To solve the expression \( \frac{7}{8} - \frac{1}{4} + \frac{11}{12} \), we first need to find a common denominator for the fractions.
The denominators are 8, 4, and 12. The least common multiple of these numbers is 24.
Now, we'll convert each fraction to have a denominator of 24:
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Convert \( \frac{7}{8} \): \[ \frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24} \]
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Convert \( \frac{1}{4} \): \[ \frac{1}{4} = \frac{1 \times 6}{4 \times 6} = \frac{6}{24} \]
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Convert \( \frac{11}{12} \): \[ \frac{11}{12} = \frac{11 \times 2}{12 \times 2} = \frac{22}{24} \]
Now, replace the original fractions with these new fractions: \[ \frac{21}{24} - \frac{6}{24} + \frac{22}{24} \]
Next, perform the operations step-by-step:
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Subtract \( \frac{6}{24} \) from \( \frac{21}{24} \): \[ \frac{21}{24} - \frac{6}{24} = \frac{21 - 6}{24} = \frac{15}{24} \]
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Add \( \frac{22}{24} \): \[ \frac{15}{24} + \frac{22}{24} = \frac{15 + 22}{24} = \frac{37}{24} \]
Thus, the final answer is: \[ \frac{37}{24} \]
This fraction is an improper fraction and can be expressed as a mixed number: \[ 1 \frac{13}{24} \]
So, the answer can be presented as \( \frac{37}{24} \) or \( 1 \frac{13}{24} \).