Question
5. \( \frac{5}{6} \times 3 \frac{1}{5}= \)
Ask by Willis Ortega. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The result is \( \frac{8}{3} \) or \( 2\frac{2}{3} \).
Solution
1. Convert the mixed number to an improper fraction:
\[
3\frac{1}{5} = \frac{3 \times 5 + 1}{5} = \frac{16}{5}
\]
2. Multiply the fractions:
\[
\frac{5}{6} \times \frac{16}{5} = \frac{5 \times 16}{6 \times 5} = \frac{80}{30}
\]
3. Simplify the fraction by canceling the common factor \(5\) and reducing:
\[
\frac{80 \div 10}{30 \div 10} = \frac{8}{3}
\]
Alternatively, you can simplify directly:
\[
\frac{5}{6} \times \frac{16}{5} = \frac{16}{6} = \frac{8}{3}
\]
Thus, the final result is:
\[
\frac{8}{3} \quad \text{or} \quad 2\frac{2}{3}
\]
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Simplify this solution Beyond the Answer
To solve \( \frac{5}{6} \times 3 \frac{1}{5} \), first convert the mixed number into an improper fraction. \( 3 \frac{1}{5} \) becomes \( \frac{16}{5} \). Now, multiply the fractions: \[ \frac{5}{6} \times \frac{16}{5} = \frac{5 \times 16}{6 \times 5} = \frac{16}{6} \] Now, simplify \( \frac{16}{6} \) to \( \frac{8}{3} \) or \( 2 \frac{2}{3} \). So, \( \frac{5}{6} \times 3 \frac{1}{5} = 2 \frac{2}{3} \).
