Problem 59 - Prealgebra

Question

Change each fraction or mixed number to a percent. $$\frac{4}{5}$$

Step-by-Step Solution

Answer

\(\frac{4}{5}\) is 80\%.

Step 1: Understand the Relationship Between Fractions and Percents

To convert a fraction to a percent, we need to understand that percent means "per hundred." Therefore, our goal is to express the given fraction so that it has a denominator of 100. This way, we can easily see how many parts out of 100 this fraction represents.

Step 2: Convert Fraction to a Decimal

To convert the fraction \(\frac{4}{5}\) to a percent, we first convert it to a decimal. We do this by dividing the numerator by the denominator. So, \(\frac{4}{5} = 4 ÷ 5 = 0.8\).

Step 3: Convert Decimal to a Percent

Now that we have the decimal value of the fraction, we convert it to a percentage by multiplying it by 100. Thus, \(0.8 \times 100 = 80\).

Step 4: Write Final Answer as a Percent

The conversion tells us that \(\frac{4}{5}\) is equal to 80 percent. Therefore, \(\frac{4}{5} = 80\%\).

Key Concepts

Fractions to Decimals

The first step in percent conversions involves changing a fraction into a decimal. A fraction is made up of two parts: the numerator, which is the top number, and the denominator, which is the bottom number. To convert a fraction like \(\frac{4}{5}\) into a decimal, we perform a simple division operation. We divide the numerator (4) by the denominator (5). This is essentially asking how many fives fit into four. In this case, dividing 4 by 5 gives us 0.8. This is the decimal representation of the fraction \(\frac{4}{5}\).

• The numerator '4' is divided by
• The denominator '5'
• Resulting in a decimal of '0.8'

Notice that sometimes the result of the division can be a repeating decimal, such as in the case of \(\frac{1}{3}\) which yields 0.333..., but in our example, the result is a finite decimal. Remember, the key to converting fractions to decimals is focusing on the division.

Mathematical Operations

Mathematical operations are a set of procedures we use to perform calculations. Converting decimals to percents is a straightforward operation—simply multiply the decimal by 100. This step leverages the idea that "percent" means "per hundred." For example, when converting the decimal 0.8 to a percent, you multiply:

• \(0.8 \times 100 = 80\)

This multiplication operation scales the decimal to a percent value, showing how it represents 80 parts per 100.Anytime you convert a decimal to a percent, remember:

• Multiply the decimal by 100
• Add a percent sign (%) to indicate the conversion

Whether dealing with small fractions yielding small decimals or larger fractions, this operation remains the same.Recognizing this, you streamline the conversion process and boost your mathematical efficiency.

Numerator and Denominator

The terms "numerator" and "denominator" are fundamental to understanding fractions. They help set up the initial step of converting a fraction to both a decimal and a percent.

• The numerator is the "part" of the whole that you are focusing on, such as the '4' in our example \(\frac{4}{5}\).
• The denominator represents the "whole" or total parts into which something is divided, like the '5' in \(\frac{4}{5}\).

In simple terms, the numerator can be thought of as how many parts you have, while the denominator is how many parts make up a whole.Recognizing the roles of these parts helps in understanding the fraction's value. For instance, if the numerator is equal to the denominator, the value is one whole (or 1.0 as a decimal). In converting to decimals, dividing the numerator by the denominator gives you a decimal value representing the fraction of the whole. This understanding is crucial for performing accurate calculations and progressing to further conversion, eventually reaching the percent form.