Problem 5 - Prealgebra

Question

Write each percent as a fraction with denominator \(100 .\) $$24 \%$$

Step-by-Step Solution

Answer

\(24\%\) as a fraction with denominator 100 is \(\frac{24}{100}\) or simplified as \(\frac{6}{25}\).

Step 1: Understand the Percent

The given percent is \(24\%\). Percents are numbers that represent a part out of 100. The symbol '%' means 'per hundred'. So \(24\%\) is essentially \(24\) out of \(100\).

Step 2: Convert Percent to Fraction

Since a percent is out of \(100\), write the given percent, \(24\%\), as a fraction whose denominator is \(100\). This gives us \(\frac{24}{100}\).

Step 3: Simplify the Fraction (if necessary)

To simplify \(\frac{24}{100}\), find the greatest common factor (GCF) of \(24\) and \(100\). The GCF is \(4\). Divide both the numerator and the denominator by \(4\) to simplify the fraction: \(\frac{24 \div 4}{100 \div 4} = \frac{6}{25}\). Therefore, the simplified fraction is \(\frac{6}{25}\).

Key Concepts

Simplifying Fractions

When you simplify a fraction, you reduce it to its smallest form where the numerator and denominator have no common factors other than 1. This process is essential because it makes fractions easier to work with and understand.
To simplify a fraction, you need to find the greatest common factor (GCF) of the numerator and the denominator. For example, in the fraction \( \frac{24}{100} \), the GCF of 24 and 100 is 4. By dividing both the numerator and the denominator by this GCF, \( \frac{24 \div 4}{100 \div 4} \), we receive the simplified fraction \( \frac{6}{25} \).

• It’s useful to simplify fractions in calculations to avoid large or cumbersome numbers.
• Simplifying can help identify equivalent fractions.
• Always check if both the numerator and the denominator can be divided by a common factor.

Simplified fractions are typically clearer and more direct in mathematical operations and problem-solving.

Greatest Common Factor

To simplify a fraction effectively, understanding the concept of the greatest common factor (GCF) is vital. The GCF is the largest number that divides both the numerator and the denominator of a fraction without leaving a remainder.
Use these steps to find the GCF:

• List the factors of each number.
• For example, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24, while the factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.
• Identify the largest factor common to both lists, which, in this case, is 4.

Knowing the GCF can greatly assist in simplifying fractions and solving math problems efficiently. It helps in reducing fractions to their simplest forms by ensuring that numbers are as small as possible but still represent the same fraction.

Understanding Percents

A percent is a way of expressing a number as a fraction of 100 and is denoted by the symbol '%'. Understanding percents allows you to easily translate between fractions, decimals, and percentages.
Here's a simple way to visualize percents:

• The percent symbol '%' means 'out of 100'. So, \( 24\% \) is simply 24 out of 100 or \( \frac{24}{100} \).
• Converting percents to fractions involves placing the percent number over 100.
• This conversion helps in comparing different values and understanding relative quantities in everyday contexts.

Percents are widely used in calculations involving discounts, interest rates, and statistics. Understanding them through their conversion to fractions is crucial for problem-solving in many areas of math and real-world applications.