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Chapter 7: Problem 61

Write each fraction or mixed number as a percent. $$ 4 \frac{1}{2} $$

Short Answer

Expert verified
\(4 \frac{1}{2}\) as a percent is \(450\%\).

Step by step solution

01

Convert the Mixed Number to an Improper Fraction

First, convert the mixed number \(4 \frac{1}{2}\) into an improper fraction. To do this, multiply the whole number part by the denominator and add the numerator. \(4 \times 2 + 1 = 9\). So, \(4 \frac{1}{2} = \frac{9}{2}\).
02

Divide the Numerator by the Denominator to Get a Decimal

Next, divide the numerator by the denominator to convert the fraction into a decimal. \(\frac{9}{2} = 4.5\).
03

Convert the Decimal to a Percent

To convert the decimal \(4.5\) to a percent, multiply it by 100. \(4.5 \times 100 = 450\). This yields \(450\%\).

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Key Concepts

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

Mixed Numbers
A mixed number combines whole numbers and fractions. It represents a quantity greater than a whole but less than the next whole number. Understanding mixed numbers is essential for converting them into other formats, such as improper fractions or decimals.

To convert a mixed number like \(4 \frac{1}{2}\) into an improper fraction, follow these steps:
  • Multiply the whole number by the fraction's denominator. In our case, \(4 \times 2 = 8\).
  • Add this result to the numerator of the fraction. So, \(8 + 1 = 9\).
  • Place this value over the original fraction's denominator. Therefore, \(4 \frac{1}{2} = \frac{9}{2}\).
After conversion, the mixed number \(4 \frac{1}{2}\) becomes the improper fraction \(\frac{9}{2}\), which can lead to easier further calculations.
Improper Fractions
An improper fraction is one where the numerator (top number) is larger than or equal to the denominator (bottom number). These fractions often need conversion to be useful in practical applications, like in calculations or measurement.

Converting an improper fraction to a decimal is the next logical step when seeking to express the fraction in a more commonly understood format. For \(\frac{9}{2}\), this would involve dividing the numerator by the denominator:
  • Perform the division: \(9 \div 2 = 4.5\).
This decimal, \(4.5\), now represents the original value in a format that is often easier to comprehend and use in other calculations, subsequently making it ready for conversion to a percentage format.
Decimal Conversion
Converting a decimal to a percent is a simple but crucial step in many mathematical and real-life scenarios. Once a value is expressed as a decimal, turning it into a percent allows clearer interpretation in terms of percentages, which are widely understood.

To convert the decimal \(4.5\) into a percent:
  • Multiply the decimal by 100. So, \(4.5 \times 100 = 450\).
Thus, the percent form of \(4.5\) is \(450\%\).

This conversion makes the information more accessible, as percentages are a familiar way of interpreting data, whether you're working on homework, budgeting, or analyzing data in daily life.

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Most popular questions from this chapter

Given the percent \(52.8647 \%,\) round as indicated. a. Round to the nearest tenth percent. b. Round to the nearest hundredth percent.

Solve. \(1.5 \%\) of 45,775 is what number?

Perform each indicated operation. See Sections 4.3 through \(4.5,4.7,\) and 5.2 through \(5.4 .\) $$78-19.46$$

Solve.What percent of 500 is \(3 ?\)

Check each answer to see if each makes the proportion a true proportion. If any proportion is not true, solve it to find the correct solution. $$\begin{aligned}&\frac{520}{b}=\frac{65}{100}\\\&\text { Is the base equal to } 800 ?\end{aligned}$$
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