Answer
$$2\cdot\frac{x^3}{3y^2}\frac{y}{x^2}=\frac{2x^3y}{3x^2y^2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2 \cdot \frac{x^3}{3y^2}\frac{y}{x^2}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2x^3}{3y^2}\frac{y}{x^2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{2x^3y}{3x^2y^2}\end{aligned} $$ | |
| ① | Multiply $2$ by $ \dfrac{x^3}{3y^2} $ to get $ \dfrac{ 2x^3 }{ 3y^2 } $. Step 1: Write $ 2 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 2 \cdot \frac{x^3}{3y^2} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{x^3}{3y^2} \xlongequal{\text{Step 2}} \frac{ 2 \cdot x^3 }{ 1 \cdot 3y^2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2x^3 }{ 3y^2 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{2x^3}{3y^2} $ by $ \dfrac{y}{x^2} $ to get $ \dfrac{ 2x^3y }{ 3x^2y^2 } $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{2x^3}{3y^2} \cdot \frac{y}{x^2} & \xlongequal{\text{Step 1}} \frac{ 2x^3 \cdot y }{ 3y^2 \cdot x^2 } \xlongequal{\text{Step 2}} \frac{ 2x^3y }{ 3x^2y^2 } \end{aligned} $$ |
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