Divide and Simplify

Explanation

We will multiply the first fraction, \(-\frac{21}{36}\), by the reciprocal of -3.  To determine the sign of the result, we will use the rule for multiplying two fractions that have the same (like) signs.

• Multiply  \(-\frac{21}{36}\) by the reciprocal of -3, which is \(-\frac13\)
  • \(-\frac{21}{36} \color{red}{ ÷ (-3)} = -\frac{21}{36} \color{red}{\left( -\frac13 \right)}\)
• Since the product of two negative  fraction is positive, drop both - signs and continue.
  • = \(\frac{21}{36} \left( \frac13 \right)\)
• Multiply the numerators.  Multiply the denominators
  • = \(\frac{21 \cdot 1}{36 \cdot 3}\)
• To simplify, factor 21 as 3 • 7.  Then remove the common factor of 3 from the numerator and denominator.
  • = \(\require{cancel} \frac{\cancel{3}^1 \cdot 7 \cdot 1}{36 \cdot \cancel{3}_1}\)
• Multiply the remaining factors in the numerator 1 • 7 • 1 = 7.  Multiply the remaining factors in the denominator.
  • = \(\frac{7}{36}\)