Solve: 2/3a + 1/4b + 1/8c + 1/4a = ? | Fraction Expression

To solve this algebraic expression problem, we proceed with the following steps:

• Step 1: Identify the Like Terms
• Step 2: Combine the Like Terms
• Step 3: Present the Final Simplified Expression

Step 1: Identify the Like Terms:
The expression given is $\frac{2}{3}a + \frac{1}{4}b + \frac{1}{8}c + \frac{1}{4}a$. Notice that the terms $\frac{2}{3}a$ and $\frac{1}{4}a$ are like terms involving $a$.

Step 2: Combine the Like Terms:
To combine $\frac{2}{3}a$ and $\frac{1}{4}a$, we need a common denominator. The least common denominator of 3 and 4 is 12.
Rewriting these fractions with a denominator of 12 gives: $\frac{2}{3}a = \frac{8}{12}a$, and $\frac{1}{4}a = \frac{3}{12}a$.
Adding these gives: $\frac{8}{12}a + \frac{3}{12}a = \frac{11}{12}a$.

Step 3: Present the Final Simplified Expression:
Now, substitute back the simplified terms involving $a$ into the expression: $\frac{11}{12}a + \frac{1}{4}b + \frac{1}{8}c$.
Therefore, the simplified expression is $\frac{11}{12}a + \frac{1}{4}b + \frac{1}{8}c$.

This matches with choice 3 in the provided options.

The final solution is: $\frac{11}{12}a + \frac{1}{4}b + \frac{1}{8}c$.