To solve the expression \( 1 \frac{1}{4} \times 5 + 1 \frac{1}{2} \times 3 + 1 \frac{3}{4} + 3 \), we first need to convert the mixed numbers into improper fractions and then perform the operations.
- Convert the mixed numbers:
- \( 1 \frac{1}{4} = \frac{5}{4} \)
- \( 1 \frac{1}{2} = \frac{3}{2} \)
- \( 1 \frac{3}{4} = \frac{7}{4} \)
Now substitute these back into the expression: \[ \frac{5}{4} \times 5 + \frac{3}{2} \times 3 + \frac{7}{4} + 3 \]
- Next, calculate each multiplication:
- \( \frac{5}{4} \times 5 = \frac{5 \times 5}{4} = \frac{25}{4} \)
- \( \frac{3}{2} \times 3 = \frac{3 \times 3}{2} = \frac{9}{2} \)
Now, rewrite the expression: \[ \frac{25}{4} + \frac{9}{2} + \frac{7}{4} + 3 \]
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Now we need a common denominator to add these fractions. The common denominator for \(4\) and \(2\) is \(4\). Rewrite \( \frac{9}{2} \) with a denominator of \(4\): \[ \frac{9}{2} = \frac{9 \times 2}{2 \times 2} = \frac{18}{4} \]
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Now, substitute this back in: \[ \frac{25}{4} + \frac{18}{4} + \frac{7}{4} + 3 \]
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Combine the fractions: \[ \frac{25 + 18 + 7}{4} + 3 = \frac{50}{4} + 3 = \frac{50}{4} + \frac{12}{4} = \frac{62}{4} \]
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Simplify \( \frac{62}{4} \): \[ \frac{62}{4} = \frac{31}{2} = 15 \frac{1}{2} = 15.5 \]
Thus, the final result is: \[ \boxed{15.5} \]