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- https://math.libretexts.org/Courses/Western_Technical_College/PrePALS_PreAlgebra/02%3A_Fractions/2.02%3A_Multiplying_Fractions\[ \begin{aligned} \frac{14}{15} \cdot \frac{30}{140} = \frac{14 \cdot 30}{15 \cdot 140} ~ & \textcolor{red}{ \text{ Multiply numerators; multiply denominators.}} \\ = \frac{(2 \cdot 7) \cdot (2 \cdot...\[ \begin{aligned} \frac{14}{15} \cdot \frac{30}{140} = \frac{14 \cdot 30}{15 \cdot 140} ~ & \textcolor{red}{ \text{ Multiply numerators; multiply denominators.}} \\ = \frac{(2 \cdot 7) \cdot (2 \cdot 3 \cdot 5)}{(3 \cdot 5) \cdot (2 \cdot 2 \cdot 5 \cdot 7)} ~ & \textcolor{red}{ \text{ Prime factor numerators and denominators.}} \\ = \frac{ \cancel{2} \cdot \cancel{7} \cdot \cancel{2} \cdot \cancel{3} \cdot \cancel{5}}{ \cancel{3} \cdot 5 \cdot \cancel{2} \cdot \cancel{2} \cdot \cancel{5} \cdo…
- https://math.libretexts.org/Courses/Honolulu_Community_College/Math_75X%3A_Introduction_to_Mathematical_Reasoning_(Kearns)/02%3A_Fractions_and_Rational_Numbers/2.04%3A_Copies_of_Fractions-_Multiplication_and_Division_with_Rational_Numbers/2.4.00%3A_Multiplying_Fractions\[ \begin{aligned} = \frac{2 \cdot 3 \cdot x}{5 \cdot 11 \cdot y} \cdot \frac{2 \cdot 5 \cdot 11 \cdot y \cdot y}{3 \cdot 5 \cdot 7 \cdot x \cdot x} ~ & \textcolor{red}{ \text{ Prime factor numerators...\[ \begin{aligned} = \frac{2 \cdot 3 \cdot x}{5 \cdot 11 \cdot y} \cdot \frac{2 \cdot 5 \cdot 11 \cdot y \cdot y}{3 \cdot 5 \cdot 7 \cdot x \cdot x} ~ & \textcolor{red}{ \text{ Prime factor numerators & denominators.}} \\ = \frac{2 \cdot \cancel{3} \cdot \cancel{x}}{5 \cdot \cancel{11} \cdot \cancel{y}} \cdot \frac{2 \cdot \cancel{5} \cdot \cancel{11} \cdot \cancel{y} \cdot y}{ \cancel{3} \cdot \cancel{5} \cdot 7 \cdot \cancel{x} \cdot x} ~ & \textcolor{red}{ \text{ Cancel common factors.}} \\ …
- https://math.libretexts.org/Courses/Barton_Community_College/Book%3A_Technical_Mathematics_(Turner)/02%3A_Fractions/2.03%3A_Multiplying_Fractions\[ \begin{aligned} = \frac{2 \cdot 3 \cdot x}{5 \cdot 11 \cdot y} \cdot \frac{2 \cdot 5 \cdot 11 \cdot y \cdot y}{3 \cdot 5 \cdot 7 \cdot x \cdot x} ~ & \textcolor{red}{ \text{ Prime factor numerators...\[ \begin{aligned} = \frac{2 \cdot 3 \cdot x}{5 \cdot 11 \cdot y} \cdot \frac{2 \cdot 5 \cdot 11 \cdot y \cdot y}{3 \cdot 5 \cdot 7 \cdot x \cdot x} ~ & \textcolor{red}{ \text{ Prime factor numerators & denominators.}} \\ = \frac{2 \cdot \cancel{3} \cdot \cancel{x}}{5 \cdot \cancel{11} \cdot \cancel{y}} \cdot \frac{2 \cdot \cancel{5} \cdot \cancel{11} \cdot \cancel{y} \cdot y}{ \cancel{3} \cdot \cancel{5} \cdot 7 \cdot \cancel{x} \cdot x} ~ & \textcolor{red}{ \text{ Cancel common factors.}} \\ …
- https://math.libretexts.org/Courses/Western_Technical_College/PrePALS_Math_with_Business_Apps/02%3A_Fractions/2.02%3A_Multiplying_Fractions\[ \begin{aligned} = \frac{2 \cdot 3 \cdot x}{5 \cdot 11 \cdot y} \cdot \frac{2 \cdot 5 \cdot 11 \cdot y \cdot y}{3 \cdot 5 \cdot 7 \cdot x \cdot x} ~ & \textcolor{red}{ \text{ Prime factor numerators...\[ \begin{aligned} = \frac{2 \cdot 3 \cdot x}{5 \cdot 11 \cdot y} \cdot \frac{2 \cdot 5 \cdot 11 \cdot y \cdot y}{3 \cdot 5 \cdot 7 \cdot x \cdot x} ~ & \textcolor{red}{ \text{ Prime factor numerators & denominators.}} \\ = \frac{2 \cdot \cancel{3} \cdot \cancel{x}}{5 \cdot \cancel{11} \cdot \cancel{y}} \cdot \frac{2 \cdot \cancel{5} \cdot \cancel{11} \cdot \cancel{y} \cdot y}{ \cancel{3} \cdot \cancel{5} \cdot 7 \cdot \cancel{x} \cdot x} ~ & \textcolor{red}{ \text{ Cancel common factors.}} \\ …
