Answer
$$\frac{x^2}{3}\frac{y^1}{2}+\frac{x^1}{2}\frac{y^2}{3}=\frac{x^2y+xy^2}{6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{x^2}{3}\frac{y^1}{2}+\frac{x^1}{2}\frac{y^2}{3}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{x^2y}{6}+\frac{xy^2}{6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{x^2y+xy^2}{6}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{x^2}{3} $ by $ \dfrac{y}{2} $ to get $ \dfrac{ x^2y }{ 6 } $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{x^2}{3} \cdot \frac{y}{2} \xlongequal{\text{Step 1}} \frac{ x^2 \cdot y }{ 3 \cdot 2 } \xlongequal{\text{Step 2}} \frac{ x^2y }{ 6 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{x}{2} $ by $ \dfrac{y^2}{3} $ to get $ \dfrac{ xy^2 }{ 6 } $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{x}{2} \cdot \frac{y^2}{3} \xlongequal{\text{Step 1}} \frac{ x \cdot y^2 }{ 2 \cdot 3 } \xlongequal{\text{Step 2}} \frac{ xy^2 }{ 6 } \end{aligned} $$ |
| ③ | Add $ \dfrac{x^2y}{6} $ and $ \dfrac{xy^2}{6} $ to get $ \dfrac{ x^2y + xy^2 }{ \color{blue}{ 6 }}$. To add expressions with the same denominators, we add the numerators and write the result over the common denominator. $$ \begin{aligned} \frac{x^2y}{6} + \frac{xy^2}{6} & = \frac{x^2y}{\color{blue}{6}} + \frac{xy^2}{\color{blue}{6}} =\frac{ x^2y + xy^2 }{ \color{blue}{ 6 }} \end{aligned} $$ |
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