Problem 136 - Introductory Algebra for College Students

Question

Explain how to reduce a fraction to its lowest terms. Give an example with your explanation.

Step-by-Step Solution

Answer

The fraction \( \frac{18}{24} \) is reduced to its lowest terms by finding the GCD of the numerator and the denominator which is 6, and dividing both by this value. The simplest form of the fraction is \( \frac{3}{4} \).

Step 1: Identify the Numerator and Denominator

Consider a fraction say, \( \frac{18}{24} \). Here, 18 is the numerator and 24 is the denominator.

Step 2: Find the Greatest Common Divisor (GCD)

Determine the greatest positive integer that divides the numbers without a remainder. In this case, 6 is the GCD of 18 and 24 because it divides both without a remainder.

Step 3: Divide the Numerator and Denominator

Next, divide both the numerator and the denominator by their GCD. This yields \( \frac{18}{6} = 3 \) and \( \frac{24}{6} = 4 \). This forms the new fraction \( \frac{3}{4} \).

Step 4: Check if Simplified

The numerator and denominator have no other common factors, hence the fraction is in its simplest form.