To solve the expression \(2 \frac{3}{4} + (1 \frac{1}{2} + 3.8)\), we'll first convert the mixed numbers to improper fractions, perform the addition, and then simplify.
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Convert the mixed numbers:
- \(2 \frac{3}{4} = 2 + \frac{3}{4} = \frac{8}{4} + \frac{3}{4} = \frac{11}{4}\)
- \(1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2}\)
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Now, add \(1 \frac{1}{2}\) and \(3.8\):
- Convert \(3.8\) to a fraction: \(3.8 = \frac{38}{10} = \frac{19}{5}\)
- Find a common denominator for \(\frac{3}{2}\) and \(\frac{19}{5}\). The least common denominator is 10.
- Convert \(\frac{3}{2}\) to have a denominator of 10: \[ \frac{3}{2} = \frac{3 \times 5}{2 \times 5} = \frac{15}{10} \]
- Now add: \[ \frac{15}{10} + \frac{19}{5} = \frac{15}{10} + \frac{19 \times 2}{5 \times 2} = \frac{15}{10} + \frac{38}{10} = \frac{15 + 38}{10} = \frac{53}{10} \]
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Now we add \(\frac{11}{4} + \frac{53}{10}\):
- Find a common denominator for \(\frac{11}{4}\) and \(\frac{53}{10}\). The least common denominator is 20.
- Convert \(\frac{11}{4}\) to have a denominator of 20: \[ \frac{11}{4} = \frac{11 \times 5}{4 \times 5} = \frac{55}{20} \]
- Convert \(\frac{53}{10}\) to have a denominator of 20: \[ \frac{53}{10} = \frac{53 \times 2}{10 \times 2} = \frac{106}{20} \]
- Now, add: \[ \frac{55}{20} + \frac{106}{20} = \frac{55 + 106}{20} = \frac{161}{20} \]
Therefore, the result of the calculation \(2 \frac{3}{4} + (1 \frac{1}{2} + 3.8)\) is \(\frac{161}{20}\), which can also be expressed as a mixed number:
\[ \frac{161}{20} = 8 \frac{1}{20} \]
So, the final answer is \(8 \frac{1}{20}\) or simply \(\frac{161}{20}\).
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