Problem 30 - Introductory Algebra for College Students

Question

Simplify each fraction by reducing it to its lowest terms. $$\frac{8}{14}$$

Step-by-Step Solution

Answer

The fraction reduced to its lowest terms is \(\frac{4}{7}\)

Step 1: Identify the greatest common divisor (gcd)

In this case, the numerator is 8 and the denominator is 14. Their largest common factor is 2.

Step 2: Divide both the numerator and denominator by their gcd

When we divide 8 by 2, we get \( \frac{8}{2} = 4 \). Then we divide 14 by 2, we get \( \frac{14}{2} = 7 \).

Step 3: Form the simplified fraction

After reducing both the numerator and denominator by their greatest common divisor, we get a new fraction \(\frac{4}{7}\) which is the fraction reduced to its lowest terms.