Divide and Simplify

Explanation

We will multiply the first fraction, \(\frac16\), by the reciprocal of the second fraction, \(-\frac{1}{18}\).  To determine the sign of the result, we will use the rule for multiplying two fractions that have different (unlike) signs.

• Multiply \(\frac16\) by the reciprocal of \(-\frac{1}{18}\), which is \(-\frac{18}{1}\)
  • \(\frac16 \color{red}{ ÷ \left(-\frac{1}{18}\right)} = \frac16 \color{red}{\left( -\frac{18}{1}\right)}\)
• Multiply the numerators.  Multiply the denominators.  since the fractions have unlike signs, make the answer negative.
  • = \(\frac{1 \cdot 18}{6 \cdot 1}\)
• To simplify, factor 18 as 3 • 6.  Then remove the common factor of 6 from the numerator and denominator.
  • = \(\require{cancel} \frac{1 \cdot 3 \cdot \cancel{6}^1}{\cancel{6}_1 \cdot 1} \)
• Multiply the remaining factors in the numerator.  Multiply the remaining factors in the denominator
  • = \(-\frac31\) = -3