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Chapter 7: Problem 9

Convert the given percent to a fraction, and simplify the result. $$ 4 \frac{1}{2} \% $$

Short Answer

Expert verified
The percent \(4 \frac{1}{2}\%\) as a fraction is \(\frac{9}{200}\).

Step by step solution

01

Convert Mixed Percentage to Improper Fraction

First, convert the mixed number percentage into an improper fraction. The percentage given is \(4 \frac{1}{2}\%\). To convert it to a fraction, calculate \(4 \times 2 + 1 = 9\). Thus, \(4 \frac{1}{2}\%\) becomes \(\frac{9}{2}\%\).
02

Change Percent to Fraction

Convert \(\frac{9}{2}\%\) to a fraction. Since percent means per hundred, divide by 100: \(\frac{9}{2} \div 100 = \frac{9}{2} \times \frac{1}{100} = \frac{9}{200}\).
03

Simplify the Fraction

Check if \(\frac{9}{200}\) can be simplified. The greatest common divisor of 9 and 200 is 1, meaning \(\frac{9}{200}\) is already in its simplest form.

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Key Concepts

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

Improper Fraction
An improper fraction is a type of fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). This means that the fraction represents a value greater than or equal to one whole.
To convert a mixed number to an improper fraction, follow these steps:
  • Multiply the whole number by the denominator of the fractional part.
  • Add the result to the numerator of the fractional part.
  • The sum becomes the numerator of the improper fraction, while the denominator remains the same.
For example, in the problem where we start with the mixed number percentage, \(4 \frac{1}{2}\%\), we convert it to the improper fraction \(\frac{9}{2}\%\) by following these steps:
  • Whole number is 4, and the fraction part is \(\frac{1}{2}\).
  • Calculate: \(4 \times 2 = 8\).
  • Add: \(8 + 1 = 9\).
  • The improper fraction becomes \(\frac{9}{2}\).
Simplifying Fractions
Simplifying fractions, also known as reducing fractions, involves making the fraction as simple as possible while keeping its value unchanged. A fraction is simplified when the greatest common divisor (GCD) of the numerator and the denominator is 1.
Here are the steps to simplify a fraction:
  • Find the GCD of both the numerator and the denominator.
  • Divide both the numerator and the denominator by the GCD.
  • The resulting fraction is the simplest form of the original fraction.
Let's consider the fraction \(\frac{9}{200}\). To simplify this, you:
  • Check if there are any common factors between 9 and 200.
  • The GCD is 1, which means 9 and 200 have no common factors other than 1.
Hence, \(\frac{9}{200}\) is already in its simplest form.
Mixed Numbers
Mixed numbers are numbers that include both a whole number and a fraction, representing values that are between whole numbers.
For instance, the mixed number \(4 \frac{1}{2}\) consists of the whole number 4 and the fraction \(\frac{1}{2}\).Mixed numbers can be converted into improper fractions, which is often necessary when performing operations such as addition, subtraction, multiplication, or division with fractions.The conversion process is helpful because it turns the number into a single numerator and denominator, simplifying further operations.Always remember:
  • Mixed numbers are useful for expressing quantities that are greater than whole numbers but less than the next whole number.
  • Changing a mixed number to an improper fraction can streamline math operations.
  • Understanding both forms allows for flexibility in mathematical calculations and better clarity, especially when simplifying or solving equations.

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Most popular questions from this chapter

In an election for class president, Chin received 5 votes, Mabel received 13 votes, and Juanita received the remaining 32 votes cast. If a pie chart is created for this voting data, what will be the degree measure of the central angle of the sector representing Chin's share of the vote? Round your answer to the nearest degree.

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