \]. This means 17 goes into 85 approximately 0.2 times.
Knowing how to perform basic division well can help with breaking down more complex problems and understanding parts of wholes better.
multiplication
Multiplication is another core mathematical operation that involves adding a number to itself a certain number of times. In the context of percentages, multiplication helps convert a decimal into a percentage.
After performing the division, you come up with a decimal. For example, in our exercise, the division results in 0.2. To convert this decimal into a percentage, you multiply by 100: \[ 0.2 \times 100 = 20\].
This final multiplication step transforms your fraction into a percentage, showing that 17 is 20% of 85.

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