$$5\cdot\dfrac{y^2}{3}\cdot9\dfrac{x}{10}y=\dfrac{45xy^3}{30}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}5 \cdot \frac{y^2}{3}\cdot9\frac{x}{10}y& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5y^2}{3}\cdot9\frac{x}{10}y \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{45y^2}{3}\frac{x}{10}y \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{45xy^2}{30}y \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{45xy^3}{30}\end{aligned} $$ | |
| ① | Multiply $5$ by $ \dfrac{y^2}{3} $ to get $ \dfrac{ 5y^2 }{ 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. $$ \begin{aligned} 5 \cdot \frac{y^2}{3} & \xlongequal{\text{Step 1}} \frac{5}{\color{red}{1}} \cdot \frac{y^2}{3} \xlongequal{\text{Step 2}} \frac{ 5 \cdot y^2 }{ 1 \cdot 3 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5y^2 }{ 3 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{5y^2}{3} $ by $ 9 $ to get $ \dfrac{ 45y^2 }{ 3 } $. Step 1: Write $ 9 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{5y^2}{3} \cdot 9 & \xlongequal{\text{Step 1}} \frac{5y^2}{3} \cdot \frac{9}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5y^2 \cdot 9 }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 45y^2 }{ 3 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{45y^2}{3} $ by $ \dfrac{x}{10} $ to get $ \dfrac{ 45xy^2 }{ 30 } $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{45y^2}{3} \cdot \frac{x}{10} \xlongequal{\text{Step 1}} \frac{ 45y^2 \cdot x }{ 3 \cdot 10 } \xlongequal{\text{Step 2}} \frac{ 45xy^2 }{ 30 } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{45xy^2}{30} $ by $ y $ to get $ \dfrac{ 45xy^3 }{ 30 } $. 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. $$ \begin{aligned} \frac{45xy^2}{30} \cdot y & \xlongequal{\text{Step 1}} \frac{45xy^2}{30} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 45xy^2 \cdot y }{ 30 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 45xy^3 }{ 30 } \end{aligned} $$ |