To simplify the expression \( \frac{5}{14}a - \frac{2}{5}c + \frac{1}{8}b - \frac{2}{5}c + \frac{3}{8}b + \frac{7}{14} \), we will first combine like terms.
Step 1: Combine the like terms involving \( c \)
- The \( c \) terms are \( -\frac{2}{5}c - \frac{2}{5}c \): \[ -\frac{2}{5}c - \frac{2}{5}c = -\frac{4}{5}c \]
Step 2: Combine the like terms involving \( b \)
- The \( b \) terms are \( \frac{1}{8}b + \frac{3}{8}b \): \[ \frac{1}{8}b + \frac{3}{8}b = \frac{4}{8}b = \frac{1}{2}b \]
Step 3: Combine the constant terms
- The constant terms are \( \frac{7}{14} \), which simplifies to \( \frac{1}{2} \): \[ \frac{7}{14} = \frac{1}{2} \]
Step 4: Write the simplified expression
Now we can combine all the simplified parts: \[ \frac{5}{14}a - \frac{4}{5}c + \frac{1}{2}b + \frac{1}{2} \]
Final simplified expression
The final simplified expression is: \[ \frac{5}{14}a - \frac{4}{5}c + \frac{1}{2}b + \frac{1}{2} \]