Question
Find and simplify the quotient \( \frac{2}{3} \div \frac{8}{9} \)
Ask by Fuentes Griffiths. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified quotient is \( \frac{3}{4} \).
Solution
Starting with the expression:
\[
\frac{2}{3} \div \frac{8}{9}
\]
We rewrite the division as multiplication by the reciprocal:
\[
\frac{2}{3} \times \frac{9}{8}
\]
Multiply the numerators and denominators:
\[
\frac{2 \times 9}{3 \times 8} = \frac{18}{24}
\]
Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is \(6\):
\[
\frac{18 \div 6}{24 \div 6} = \frac{3}{4}
\]
Thus, the simplified quotient is:
\[
\frac{3}{4}
\]
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Simplify this solution Extra Insights
To simplify the quotient \( \frac{2}{3} \div \frac{8}{9} \), we first convert the division of fractions into multiplication by the reciprocal. This gives us: \[ \frac{2}{3} \div \frac{8}{9} = \frac{2}{3} \times \frac{9}{8} \] Next, we multiply the numerators together and the denominators together: \[ \frac{2 \times 9}{3 \times 8} = \frac{18}{24} \] Now, we simplify \( \frac{18}{24} \) by finding the greatest common divisor (GCD) of 18 and 24, which is 6. We then divide both the numerator and the denominator by 6: \[ \frac{18 \div 6}{24 \div 6} = \frac{3}{4} \] Thus, the simplified quotient is: \[ \boxed{\frac{3}{4}} \]
