Divide and Simplify

Explanation

We will multiply the first fraction, \(\frac{9}{16}\), by the reciprocal of the second fraction, \(\frac{3}{20}\).  Then, if possible, we will simplify the result.

• Multiply \(\frac{9}{16}\) by the reciprocal of \(\frac{3}{20}\), which is \(\frac{20}{3}\)
  • \(\frac{9}{16} \color{red}{ ÷ \frac{3}{20}} = \frac{9}{16} \color{red} {\cdot \frac{20}{3}}\)
• Multiply the numerators.  Multiply the denominators.
  • = \(\frac{9 \cdot 20}{16 \cdot 3}\)
• To simplify, factor 9 as 3 • 3, factor 20 as 4 • 5, and factor 16 as 4 • 4.  Then remove out the common factors of 3 and 4 from the numerator and denominator.
  • = \(\require{cancel} \frac{\cancel{3}^1 \cdot 3 \cdot \cancel{4}^1 \cdot 5}{\cancel{4}_1 \cdot 4 \cdot \cancel{3}_1}\)
• Multiply the remaining factors in the numerator: 1 • 3 • 1 • 5 = 15.  Multiply the remaining factors in the denominator: 1 • 4 • 1 = 4
  • = \(\frac{15}{4}\)