To add the mixed numbers \(2 \frac{3}{4}\) and \(1 \frac{1}{6}\), we first convert them to improper fractions.
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Convert \(2 \frac{3}{4}\): \[ 2 \frac{3}{4} = 2 \times 4 + 3 = 8 + 3 = 11 \Rightarrow \frac{11}{4} \]
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Convert \(1 \frac{1}{6}\): \[ 1 \frac{1}{6} = 1 \times 6 + 1 = 6 + 1 = 7 \Rightarrow \frac{7}{6} \]
Now we add the two improper fractions:
\[ \frac{11}{4} + \frac{7}{6} \]
To add these fractions, 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 \(\frac{7}{6}\) to a fraction with a denominator of 12: \[ \frac{7}{6} = \frac{7 \times 2}{6 \times 2} = \frac{14}{12} \]
Now, we can add the two fractions:
\[ \frac{33}{12} + \frac{14}{12} = \frac{33 + 14}{12} = \frac{47}{12} \]
Next, we convert \(\frac{47}{12}\) back to a mixed number. To do this, we divide 47 by 12:
- \(12\) goes into \(47\) three times (\(12 \times 3 = 36\)).
- The remainder is \(47 - 36 = 11\).
So,
\[ \frac{47}{12} = 3 \frac{11}{12} \]
Thus, the answer as a mixed number in simplest form is \(3 \frac{11}{12}\).
The whole number part is \(3\).
In conclusion, the answer is: Whole number: 3 Fraction part: \(11/12\) So the answer is \(3\).
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