To add the mixed numbers \(1 \frac{3}{4}\) and \(3 \frac{3}{4}\), follow these steps:
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Convert each mixed number to an improper fraction:
- For \(1 \frac{3}{4}\): \[ 1 \times 4 + 3 = 4 + 3 = 7 \quad \Rightarrow \quad 1 \frac{3}{4} = \frac{7}{4} \]
- For \(3 \frac{3}{4}\): \[ 3 \times 4 + 3 = 12 + 3 = 15 \quad \Rightarrow \quad 3 \frac{3}{4} = \frac{15}{4} \]
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Add the improper fractions: \[ \frac{7}{4} + \frac{15}{4} = \frac{7 + 15}{4} = \frac{22}{4} \]
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Simplify the fraction: \[ \frac{22}{4} = \frac{11}{2} \]
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Convert back to a mixed number: \(\frac{11}{2}\) can be expressed as: \[ 11 \div 2 = 5 \quad \text{with a remainder of } 1, \] which gives \(5 \frac{1}{2}\).
So, \(1 \frac{3}{4} + 3 \frac{3}{4} = 5 \frac{1}{2}\).