To add \(2 \frac{3}{4}\) and \( \frac{5}{6} \), we first convert \(2 \frac{3}{4}\) to an improper fraction.
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Convert \(2 \frac{3}{4}\): \[ 2 = \frac{2 \times 4}{4} = \frac{8}{4} \] So, \[ 2 \frac{3}{4} = \frac{8}{4} + \frac{3}{4} = \frac{11}{4} \]
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Now, we need to add \(\frac{11}{4}\) and \(\frac{5}{6}\). To do this, we need a common denominator. The least common multiple of 4 and 6 is 12.
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Convert \(\frac{11}{4}\) to a fraction with a denominator of 12: \[ \frac{11}{4} = \frac{11 \times 3}{4 \times 3} = \frac{33}{12} \]
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Convert \(\frac{5}{6}\) to a fraction with a denominator of 12: \[ \frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12} \]
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Now, add the two fractions: \[ \frac{33}{12} + \frac{10}{12} = \frac{33 + 10}{12} = \frac{43}{12} \]
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Convert \(\frac{43}{12}\) back to a mixed number. Divide 43 by 12:
- 43 divided by 12 is 3 with a remainder of 7.
- Therefore, \(\frac{43}{12} = 3 \frac{7}{12}\).
Thus, the final result is: \[ 2 \frac{3}{4} + \frac{5}{6} = 3 \frac{7}{12} \]