To add the fractions \( \frac{5}{6} \) and \( -\frac{3}{8} \), we first need a common denominator. The denominators are 6 and 8.
The least common multiple (LCM) of 6 and 8 is 24. We will convert both fractions to have this common denominator.
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Convert \( \frac{5}{6} \): \[ \frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24} \]
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Convert \( -\frac{3}{8} \): \[ -\frac{3}{8} = -\frac{3 \times 3}{8 \times 3} = -\frac{9}{24} \]
Now, we can add the two fractions: \[ \frac{20}{24} - \frac{9}{24} = \frac{20 - 9}{24} = \frac{11}{24} \]
The fraction \( \frac{11}{24} \) is already in its simplest form, as 11 is a prime number and does not divide 24.
Thus, the final answer is: \[ \frac{11}{24} \]
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