(1)/(3)+(4)/(12) (5)/(12) (6)/(12) (8)/(12)

To add the fractions \(\frac{1}{3}\) and \(\frac{4}{12}\), we need to find a common denominator. The least common denominator (LCD) of 3 and 12 is 12.<br /><br />First, convert \(\frac{1}{3}\) to a fraction with a denominator of 12:<br />\[<br />\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}<br />\]<br /><br />Now, we can add \(\frac{4}{12}\) and \(\frac{4}{12}\):<br />\[<br />\frac{4}{12} + \frac{4}{12} = \frac{4 + 4}{12} = \frac{8}{12}<br />\]<br /><br />Next, simplify \(\frac{8}{12}\) by dividing the numerator and the denominator by their greatest common divisor (GCD), which is 4:<br />\[<br />\frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3}<br />\]<br /><br />So, the final answer is:<br />\[<br />\frac{1}{3} + \frac{4}{12} = \frac{2}{3}<br />\]