What is the quotient of −5/9÷ 1/5

? Write the answer as a mixed number.(1 point)

1 answer

To find the quotient of \(-\frac{5}{9} \div \frac{1}{5}\), you can multiply by the reciprocal of \(\frac{1}{5}\):

\[ -\frac{5}{9} \div \frac{1}{5} = -\frac{5}{9} \times \frac{5}{1} = -\frac{5 \times 5}{9 \times 1} = -\frac{25}{9} \]

Now, to convert \(-\frac{25}{9}\) to a mixed number, divide \(25\) by \(9\):

  • \(25 \div 9 = 2\) (since \(9 \times 2 = 18\) and \(9 \times 3 = 27\) which exceeds 25).
  • The remainder is \(25 - 18 = 7\).

Thus, \(-\frac{25}{9}\) can be written as the mixed number:

\[ -2 \frac{7}{9} \]

Therefore, the answer is:

\[ -2 \frac{7}{9} \]