Are the following fractions in simplest form?

Explanation

Strategy We will determine whether the numerator and denominator have any common factors other than 1.

WHY If the numerator and denominator have no common factors other than 1, the fraction is in simplest form.

Solution

1. The factors of the numerator, 12, are: 1, 2, 3, 4, 6, 12
   The factors of the denominator, 27, are: 1, 3, 9, 27
   Since the numerator and denominator have a common factor of 3, the fraction \(\frac{12}{27}\) is not in simplest form.
2. The factors of the numerator, 5, are: 1, 5
   The factors of the denominator, 8, are: 1, 2, 4, 8
   Since the only common factor of the numerator and denominator is 1, the fraction \(\frac{5}{8}\) is in simplest form.