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Chapter 7: Problem 23

Write each percent as a fraction or mixed number in simplest form. $$ 8 \% $$

Short Answer

Expert verified
8% is equivalent to \( \frac{2}{25} \) as a fraction.

Step by step solution

01

Understand the Definition of Percent

The term 'percent' means 'out of 100.' So when you see 8%, it means 8 out of 100, which can be represented as \( \frac{8}{100} \).
02

Simplify the Fraction

To simplify the fraction \( \frac{8}{100} \), we need to find the greatest common factor (GCF) of the numerator and the denominator. The GCF of 8 and 100 is 4.
03

Divide by the GCF

Divide both the numerator and the denominator by the GCF (4) to simplify the fraction: \( \frac{8 \div 4}{100 \div 4} = \frac{2}{25} \).
04

Conclusion

The fraction equivalent to 8% in simplest form is \( \frac{2}{25} \).

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Key Concepts

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

Simplifying Fractions
When we talk about simplifying fractions, what we're really discussing is the process of making a fraction as simple as possible. This means rewriting it using the smallest numbers that still represent the same value.
To do this, we divide both the numerator (the top number) and the denominator (the bottom number) by their greatest common factor (GCF).
Here's a simple guide to follow:
  • Find the GCF of the numerator and the denominator.
  • Divide both the numerator and the denominator by the GCF.
  • Write down your new, simplified fraction.
So, if you have a fraction like \( \frac{8}{100} \), you find that the GCF is 4. Then, you divide the top and bottom by 4 to get \( \frac{2}{25} \). And that's simplification! It may seem basic, but it's a super useful skill when working with fractions.
Greatest Common Factor
The greatest common factor, often abbreviated as GCF, is the largest number that divides both the numerator and the denominator of a fraction without leaving a remainder. Understanding how to find the GCF is critical for simplifying fractions.
To find the GCF, list all the factors of each number and see what the biggest one they have in common is. For example, let's look at the numbers 8 and 100.
**Factors of 8**: 1, 2, 4, 8
**Factors of 100**: 1, 2, 4, 5, 10, 20, 25, 50, 100
  • Common factors of 8 and 100 are 1, 2, and 4.
  • The greatest of these common factors is 4.
Once you find the GCF, you can use it to simplify your fraction, making it easier to work with. This skill is quite beneficial, especially in more complicated math problems where simplicity is key.
Understanding Percents
In mathematics, a percent is a way of expressing a number as a fraction of 100. In fact, the word 'percent' comes from a Latin term meaning 'by the hundred'.
When you see a percentage like 8%, you can think of it as a tiny slice out of a pie made up of 100 equal slices.
To convert a percent to a fraction, you start by writing the percent number over 100. Therefore, 8% becomes \( \frac{8}{100} \).
  • Percent -> Fraction: Place the percent number over 100.
  • Simplify the fraction by using the GCF.
  • 8% simplifies to \( \frac{2}{25} \).
Understanding percentages helps when dealing with statistics, finance, and everyday math scenarios like discounts and interest rates. Knowing how to convert them into fractions can make calculations much more approachable.

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Most popular questions from this chapter

Write each percent as a decimal and a fraction. In \(2016,\) geothermal sources accounted for \(66 \%\) of Iceland's energy use.

In \(2015,\) the United States' share of global passenger vehicle production was \(0.1496 .\) Write this decimal as a percent.

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

In \(2016,\) the U.S. Postal Service processed and delivered approximately \(47 \%\) of the world's card and letter mail volume. Write this percent as a decimal.

Explain what errors were made by each student when solving percent of increase or decrease problems and then correct the errors. See the Concept Checks in this section. "The population of a certain rural town was 150 in 1990, 180 in 2000, and 150 in 2010." The percent of increase from 1990 to 2000 is the same as the percent decrease from 2000 to \(2010 .\) True or false? Chris's answer: True because they had the same amount of increase as the amount of decrease.
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