Question
Write your answer in simplest form. \( 3 \div \frac{5}{6} \)
Ask by Parry May. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( \frac{18}{5} \)
Solution
To simplify the expression \( 3 \div \frac{5}{6} \), you can follow these steps:
1. **Understand Division by a Fraction**:
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of \(\frac{5}{6}\) is \(\frac{6}{5}\).
2. **Set Up the Multiplication**:
\[
3 \div \frac{5}{6} = 3 \times \frac{6}{5}
\]
3. **Perform the Multiplication**:
\[
3 \times \frac{6}{5} = \frac{18}{5}
\]
4. **Simplify (if necessary)**:
The fraction \(\frac{18}{5}\) is already in its simplest form. If you prefer a mixed number, it can be written as:
\[
3 \frac{3}{5}
\]
**Final Answer:**
\[
3 \div \frac{5}{6} = \frac{18}{5}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To simplify \( 3 \div \frac{5}{6} \), you can multiply 3 by the reciprocal of \(\frac{5}{6}\), which is \(\frac{6}{5}\). Therefore, the expression becomes: \[ 3 \times \frac{6}{5} = \frac{18}{5} \] So the simplest form of \( 3 \div \frac{5}{6} \) is \(\frac{18}{5}\), or 3.6 in decimal form if you prefer!
