$$\dfrac{x}{5}xyx=\dfrac{x^3y}{5}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{x}{5}xyx& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{x^2}{5}yx \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{x^2y}{5}x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{x^3y}{5}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{x}{5} $ by $ x $ to get $ \dfrac{ x^2 }{ 5 } $. 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. $$ \begin{aligned} \frac{x}{5} \cdot x & \xlongequal{\text{Step 1}} \frac{x}{5} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ x \cdot x }{ 5 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ x^2 }{ 5 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{x^2}{5} $ by $ y $ to get $ \dfrac{ x^2y }{ 5 } $. 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. $$ \begin{aligned} \frac{x^2}{5} \cdot y & \xlongequal{\text{Step 1}} \frac{x^2}{5} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ x^2 \cdot y }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x^2y }{ 5 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{x^2y}{5} $ by $ x $ to get $ \dfrac{ x^3y }{ 5 } $. 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. $$ \begin{aligned} \frac{x^2y}{5} \cdot x & \xlongequal{\text{Step 1}} \frac{x^2y}{5} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ x^2y \cdot x }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x^3y }{ 5 } \end{aligned} $$ |