Question
Divide: \( 4 \frac{2}{3} \div 3 \frac{3}{4} \) \( 1 \frac{1}{2} \) \( \frac{6}{105} \) \( 1 \frac{11}{45} \) \( 1 \frac{8}{9} \)
Ask by Wade Cole. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The answer is \( 1 \frac{11}{45} \).
Solution
To divide \( 4 \frac{2}{3} \) by \( 3 \frac{3}{4} \), follow these steps:
1. **Convert Mixed Numbers to Improper Fractions:**
- \( 4 \frac{2}{3} = \frac{4 \times 3 + 2}{3} = \frac{14}{3} \)
- \( 3 \frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{15}{4} \)
2. **Set Up the Division:**
\[
\frac{14}{3} \div \frac{15}{4} = \frac{14}{3} \times \frac{4}{15}
\]
3. **Multiply the Fractions:**
\[
\frac{14 \times 4}{3 \times 15} = \frac{56}{45}
\]
4. **Simplify or Convert Back to a Mixed Number:**
- \( \frac{56}{45} = 1 \frac{11}{45} \)
**Final Answer:** \( 1 \frac{11}{45} \)
Among the options provided, the correct answer is:
\( 1 \frac{11}{45} \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To solve \( 4 \frac{2}{3} \div 3 \frac{3}{4} \), we first convert the mixed numbers to improper fractions. 1. \( 4 \frac{2}{3} = \frac{14}{3} \) 2. \( 3 \frac{3}{4} = \frac{15}{4} \) Now, we can rewrite the problem as: \[ \frac{14}{3} \div \frac{15}{4} \] To divide by a fraction, we multiply by its reciprocal: \[ \frac{14}{3} \times \frac{4}{15} = \frac{14 \times 4}{3 \times 15} = \frac{56}{45} \] Next, we convert \( \frac{56}{45} \) back into a mixed number: \[ 56 \div 45 = 1 \text{ R } 11 \quad \Rightarrow \quad 1 \frac{11}{45} \] Thus, the final answer is \( 1 \frac{11}{45} \).
