Divide. Write your answer as a fraction or mixed number in simplest form.

- 5/12 divided by ( - 25/18 )

1 answer

To divide \(-\frac{5}{12}\) by \(-\frac{25}{18}\), you can multiply by the reciprocal of the divisor.

The reciprocal of \(-\frac{25}{18}\) is \(-\frac{18}{25}\).

So, we have:

\[ -\frac{5}{12} \div -\frac{25}{18} = -\frac{5}{12} \times -\frac{18}{25} \]

The negatives cancel each other out, so we have:

\[ \frac{5}{12} \times \frac{18}{25} \]

Now we multiply the numerators and the denominators:

\[ \frac{5 \times 18}{12 \times 25} = \frac{90}{300} \]

Next, we simplify \(\frac{90}{300}\) by finding the greatest common divisor (GCD) of 90 and 300. The GCD is 90.

Now divide both the numerator and the denominator by their GCD:

\[ \frac{90 \div 90}{300 \div 90} = \frac{1}{3.33} = \frac{1}{3} \]

Thus, the final answer is:

\[ \frac{3}{10} \]

So, the simplest form of \(-\frac{5}{12}\) divided by \(-\frac{25}{18}\) is

\(\frac{3}{10}\).