$$-5\cdot\dfrac{x}{3}y\dfrac{y^2}{25}x=\dfrac{5x^2y^3}{75}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-5 \cdot \frac{x}{3}y\frac{y^2}{25}x& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5x}{3}y\frac{y^2}{25}x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{5xy}{3}\frac{y^2}{25}x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{5xy^3}{75}x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{5x^2y^3}{75}\end{aligned} $$ | |
| ① | Multiply $5$ by $ \dfrac{x}{3} $ to get $ \dfrac{ 5x }{ 3 } $. Step 1: Write $ 5 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 5 \cdot \frac{x}{3} & \xlongequal{\text{Step 1}} \frac{5}{\color{red}{1}} \cdot \frac{x}{3} \xlongequal{\text{Step 2}} \frac{ 5 \cdot x }{ 1 \cdot 3 } \xlongequal{\text{Step 3}} \frac{ 5x }{ 3 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{5x}{3} $ by $ y $ to get $ \dfrac{ 5xy }{ 3 } $. 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. $$ \begin{aligned} \frac{5x}{3} \cdot y & \xlongequal{\text{Step 1}} \frac{5x}{3} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5x \cdot y }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5xy }{ 3 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{5xy}{3} $ by $ \dfrac{y^2}{25} $ to get $ \dfrac{ 5xy^3 }{ 75 } $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{5xy}{3} \cdot \frac{y^2}{25} \xlongequal{\text{Step 1}} \frac{ 5xy \cdot y^2 }{ 3 \cdot 25 } \xlongequal{\text{Step 2}} \frac{ 5xy^3 }{ 75 } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{5xy^3}{75} $ by $ x $ to get $ \dfrac{ 5x^2y^3 }{ 75 } $. 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. $$ \begin{aligned} \frac{5xy^3}{75} \cdot x & \xlongequal{\text{Step 1}} \frac{5xy^3}{75} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5xy^3 \cdot x }{ 75 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^2y^3 }{ 75 } \end{aligned} $$ |