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