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Chapter 7: Problem 53

Solve the problem using a percent equation. What is \(18 \frac{1}{2} \%\) of \(3000 ?\)

Short Answer

Expert verified
18.5% of 3000 is 555.

Step by step solution

01

Convert the Mixed Number to an Improper Fraction

Convert the mixed number, 18 \( \frac{1}{2} \) \%, to an improper fraction. First, convert \( \frac{1}{2} \) to a fraction: \( 18 + \frac{1}{2} = \frac{37}{2} \).
02

Convert the Improper Fraction to a Decimal

Convert the improper fraction \( \frac{37}{2} \) \% into a decimal by dividing the numerator by the denominator: \( \frac{37}{2} = 18.5 \).
03

Set Up the Percent Equation

Write the percent equation to find 18.5% of 3000. The formula is \( \text{Percentage} = \text{Percent (as a decimal)} \times \text{Whole} \). Here, the percent (as a decimal) is 0.185, and the whole is 3000.
04

Calculate the Percentage

Multiply the decimal form of the percentage by the whole: \( 0.185 \times 3000 = 555 \).
05

Interpret the Result

The final result shows that 18.5% of 3000 is 555.

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Key Concepts

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

Mixed Number to Improper Fraction
Understanding how to convert a mixed number to an improper fraction is essential for solving percentage problems like these. A mixed number consists of a whole number and a fraction. To convert it:
  • Multiply the whole number by the denominator of the fraction part.
  • Add the resulting product to the numerator of the fraction part.
  • Place the sum (numerator) over the original denominator.
For instance, to convert \(18 \frac{1}{2}\):
  • Multiply 18 (whole number) by 2 (denominator): 18 脳 2 = 36.
  • Add the numerator (1) to this product: 36 + 1 = 37.
  • The improper fraction is \(\frac{37}{2}\).
Decimal Conversion
Converting fractions to decimals is crucial, especially when dealing with percentages. To convert an improper fraction to a decimal:
  • Simply divide the numerator by the denominator.
For example, \(\frac{37}{2}\) becomes 18.5 when you divide 37 by 2. This conversion makes it easier to use in calculations involving percentages.
Decimals are handy because they align well with the concept of percentages, which are often expressed in decimal form for simplicity. So, 18.5% can be written as 0.185.
Percentage Calculation
Calculating a percentage of a number involves using the percent as a decimal. The key formula here is:
  • \[\text{Percentage} = \text{Percent (as a decimal)} \times \text{Whole Number}\]
This equation helps you find out what a specific percentage of a larger number is. For example, if you want to find 18.5% of 3000:
  • Convert 18.5% to a decimal: 0.185.
  • Multiply the decimal by the whole number: 0.185 脳 3000 = 555.
  • This means 18.5% of 3000 is 555.
Understanding this process allows you to tackle various percentage problems efficiently.
Percent Formula
The percent formula is a fundamental tool in math. It allows you to determine what a certain percentage of a whole number is. The formula is:
  • \[\text{Percentage} = \left( \frac{\text{Percent}}{100} \right) \times \text{Whole Number}\]
Essentially, you:
  • Convert the percent to a fraction of 100 (which is the same as converting it to its decimal form).
  • Multiply this fraction by the whole number to find the percentage amount.
This break-down demonstrates how percentages, fractions, and decimals are interconnected. For example, for 18.5% of 3000:
  • Write 18.5% as 0.185.
  • Then multiply by 3000: \(0.185 \times 3000 = 555\).
Utilizing this formula can simplify your percentage calculations significantly.

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