Problem 64 - Algebra 1: Concepts and Skills

Question

Write the percent as a fraction or as a mixed number in simplest form. (Skills Review p. 768 ) $$ 8 \% $$

Step-by-Step Solution

Answer

The percent \(8\%\) as a fraction in simplest form is \( \frac{2}{25} \).

Step 1: Convert the percent into a fraction

A percent can be converted into a fraction by putting it over 100. So, \(8\%\) is equal to the fraction \( \frac{8}{100} \).

Step 2: Simplify the fraction

Now, let's simplify this fraction to its lowest terms. The highest number that can divide both 8 and 100 is 4. Divide the numerator and the denominator by 4 to simplify the fraction. That gives us \( \frac{8}{100} = \frac{8 \div 4}{100 \div 4} = \frac{2}{25} \).

Key Concepts

Fractions

Fractions are a way to represent parts of a whole number. They consist of a numerator, which is the top number, and a denominator, which is the bottom number. For example, in the fraction \( \frac{8}{100} \), 8 is the numerator, and 100 is the denominator, indicating that the whole is divided into 100 equal parts and 8 out of those parts are being considered. Understanding fractions is crucial because they help us express values that aren't whole numbers. When you're dealing with percentages, these are often converted to fractions to make calculations easier and more precise.

When converting percentages to fractions, you start by placing the percentage value over 100, forming a fraction that represents the percentage of a whole. This is why \(8\%\) becomes \(\frac{8}{100}\), because percent literally means "per hundred."

• Numerator: Represents the parts you have.
• Denominator: Represents the total parts or the size of the whole.

Simplifying Fractions

Simplifying fractions is the process of reducing them to their smallest (or simplest) form. The simplest form has numerators and denominators that can no longer be evenly divided by any number other than 1. Simplifying helps in making fractions easier to understand and work with in calculations.

To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and the denominator. In the example of \(\frac{8}{100}\), the GCD is 4, as 4 is the largest number that divides both 8 and 100 without leaving a remainder. By dividing both the numerator and the denominator by 4, you end up with the simplest form of \(\frac{2}{25}\).

• Find the greatest common divisor (GCD).
• Divide the numerator and denominator by the GCD.
• The resulting fraction is fully simplified.

Simplifying fractions is essential for comparing, adding, and subtracting fractions accurately, as well as for clear communication of quantities.

Percentages

Percentages are a way of expressing any number as a part of 100, making them a handy representation for comparisons and statistics. When you see a percentage, it's simply a fraction with a denominator of 100. Converting a percentage to a fraction is straightforward: just put the percentage over 100.

The conversion process allows percentages to be used in various mathematical operations alongside fractions. For instance, to deal with \(8\%\), you convert it into \(\frac{8}{100}\), simplifying calculations in scenarios where you're comparing proportions or dealing with amounts less than a whole.

• Percent means "per hundred."
• Convert by placing the percentage number over 100.
• Simplify further if needed for clarity and calculation ease.

Using percentages is common in everyday life, like in financial calculations (interest rates), statistical data (poll results), and sales (discount percentages). This makes understanding how to convert between percentages and fractions incredibly useful.