Problem 44 - Basic College Mathematics

Question

Simplify. $$ \frac{8}{8} $$

Step-by-Step Solution

Answer

1

Step 1: Identify the Fraction

The problem presents the fraction \(\frac{8}{8}\). This fraction has the same numerator and denominator.

Step 2: Simplify the Fraction

When the numerator and the denominator of a fraction are the same, the fraction simplifies to 1. Therefore, \(\frac{8}{8} = 1\).

Key Concepts

Numerator and Denominator

Understanding the numerator and denominator is crucial for simplifying fractions. The **numerator** is the number on top of the fraction. In our example \( \frac{8}{8} \), the numerator is 8. The **denominator** is the number on the bottom. So, in this case, the denominator is also 8. The numerator tells you how many parts you have, while the denominator tells you how many equal parts the whole is divided into. Knowing these roles helps when you simplify fractions, as you need to see how these numbers relate to each other.

Basic Arithmetic

Basic arithmetic operations like addition, subtraction, multiplication, and division are key to solving fraction problems. When simplifying fractions, division is often the most useful operation. For \( \frac{8}{8} \), we see that the numerator (8) divided by the denominator (8) equals 1. Division helps us understand that when the numerator and the denominator are the same, the fraction always simplifies to 1. Practicing these operations helps you become comfortable handling numbers within fractions.

Fraction Simplification

Simplifying fractions makes them easier to work with. To simplify a fraction, you look for common factors in the numerator and denominator. If both numbers are the same, like \( \frac{8}{8} \), they can be divided by themselves, giving you 1. This is the basic principle behind simplifying fractions. Always check if there are other common factors. For example, for \( \frac{24}{32} \), you could divide by the common factor 8 to get \( \frac{3}{4} \). Simplifying fractions helps make calculations quicker and more intuitive.