$$6\cdot\dfrac{x}{10}x\cdot6\dfrac{x}{3}x^3=\dfrac{36x^6}{30}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}6 \cdot \frac{x}{10}x\cdot6\frac{x}{3}x^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{6x}{10}x\cdot6\frac{x}{3}x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6x^2}{10}\cdot6\frac{x}{3}x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{36x^2}{10}\frac{x}{3}x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{36x^3}{30}x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{36x^6}{30}\end{aligned} $$ | |
| ① | Multiply $6$ by $ \dfrac{x}{10} $ to get $ \dfrac{ 6x }{ 10 } $. 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. $$ \begin{aligned} 6 \cdot \frac{x}{10} & \xlongequal{\text{Step 1}} \frac{6}{\color{red}{1}} \cdot \frac{x}{10} \xlongequal{\text{Step 2}} \frac{ 6 \cdot x }{ 1 \cdot 10 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 6x }{ 10 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{6x}{10} $ by $ x $ to get $ \dfrac{ 6x^2 }{ 10 } $. 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. $$ \begin{aligned} \frac{6x}{10} \cdot x & \xlongequal{\text{Step 1}} \frac{6x}{10} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 6x \cdot x }{ 10 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 6x^2 }{ 10 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{6x^2}{10} $ by $ 6 $ to get $ \dfrac{ 36x^2 }{ 10 } $. 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. $$ \begin{aligned} \frac{6x^2}{10} \cdot 6 & \xlongequal{\text{Step 1}} \frac{6x^2}{10} \cdot \frac{6}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 6x^2 \cdot 6 }{ 10 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 36x^2 }{ 10 } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{36x^2}{10} $ by $ \dfrac{x}{3} $ to get $ \dfrac{ 36x^3 }{ 30 } $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{36x^2}{10} \cdot \frac{x}{3} \xlongequal{\text{Step 1}} \frac{ 36x^2 \cdot x }{ 10 \cdot 3 } \xlongequal{\text{Step 2}} \frac{ 36x^3 }{ 30 } \end{aligned} $$ |
| ⑤ | Multiply $ \dfrac{36x^3}{30} $ by $ x^3 $ to get $ \dfrac{ 36x^6 }{ 30 } $. Step 1: Write $ x^3 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{36x^3}{30} \cdot x^3 & \xlongequal{\text{Step 1}} \frac{36x^3}{30} \cdot \frac{x^3}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 36x^3 \cdot x^3 }{ 30 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 36x^6 }{ 30 } \end{aligned} $$ |