Question
\( \left(\frac{2}{3} \div \frac{3}{2}\right) \cdot \frac{5}{6}=\square \) (Simplify your answer.)
Ask by Wagner Reed. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified answer is \( \frac{10}{27} \) or approximately \( 0.\dot{3}7\dot{0} \).
Solution
Calculate or simplify the expression \( (2/3) \div (3/2) \cdot (5/6) \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{2}{3}\div \frac{3}{2}\times \frac{5}{6}\)
- step1: Divide the terms:
\(\frac{4}{9}\times \frac{5}{6}\)
- step2: Reduce the numbers:
\(\frac{2}{9}\times \frac{5}{3}\)
- step3: Multiply the fractions:
\(\frac{2\times 5}{9\times 3}\)
- step4: Multiply:
\(\frac{10}{27}\)
The simplified expression is \( \frac{10}{27} \) or \( 0.\dot{3}7\dot{0} \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To solve \( \left(\frac{2}{3} \div \frac{3}{2}\right) \cdot \frac{5}{6} \), we first perform the division. Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{2}{3} \div \frac{3}{2} = \frac{2}{3} \cdot \frac{2}{3} = \frac{4}{9} \] Now, we multiply this result by \( \frac{5}{6} \): \[ \frac{4}{9} \cdot \frac{5}{6} = \frac{4 \cdot 5}{9 \cdot 6} = \frac{20}{54} \] Next, we simplify \( \frac{20}{54} \) by finding the greatest common divisor (GCD) of 20 and 54, which is 2: \[ \frac{20 \div 2}{54 \div 2} = \frac{10}{27} \] The final simplified answer is: \[ \frac{10}{27} \]
