To find the quotient of \( \frac{8}{9} \div 6 \), you can rewrite the division of a fraction by a whole number as a multiplication by the reciprocal of the whole number.
So, \( \frac{8}{9} \div 6 \) can be rewritten as:
\[ \frac{8}{9} \times \frac{1}{6} \]
Now, multiply the numerators and the denominators:
\[ \frac{8 \times 1}{9 \times 6} = \frac{8}{54} \]
Next, simplify the fraction \( \frac{8}{54} \). The greatest common divisor of 8 and 54 is 2.
Dividing both the numerator and the denominator by 2 gives:
\[ \frac{8 \div 2}{54 \div 2} = \frac{4}{27} \]
Thus, the quotient of \( \frac{8}{9} \div 6 \) is \( \frac{4}{27} \).
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