$$7\cdot\dfrac{\dfrac{\dfrac{x^2}{6}}{7}}{8}x^2=\dfrac{7x^4}{336}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}7 \cdot \frac{\frac{\frac{x^2}{6}}{7}}{8}x^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}7 \cdot \frac{\frac{x^2}{42}}{8}x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}7 \cdot \frac{x^2}{336}x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{7x^2}{336}x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{7x^4}{336}\end{aligned} $$ | |
| ① | Divide $ \dfrac{x^2}{6} $ by $ 7 $ to get $ \dfrac{ x^2 }{ 42 } $. 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. $$ \begin{aligned} \frac{ \frac{x^2}{6} }{7} & \xlongequal{\text{Step 1}} \frac{x^2}{6} \cdot \frac{\color{blue}{1}}{\color{blue}{7}} \xlongequal{\text{Step 2}} \frac{ x^2 \cdot 1 }{ 6 \cdot 7 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x^2 }{ 42 } \end{aligned} $$ |
| ② | Divide $ \dfrac{x^2}{42} $ by $ 8 $ to get $ \dfrac{ x^2 }{ 336 } $. 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. $$ \begin{aligned} \frac{ \frac{x^2}{42} }{8} & \xlongequal{\text{Step 1}} \frac{x^2}{42} \cdot \frac{\color{blue}{1}}{\color{blue}{8}} \xlongequal{\text{Step 2}} \frac{ x^2 \cdot 1 }{ 42 \cdot 8 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x^2 }{ 336 } \end{aligned} $$ |
| ③ | Multiply $7$ by $ \dfrac{x^2}{336} $ to get $ \dfrac{ 7x^2 }{ 336 } $. Step 1: Write $ 7 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 7 \cdot \frac{x^2}{336} & \xlongequal{\text{Step 1}} \frac{7}{\color{red}{1}} \cdot \frac{x^2}{336} \xlongequal{\text{Step 2}} \frac{ 7 \cdot x^2 }{ 1 \cdot 336 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 7x^2 }{ 336 } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{7x^2}{336} $ by $ x^2 $ to get $ \dfrac{ 7x^4 }{ 336 } $. Step 1: Write $ x^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{7x^2}{336} \cdot x^2 & \xlongequal{\text{Step 1}} \frac{7x^2}{336} \cdot \frac{x^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 7x^2 \cdot x^2 }{ 336 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 7x^4 }{ 336 } \end{aligned} $$ |