Pregunta
Multiply. \[ 1 \frac{1}{2} \times 2 \frac{1}{2} \] Write your answer as a mixed number in simplest form.
Ask by Maxwell Mcfarlane. in the United States
Jan 24,2025
Solución de tutoría real
Respuesta verificada por el tutor
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The product of \( 1 \frac{1}{2} \) and \( 2 \frac{1}{2} \) is \( 3 \frac{3}{4} \).
Solución
To multiply the mixed numbers \( 1 \frac{1}{2} \) and \( 2 \frac{1}{2} \), follow these steps:
1. **Convert to Improper Fractions:**
\[
1 \frac{1}{2} = \frac{3}{2} \quad \text{and} \quad 2 \frac{1}{2} = \frac{5}{2}
\]
2. **Multiply the Improper Fractions:**
\[
\frac{3}{2} \times \frac{5}{2} = \frac{15}{4}
\]
3. **Convert Back to a Mixed Number:**
\[
\frac{15}{4} = 3 \frac{3}{4}
\]
**Final Answer:**
\[
3 \frac{3}{4}
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Beyond the Answer
To multiply \(1 \frac{1}{2}\) by \(2 \frac{1}{2}\), first convert the mixed numbers into improper fractions. For \(1 \frac{1}{2}\): \[ 1 \frac{1}{2} = 1 \times 2 + 1 = 2 + 1 = 3 \] So, \(1 \frac{1}{2} = \frac{3}{2}\). For \(2 \frac{1}{2}\): \[ 2 \frac{1}{2} = 2 \times 2 + 1 = 4 + 1 = 5 \] Thus, \(2 \frac{1}{2} = \frac{5}{2}\). Now, multiply these two improper fractions: \[ \frac{3}{2} \times \frac{5}{2} = \frac{3 \times 5}{2 \times 2} = \frac{15}{4}. \] Next, convert \(\frac{15}{4}\) back to a mixed number: \[ 15 \div 4 = 3 \quad \text{with a remainder of } 3. \] So, \(\frac{15}{4} = 3 \frac{3}{4}\). The final answer is: \[ \boxed{3 \frac{3}{4}}. \]
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