Problem 6 - Elementary Algebra Within Reach

Question

Convert the decimal or fraction to a percent. $$\frac{1}{4}$$

Step-by-Step Solution

Answer

The fraction \( \frac{1}{4} \) converts to 25%.

Step 1: Understanding fractions and percentages

A fraction represents a part of a whole. A percentage represents a part of a whole as well, but the whole is always made up of 100 parts. So, to convert a fraction into a percentage, you have to express it as a part out of 100.

Step 2: Convert the fraction to decimal

Before changing the fraction into a percent, it is often easier to first convert it to a decimal. To do this, divide the numerator (top number) by the denominator (bottom number). In this case, divide 1 by 4. So, \( \frac{1}{4} = 0.25 \).

Step 3: Convert the decimal to a percentage

To convert a decimal to a percentage, multiply it by 100. Multiplying 0.25 by 100 will give 25.

Step 4: Adding the percent sign

The last step is to add a % sign to your answer. So, \( \frac{1}{4} \) = 25%.

Key Concepts

Understanding Fractions

Fractions are one of the most fundamental concepts in mathematics, describing parts of a whole.
Each fraction consists of two numbers: the numerator and the denominator.

• The numerator is the top number, indicating how many parts we have.
• The denominator is the bottom number, indicating the total number of equal parts the whole is divided into.

For instance, the fraction \( \frac{1}{4} \) means we have one part out of a total of four parts. Fractions are useful for representing amounts that are less than a whole, especially when dealing with equal parts.

Decimal Conversion Simplified

Decimal conversion is an essential step when working with fractions and percentages.
Converting a fraction to a decimal makes it more straightforward to perform further calculations, such as percent conversion. To convert a fraction to a decimal, follow these simple steps:

• Divide the numerator by the denominator.
• For \( \frac{1}{4} \), divide 1 by 4, resulting in 0.25.

Converting fractions to decimals is not just for convenience; it allows you to perform mathematical operations more easily and understand the number better in different contexts.

Mathematical Operations and Percent Conversion

Once we have a fraction in decimal form, converting it to a percent becomes simple. The key operation in this conversion is multiplication:

• Multiply the decimal by 100 to find the percentage.
• In our example, multiply 0.25 by 100 to get 25.

Finally, add the percent sign to indicate the result is a percentage, thus completing the conversion from a fraction to a percent. Percentages are an intuitive way to express ratios and proportions, as they relate quantities to 100, making them easier to compare and understand in various everyday situations.