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Chapter 0: Problem 176

Write each percent as a fraction. Give answers in lowest terms. See Example 13. $$ 8 \% $$

Short Answer

Expert verified
\(\frac{2}{25}\)

Step by step solution

01

Convert Percent to Fraction

First, recognize that a percent is a ratio per 100. Therefore, 8% can be written as: \(\frac{8}{100}\)
02

Simplify the Fraction

Next, simplify the fraction \(\frac{8}{100}\). Both the numerator (8) and the denominator (100) can be divided by their greatest common divisor, which is 4. This gives: \(\frac{8 \div 4}{100 \div 4} = \frac{2}{25}\)

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Key Concepts

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

simplifying fractions
Simplifying fractions means reducing them to their simplest form. This process involves finding a common number that divides evenly into both the numerator and the denominator.
To simplify \(\frac{8}{100}\), we first identify the greatest common divisor (GCD) of 8 and 100. In this case, the GCD is 4.
We then divide both the numerator and the denominator by this GCD:
- \(8 \div 4 = 2\)
- \(100 \div 4 = 25\)
Therefore, simplifying \(\frac{8}{100}\) results in \(\frac{2}{25}\).
Always verify that there are no common factors other than 1 between the new numerator and the denominator. If not, you have simplified the fraction correctly.
greatest common divisor
The greatest common divisor (GCD) is the largest number that evenly divides two or more numbers. Finding the GCD is essential for simplifying fractions.
To find the GCD of 8 and 100:
- List the factors of each number:
- Factors of 8: 1, 2, 4, 8
- Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
- Identify the largest common factor between them:
- Common factors of 8 and 100: 1, 2, 4
The greatest of these common factors is 4, so 4 is the GCD.
Using the GCD helps us reduce the fraction \(\frac{8}{100}\) to \(\frac{2}{25}\).
ratio
A ratio compares two quantities, showing how many times one value contains another.
Percentages are essentially ratios per 100. Hence, 8% means 8 out of 100 or \(\frac{8}{100}\).
The process of converting a percent to a fraction is simple:
- Write the percent as a ratio over 100:
- 8% becomes \(\frac{8}{100}\)
- Simplify this fraction, if possible:
- Divide by the GCD, which we found to be 4, resulting in \(\frac{2}{25}\).
Understanding ratios and how they relate to percentages helps make sense of their fractional representation.

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Most popular questions from this chapter

The following problems provide more practice on operations with fractions and decimals. Perform the indicated operations. $$ \frac{9}{20}\left(-\frac{7}{15}\right) $$

Find each absolute value and simplify if needed. $$ |-9|-|-3| $$

Solve each problem. The table shows the percent change in population from 2010 through 2016 for selected metropolitan areas. $$ \begin{array}{|l|c|} \hline \text { Metropolitan Area } & \text { Percent Change } \\ \hline \text { Detroit } & -5.8 \\ \text { Houston } & 9.7 \\ \text { Las Vegas } & 8.3 \\ \text { New Orleans } & 13.9 \\ \text { Phoenix } & 11.6 \\ \text { Toledo } & -3.0 \\ \hline \end{array} $$ (a) Which metropolitan area had the greatest change in population? What was this change? Was it an increase or a decrease? (b) Which metropolitan area had the least change in population? What was this change? Was it an increase or a decrease?

Give (a) the additive inverse and (b) the absolute value of each number. $$ -14 $$

The distributive property can be used to mentally perform calculations. $$\begin{array}{l}38 \cdot 17+38 \cdot 3 \\\=38(17+3) \\\=38(20) \\\=760\end{array} $$Use the distributive property to calculate each value mentally. $$ 27 \cdot 60+27 \cdot 40 $$
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