The properties of commutativity, associatitivy and distributivity of fractions are presented. These properties along with other rules of fractions may be used to simplify and factor expressions including fractions.
Do NOT use the calculator to answer the questions.
Distributivity of Multiplication Over Addition of Fractions
\( \color{red}{\dfrac{a}{b}} \left(\dfrac{c}{d} + \dfrac{e}{f} \right) = \left(\color{red}{\dfrac{a}{b}} \times \dfrac{c}{d} \right) + \left( \color{red}{\dfrac{a}{b}} \times \dfrac{e}{f} \right ) \)
NOTE that when using the above distributivity from right to left, we say that we are factoring out (writing as a product) the fraction \( \dfrac{a}{b} \)
\( \left(\color{red}{\dfrac{a}{b}} \times \dfrac{c}{d} \right) + \left( \color{red}{\dfrac{a}{b}} \times \dfrac{e}{f} \right ) = \color{red}{\dfrac{a}{b}} \left(\dfrac{c}{d} + \dfrac{e}{f} \right) \)