Solve the Fraction Addition: 3/10 + 1/5 + 4/6

To solve the problem of adding the fractions $\frac{3}{10}+\frac{1}{5}+\frac{4}{6}$, we follow these steps:

• Find the common denominator: The denominators are 10, 5, and 6. The least common multiple (LCM) of these numbers is 30.
• Convert each fraction to have the denominator 30:
  - $\frac{3}{10} = \frac{3 \times 3}{10 \times 3} = \frac{9}{30}$
  - $\frac{1}{5} = \frac{1 \times 6}{5 \times 6} = \frac{6}{30}$
  - $\frac{4}{6} = \frac{4 \times 5}{6 \times 5} = \frac{20}{30}$
• Add the converted fractions together:
  - $\frac{9}{30} + \frac{6}{30} + \frac{20}{30} = \frac{9 + 6 + 20}{30} = \frac{35}{30}$
• Simplify the fraction $\frac{35}{30}$:
  - The greatest common divisor (GCD) of 35 and 30 is 5. Thus, $\frac{35}{30} = \frac{35 \div 5}{30 \div 5} = \frac{7}{6}$.

Therefore, the solution to the problem is $\frac{7}{6}$.