Question

which explains how to find the quotient of the given division?
write (-3\frac{1}{3}) as (-\frac{9}{3}). then, rewrite (\frac{-3\frac{1}{3}}{\frac{1}{9}}) as (-\frac{9}{3} \times \frac{1}{9}). the quotient is (-1\frac{1}{3}).

write (-3\frac{1}{3}) as (-\frac{13}{3}), and find the reciprocal of (\frac{4}{9}) as (\frac{9}{4}). then, rewrite (\frac{-3\frac{1}{3}}{\frac{1}{9}}) as (-\frac{13}{3} \times \frac{9}{4}). the quotient is (-9\frac{3}{4}).

write (-3\frac{1}{3}) as (-\frac{10}{3}). then, rewrite (\frac{-3\frac{1}{3}}{\frac{1}{9}}) as (-\frac{10}{3} \times \frac{1}{9}). the quotient is (-1\frac{11}{27} = -1\frac{11}{27}).

(note: the original ocr had some formatting issues; the above is a cleaned-up version of the division problem explanations.)

Explanation:

Step1: Convert mixed number to improper fraction

$-3\frac{1}{3} = -\frac{3\times3 + 1}{3} = -\frac{10}{3}$

Step2: Rewrite division as multiplication by reciprocal

Dividing by $\frac{4}{9}$ is equal to multiplying by $\frac{9}{4}$, so:
$-\frac{10}{3} \div \frac{4}{9} = -\frac{10}{3} \times \frac{9}{4}$

Step3: Calculate the product

Multiply numerators and denominators:
$-\frac{10\times9}{3\times4} = -\frac{90}{12} = -\frac{15}{2} = -1\frac{13}{27}$

Answer:

The correct explanation is:
Write $-3\frac{1}{3}$ as $-\frac{10}{3}$. Then, rewrite $\frac{-3\frac{1}{3}}{\frac{4}{9}}$ as $-\frac{10}{3} \times \frac{9}{4}$. The quotient is $-1\frac{13}{27}$.