Answer
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3\frac{n^4}{2}}{\frac{2}{6}n^3}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{ \frac{3n^4}{2} }{ \frac{ 2 : \color{orangered}{ 2 } }{ 6 : \color{orangered}{ 2 }} \cdot n^3 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\frac{3n^4}{2}}{\frac{1}{3}n^3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{\frac{3n^4}{2}}{\frac{n^3}{3}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}\frac{9n^4}{2n^3}\end{aligned} $$ | |
| ① | Multiply $3$ by $ \dfrac{n^4}{2} $ to get $ \dfrac{ 3n^4 }{ 2 } $. 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. $$ \begin{aligned} 3 \cdot \frac{n^4}{2} & \xlongequal{\text{Step 1}} \frac{3}{\color{red}{1}} \cdot \frac{n^4}{2} \xlongequal{\text{Step 2}} \frac{ 3 \cdot n^4 }{ 1 \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3n^4 }{ 2 } \end{aligned} $$ |
| ② | Divide both the top and bottom numbers by $ \color{orangered}{ 2 } $. |
| ③ | Multiply $3$ by $ \dfrac{n^4}{2} $ to get $ \dfrac{ 3n^4 }{ 2 } $. 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. $$ \begin{aligned} 3 \cdot \frac{n^4}{2} & \xlongequal{\text{Step 1}} \frac{3}{\color{red}{1}} \cdot \frac{n^4}{2} \xlongequal{\text{Step 2}} \frac{ 3 \cdot n^4 }{ 1 \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3n^4 }{ 2 } \end{aligned} $$ |
| ④ | Multiply $3$ by $ \dfrac{n^4}{2} $ to get $ \dfrac{ 3n^4 }{ 2 } $. 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. $$ \begin{aligned} 3 \cdot \frac{n^4}{2} & \xlongequal{\text{Step 1}} \frac{3}{\color{red}{1}} \cdot \frac{n^4}{2} \xlongequal{\text{Step 2}} \frac{ 3 \cdot n^4 }{ 1 \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3n^4 }{ 2 } \end{aligned} $$ |
| ⑤ | Multiply $ \dfrac{1}{3} $ by $ n^3 $ to get $ \dfrac{ n^3 }{ 3 } $. Step 1: Write $ n^3 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{1}{3} \cdot n^3 & \xlongequal{\text{Step 1}} \frac{1}{3} \cdot \frac{n^3}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot n^3 }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ n^3 }{ 3 } \end{aligned} $$ |
| ⑥ | Divide $ \dfrac{3n^4}{2} $ by $ \dfrac{n^3}{3} $ to get $ \dfrac{ 9n^4 }{ 2n^3 } $. Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{ \frac{3n^4}{2} }{ \frac{\color{blue}{n^3}}{\color{blue}{3}} } & \xlongequal{\text{Step 1}} \frac{3n^4}{2} \cdot \frac{\color{blue}{3}}{\color{blue}{n^3}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 3n^4 \cdot 3 }{ 2 \cdot n^3 } \xlongequal{\text{Step 3}} \frac{ 9n^4 }{ 2n^3 } \end{aligned} $$ |