Bot GPT 4-o mini To simplify the expression \( \frac{5}{14}a - \frac{2}{5}c + \frac{1}{8}b - \frac{2}{5}c + \frac{3}{8}b + \frac{7}{14}a \), we can group the like terms together.
First, we can combine the terms with \( a \): \[ \frac{5}{14}a + \frac{7}{14}a = \frac{5 + 7}{14}a = \frac{12}{14}a = \frac{6}{7}a \]
Next, we combine the terms with \( c \): \[ -\frac{2}{5}c - \frac{2}{5}c = -\frac{4}{5}c \]
Finally, we combine the terms with \( b \): \[ \frac{1}{8}b + \frac{3}{8}b = \frac{1 + 3}{8}b = \frac{4}{8}b = \frac{1}{2}b \]
Now, we can put it all together: \[ \frac{6}{7}a - \frac{4}{5}c + \frac{1}{2}b \]
Thus, the simplified expression is: \[ \frac{6}{7}a - \frac{4}{5}c + \frac{1}{2}b \]
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