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