Solve: 1/2 + 3/4 + 6/8 Addition of Mixed Denominators

To solve this problem, we will add the fractions $\frac{1}{2}$, $\frac{3}{4}$, and $\frac{6}{8}$ by first converting each to have a common denominator:

Step 1: Find the Least Common Denominator (LCD). The denominators are $2$, $4$, and $8$. The LCM of these numbers is $8$.

Step 2: Rewrite each fraction with the denominator of $8$.

• $\frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8}$
• $\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}$
• $\frac{6}{8}$ is already expressed with a denominator of $8$.

Step 3: Add the fractions:

$\frac{4}{8} + \frac{6}{8} + \frac{6}{8} = \frac{4 + 6 + 6}{8} = \frac{16}{8}$

Step 4: Simplify the fraction:

$\frac{16}{8} = 2$

Therefore, the sum of the fractions $\frac{1}{2} + \frac{3}{4} + \frac{6}{8} = 2$.