$$4\cdot\dfrac{a}{6}\dfrac{b^2}{20}\dfrac{a^3}{12}b=\dfrac{4a^4b^3}{1440}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4 \cdot \frac{a}{6}\frac{b^2}{20}\frac{a^3}{12}b& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4a}{6}\frac{b^2}{20}\frac{a^3}{12}b \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{4ab^2}{120}\frac{a^3}{12}b \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{4a^4b^2}{1440}b \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{4a^4b^3}{1440}\end{aligned} $$ | |
| ① | Multiply $4$ by $ \dfrac{a}{6} $ to get $ \dfrac{ 4a }{ 6 } $. Step 1: Write $ 4 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 4 \cdot \frac{a}{6} & \xlongequal{\text{Step 1}} \frac{4}{\color{red}{1}} \cdot \frac{a}{6} \xlongequal{\text{Step 2}} \frac{ 4 \cdot a }{ 1 \cdot 6 } \xlongequal{\text{Step 3}} \frac{ 4a }{ 6 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{4a}{6} $ by $ \dfrac{b^2}{20} $ to get $ \dfrac{ 4ab^2 }{ 120 } $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{4a}{6} \cdot \frac{b^2}{20} \xlongequal{\text{Step 1}} \frac{ 4a \cdot b^2 }{ 6 \cdot 20 } \xlongequal{\text{Step 2}} \frac{ 4ab^2 }{ 120 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{4ab^2}{120} $ by $ \dfrac{a^3}{12} $ to get $ \dfrac{ 4a^4b^2 }{ 1440 } $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{4ab^2}{120} \cdot \frac{a^3}{12} & \xlongequal{\text{Step 1}} \frac{ 4ab^2 \cdot a^3 }{ 120 \cdot 12 } \xlongequal{\text{Step 2}} \frac{ 4a^4b^2 }{ 1440 } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{4a^4b^2}{1440} $ by $ b $ to get $ \dfrac{ 4a^4b^3 }{ 1440 } $. Step 1: Write $ b $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{4a^4b^2}{1440} \cdot b & \xlongequal{\text{Step 1}} \frac{4a^4b^2}{1440} \cdot \frac{b}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 4a^4b^2 \cdot b }{ 1440 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4a^4b^3 }{ 1440 } \end{aligned} $$ |