$$7\cdot\dfrac{x}{4}\dfrac{y^3}{21}\dfrac{x^3}{8}y=\dfrac{7x^4y^4}{672}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}7 \cdot \frac{x}{4}\frac{y^3}{21}\frac{x^3}{8}y& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{7x}{4}\frac{y^3}{21}\frac{x^3}{8}y \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{7xy^3}{84}\frac{x^3}{8}y \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{7x^4y^3}{672}y \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{7x^4y^4}{672}\end{aligned} $$ | |
| ① | Multiply $7$ by $ \dfrac{x}{4} $ to get $ \dfrac{ 7x }{ 4 } $. 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. $$ \begin{aligned} 7 \cdot \frac{x}{4} & \xlongequal{\text{Step 1}} \frac{7}{\color{red}{1}} \cdot \frac{x}{4} \xlongequal{\text{Step 2}} \frac{ 7 \cdot x }{ 1 \cdot 4 } \xlongequal{\text{Step 3}} \frac{ 7x }{ 4 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{7x}{4} $ by $ \dfrac{y^3}{21} $ to get $ \dfrac{ 7xy^3 }{ 84 } $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{7x}{4} \cdot \frac{y^3}{21} \xlongequal{\text{Step 1}} \frac{ 7x \cdot y^3 }{ 4 \cdot 21 } \xlongequal{\text{Step 2}} \frac{ 7xy^3 }{ 84 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{7xy^3}{84} $ by $ \dfrac{x^3}{8} $ to get $ \dfrac{ 7x^4y^3 }{ 672 } $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{7xy^3}{84} \cdot \frac{x^3}{8} & \xlongequal{\text{Step 1}} \frac{ 7xy^3 \cdot x^3 }{ 84 \cdot 8 } \xlongequal{\text{Step 2}} \frac{ 7x^4y^3 }{ 672 } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{7x^4y^3}{672} $ by $ y $ to get $ \dfrac{ 7x^4y^4 }{ 672 } $. 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. $$ \begin{aligned} \frac{7x^4y^3}{672} \cdot y & \xlongequal{\text{Step 1}} \frac{7x^4y^3}{672} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 7x^4y^3 \cdot y }{ 672 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 7x^4y^4 }{ 672 } \end{aligned} $$ |