$$4\cdot\dfrac{x^2}{10x}\cdot3xy=\dfrac{12x^3y}{10x}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4 \cdot \frac{x^2}{10x}\cdot3xy& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4x^2}{10x}\cdot3xy \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{12x^2}{10x}xy \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{12x^3}{10x}y \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{12x^3y}{10x}\end{aligned} $$ | |
| ① | Multiply $4$ by $ \dfrac{x^2}{10x} $ to get $ \dfrac{ 4x^2 }{ 10x } $. Step 1: Write $ 4 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 4 \cdot \frac{x^2}{10x} & \xlongequal{\text{Step 1}} \frac{4}{\color{red}{1}} \cdot \frac{x^2}{10x} \xlongequal{\text{Step 2}} \frac{ 4 \cdot x^2 }{ 1 \cdot 10x } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4x^2 }{ 10x } \end{aligned} $$ |
| ② | Multiply $ \dfrac{4x^2}{10x} $ by $ 3 $ to get $ \dfrac{ 12x^2 }{ 10x } $. Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{4x^2}{10x} \cdot 3 & \xlongequal{\text{Step 1}} \frac{4x^2}{10x} \cdot \frac{3}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 4x^2 \cdot 3 }{ 10x \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 12x^2 }{ 10x } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{12x^2}{10x} $ by $ x $ to get $ \dfrac{ 12x^3 }{ 10x } $. Step 1: Write $ x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{12x^2}{10x} \cdot x & \xlongequal{\text{Step 1}} \frac{12x^2}{10x} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 12x^2 \cdot x }{ 10x \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 12x^3 }{ 10x } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{12x^3}{10x} $ by $ y $ to get $ \dfrac{ 12x^3y }{ 10x } $. 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. $$ \begin{aligned} \frac{12x^3}{10x} \cdot y & \xlongequal{\text{Step 1}} \frac{12x^3}{10x} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 12x^3 \cdot y }{ 10x \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 12x^3y }{ 10x } \end{aligned} $$ |