Answer
$$6\cdot\frac{x}{2}y=\frac{6xy}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}6 \cdot \frac{x}{2}y& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{6x}{2}y \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6xy}{2}\end{aligned} $$ | |
| ① | Multiply $6$ by $ \dfrac{x}{2} $ to get $ \dfrac{ 6x }{ 2 } $. Step 1: Write $ 6 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 6 \cdot \frac{x}{2} & \xlongequal{\text{Step 1}} \frac{6}{\color{red}{1}} \cdot \frac{x}{2} \xlongequal{\text{Step 2}} \frac{ 6 \cdot x }{ 1 \cdot 2 } \xlongequal{\text{Step 3}} \frac{ 6x }{ 2 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{6x}{2} $ by $ y $ to get $ \dfrac{ 6xy }{ 2 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{6x}{2} \cdot y & \xlongequal{\text{Step 1}} \frac{6x}{2} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 6x \cdot y }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 6xy }{ 2 } \end{aligned} $$ |
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