To add the fractions \( \frac{3}{4} + \frac{2}{3} + \frac{1}{8} \), we first need to find a common denominator.
The denominators are 4, 3, and 8. The least common multiple (LCM) of these numbers is 24.
Next, we convert each fraction to have the common denominator of 24:
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Convert \( \frac{3}{4} \): \[ \frac{3}{4} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24} \]
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Convert \( \frac{2}{3} \): \[ \frac{2}{3} = \frac{2 \times 8}{3 \times 8} = \frac{16}{24} \]
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Convert \( \frac{1}{8} \): \[ \frac{1}{8} = \frac{1 \times 3}{8 \times 3} = \frac{3}{24} \]
Now we can add the fractions: \[ \frac{18}{24} + \frac{16}{24} + \frac{3}{24} = \frac{18 + 16 + 3}{24} = \frac{37}{24} \]
The result \( \frac{37}{24} \) is an improper fraction, which can also be expressed as a mixed number: \[ \frac{37}{24} = 1 \frac{13}{24} \]
Thus, the simplified result is: \[ \frac{37}{24} \quad \text{or} \quad 1 \frac{13}{24} \]
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