To simplify the expression \( \frac{5}{14}a - 25c + \frac{1}{8}b - \frac{2}{5}c + \frac{3}{8}b + \frac{7}{14}a \), we can group and combine like terms.
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Combine the \( a \) terms: \[ \frac{5}{14}a + \frac{7}{14}a = \left(\frac{5 + 7}{14}\right)a = \frac{12}{14}a = \frac{6}{7}a \]
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Combine the \( b \) terms: \[ \frac{1}{8}b + \frac{3}{8}b = \left(\frac{1 + 3}{8}\right)b = \frac{4}{8}b = \frac{1}{2}b \]
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Combine the \( c \) terms: \[ -25c - \frac{2}{5}c = -25c - 0.4c = -25.4c \] To combine \( -25c \) and \( -\frac{2}{5}c \), it's best to express both with a common denominator: \[ -25c = -\frac{125}{5}c \quad \text{(because } -25 = -\frac{125}{5} \text{)} \] Now we can combine: \[ -\frac{125}{5}c - \frac{2}{5}c = -\frac{125 + 2}{5}c = -\frac{127}{5}c \]
Now, we put everything together: \[ \frac{6}{7}a + \frac{1}{2}b - \frac{127}{5}c \]
Thus, the simplified expression is: \[ \frac{6}{7}a + \frac{1}{2}b - \frac{127}{5}c \]
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