1/6+3/10

To add the fractions \( \frac{1}{6} \) and \( \frac{3}{10} \), we need to find a common denominator. The least common multiple (LCM) of 6 and 10 is 30.

Now, let's convert each fraction to have this common denominator:

1. For \( \frac{1}{6} \): \[ \frac{1}{6} = \frac{1 \times 5}{6 \times 5} = \frac{5}{30} \]

2. For \( \frac{3}{10} \): \[ \frac{3}{10} = \frac{3 \times 3}{10 \times 3} = \frac{9}{30} \]

Now, we can add the two fractions: \[ \frac{5}{30} + \frac{9}{30} = \frac{5 + 9}{30} = \frac{14}{30} \]

Next, we can simplify \( \frac{14}{30} \) by dividing the numerator and denominator by their greatest common divisor, which is 2: \[ \frac{14 \div 2}{30 \div 2} = \frac{7}{15} \]

Thus, \[ \frac{1}{6} + \frac{3}{10} = \frac{7}{15} \]