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Chapter 6: Problem 67

In the following exercises, convert each fraction to a percent. $$\frac{3}{8}$$

Short Answer

Expert verified
37.5%

Step by step solution

01

Understand the Problem

The goal is to convert the fraction \(\frac{3}{8}\) into a percentage.
02

Convert Fraction to Decimal

Divide the numerator (3) by the denominator (8): \[ \frac{3}{8} = 0.375 \]
03

Convert Decimal to Percent

Multiply the decimal by 100 to convert it to a percentage: \[ 0.375 \times 100 = 37.5 \]
04

Write the Final Answer

The fraction \(\frac{3}{8}\) is equal to 37.5%.

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Key Concepts

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

Fractions
Fractions represent a part of a whole. They consist of a numerator (the top number) and a denominator (the bottom number). For example, in the fraction \( \frac{3}{8} \), 3 is the numerator and 8 is the denominator. This tells us that we have 3 parts out of a total of 8 parts.
Fractions are a way to express numbers that are not whole and are used in various areas of mathematics.
When working with fractions, it is often useful to convert them to decimals or percentages to better understand or compare them.
Decimal Conversion
Decimal conversion involves changing a fraction into a decimal number. To convert \( \frac{3}{8} \) to a decimal, you divide the numerator (3) by the denominator (8).
Performing this division, we get:
\[ \frac{3}{8} = 0.375 \]
The division tells us that \( \frac{3}{8} \) is equal to 0.375 in decimal form.
This step is crucial when converting fractions to percentages because percentages are often easier to understand as they are more commonly used in daily life.
Percentages
Percentages are a way to express a number as a part of 100. To convert a decimal to a percentage, you multiply the decimal number by 100.
In our example, we converted \( \frac{3}{8} \) to 0.375 in the previous step. Now we take this decimal and convert it to a percentage:
  • Multiply by 100:
\[ 0.375 \times 100 = 37.5 \]
Therefore, \( \frac{3}{8} \) is equal to 37.5%.
This means that 3 out of 8 parts is the same as 37.5 out of 100 parts. Percentages make it easier to compare fractions with different denominators, as they scale the values to a common base of 100.

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Most popular questions from this chapter

In the following exercises, solve the percent problem. Solve for a: \(\frac{12}{a}=\frac{-15}{65}\)

Solve the applications of percents. Geneva treated her parents to dinner at their favorite restaurant. The bill was $74.25. She wants to leave 16% of the total bill as a tip. How much should the tip be?

Determine whether each equation is a proportion. $$ \frac{16}{7}=\frac{48}{23} $$

In the following exercises, solve the percent problem. Yuki's monthly paycheck is \(\$ 3,825\) . She pays \(\$ 918\) for rent. What percent of her paycheck goes to rent?

In the following exercises, determine whether each equation is a proportion. $$ \frac{5}{13}=\frac{30}{78} $$
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