$$(-2ab)\cdot\dfrac{1}{6}bc(-3ac)=\dfrac{6a^2b^2c^2}{6}$$
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. $$ \begin{aligned} -2ab \cdot \frac{1}{6} & \xlongequal{\text{Step 1}} \frac{-2ab}{\color{red}{1}} \cdot \frac{1}{6} \xlongequal{\text{Step 2}} \frac{ \left( -2ab \right) \cdot 1 }{ 1 \cdot 6 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -2ab }{ 6 } \end{aligned} $$ |
| 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. $$ \begin{aligned} \frac{-2ab}{6} \cdot b & \xlongequal{\text{Step 1}} \frac{-2ab}{6} \cdot \frac{b}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( -2ab \right) \cdot b }{ 6 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -2ab^2 }{ 6 } \end{aligned} $$ |
| 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. $$ \begin{aligned} \frac{-2ab^2}{6} \cdot c & \xlongequal{\text{Step 1}} \frac{-2ab^2}{6} \cdot \frac{c}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( -2ab^2 \right) \cdot c }{ 6 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -2ab^2c }{ 6 } \end{aligned} $$ |
| 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. $$ \begin{aligned} \frac{-2ab^2c}{6} \cdot -3ac & \xlongequal{\text{Step 1}} \frac{-2ab^2c}{6} \cdot \frac{-3ac}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( -2ab^2c \right) \cdot \left( -3ac \right) }{ 6 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 6a^2b^2c^2 }{ 6 } \end{aligned} $$ |