$$3\cdot\dfrac{m^2}{4}m^7n^2=\dfrac{3m^9n^2}{4}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3 \cdot \frac{m^2}{4}m^7n^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3m^2}{4}m^7n^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{3m^9}{4}n^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{3m^9n^2}{4}\end{aligned} $$ | |
| ① | Multiply $3$ by $ \dfrac{m^2}{4} $ to get $ \dfrac{ 3m^2 }{ 4 } $. 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. $$ \begin{aligned} 3 \cdot \frac{m^2}{4} & \xlongequal{\text{Step 1}} \frac{3}{\color{red}{1}} \cdot \frac{m^2}{4} \xlongequal{\text{Step 2}} \frac{ 3 \cdot m^2 }{ 1 \cdot 4 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3m^2 }{ 4 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{3m^2}{4} $ by $ m^7 $ to get $ \dfrac{ 3m^9 }{ 4 } $. Step 1: Write $ m^7 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{3m^2}{4} \cdot m^7 & \xlongequal{\text{Step 1}} \frac{3m^2}{4} \cdot \frac{m^7}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 3m^2 \cdot m^7 }{ 4 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3m^9 }{ 4 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{3m^9}{4} $ by $ n^2 $ to get $ \dfrac{ 3m^9n^2 }{ 4 } $. Step 1: Write $ n^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{3m^9}{4} \cdot n^2 & \xlongequal{\text{Step 1}} \frac{3m^9}{4} \cdot \frac{n^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 3m^9 \cdot n^2 }{ 4 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3m^9n^2 }{ 4 } \end{aligned} $$ |