Questions: Add and simplify. 1/15 + 5/12 = (Simplify your answer. Type a whole number or a fraction.)

Solution Steps

To add the fractions \(\frac{1}{15}\) and \(\frac{5}{12}\), we need to find a common denominator. The least common multiple (LCM) of 15 and 12 will serve as the common denominator. Once we have the common denominator, we convert each fraction to an equivalent fraction with this common denominator and then add the numerators. Finally, we simplify the resulting fraction if possible.

To add the fractions \( \frac{1}{15} \) and \( \frac{5}{12} \), we first determine the least common multiple (LCM) of the denominators 15 and 12. The LCM is calculated as follows: \[ \text{lcm}(15, 12) = 60 \]

Next, we convert each fraction to have the common denominator of 60: \[ \frac{1}{15} = \frac{1 \times 4}{15 \times 4} = \frac{4}{60} \] \[ \frac{5}{12} = \frac{5 \times 5}{12 \times 5} = \frac{25}{60} \]

Now that both fractions have the same denominator, we can add them: \[ \frac{4}{60} + \frac{25}{60} = \frac{4 + 25}{60} = \frac{29}{60} \]

The fraction \( \frac{29}{60} \) is already in its simplest form since the greatest common divisor (GCD) of 29 and 60 is 1.

Final Answer