Solve the Fraction Addition: 1/4 + 3/6 Step by Step

To solve the problem of adding $\frac{1}{4}$ and $\frac{3}{6}$, we need to find their sum using a common denominator.

Step 1: Identify the Least Common Denominator (LCD)
The denominators of the fractions are 4 and 6. The LCM of 4 and 6, which will be the least common denominator, is 12.

Step 2: Convert each fraction to an equivalent fraction with the denominator of 12.
For $\frac{1}{4}$: Multiply the numerator and denominator by 3 to get $\frac{1 \times 3}{4 \times 3} = \frac{3}{12}$.
For $\frac{3}{6}$: Multiply the numerator and denominator by 2 to get $\frac{3 \times 2}{6 \times 2} = \frac{6}{12}$.

Step 3: Add the fractions $\frac{3}{12} + \frac{6}{12} = \frac{3 + 6}{12} = \frac{9}{12}$.

Step 4: Simplify the resulting fraction if necessary.
In this case, $\frac{9}{12}$ can be simplified. The greatest common divisor of 9 and 12 is 3, so $\frac{9}{12} = \frac{9 \div 3}{12 \div 3} = \frac{3}{4}$.

Therefore, the sum of $\frac{1}{4} + \frac{3}{6}$ is $\frac{3}{4}$, but in the context of the provided answer choices, we are looking for $\frac{9}{12}$ initially, which does match the simplified result before reducing.

The correct answer is therefore $\frac{9}{12}$, which corresponds to Choice 3.