Problem 44 - Basic College Mathematics

Question

$$ \frac{8}{8} $$

Step-by-Step Solution

Answer

The answer is 1.

Step 1: Understand the Fraction

Recognize that the given problem is a fraction. In this case, the fraction is \( \frac{8}{8} \).

Step 2: Simplify the Fraction

Simplify the fraction \( \frac{8}{8} \) by dividing the numerator by the denominator. Since both the numerator and the denominator are the same, \( 8 \div 8 = 1 \).

Step 3: Verify the Result

Verify that the value obtained is indeed correct. Any fraction where the numerator and denominator are the same simplifies to 1. Thus, \( \frac{8}{8} = 1 \).

Key Concepts

Numerator

When working with fractions, it's important to understand what a numerator is. The numerator is the top part of a fraction. It represents how many parts of a whole we are considering. For example, in the fraction \( \frac{8}{8} \), the number 8 at the top is the numerator. This tells us we have 8 parts out of a total number of parts defined by the denominator. Remember:

• The numerator is the top part of the fraction.
• It indicates the number of parts you have.
• In \( \frac{8}{8} \), the numerator is 8.

Denominator

The denominator is a key element in understanding fractions. It is the bottom part of a fraction and shows the total number of equal parts the whole is divided into. In the fraction \( \frac{8}{8} \), the denominator is also 8. This means the whole is divided into 8 equal parts. It's crucial to recognize:

• The denominator is at the bottom of the fraction.
• It depicts the total parts of the whole.
• For \( \frac{8}{8} \), the denominator is 8, same as the numerator.

Simplification

Fraction simplification is the process of making a fraction as simple as possible. This is done by dividing both the numerator and the denominator by their greatest common divisor (GCD). Here are steps to simplify a fraction, using \( \frac{8}{8} \) as an example:

• Identify the GCD of the numerator and the denominator.
• In this case, the GCD is 8 because 8 is the largest number that divides both 8 and 8.
• Divide both the numerator and the denominator by their GCD: \( \frac{8}{8} \rightarrow \frac{8 \div 8}{8 \div 8} \rightarrow \frac{1}{1} \).
• This simplifies the fraction to 1, as any number over itself equals 1.
• Thus, \( \frac{8}{8} = 1 \).

Simplification helps us understand fractions better and work with them more easily in math problems!