Answer
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{1}{2}ax\cdot6& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{a}{2}x\cdot6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{ax}{2}\cdot6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{6ax}{2}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{1}{2} $ by $ a $ to get $ \dfrac{ a }{ 2 } $. Step 1: Write $ a $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{1}{2} \cdot a & \xlongequal{\text{Step 1}} \frac{1}{2} \cdot \frac{a}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot a }{ 2 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ a }{ 2 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{a}{2} $ by $ x $ to get $ \dfrac{ ax }{ 2 } $. Step 1: Write $ x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{a}{2} \cdot x & \xlongequal{\text{Step 1}} \frac{a}{2} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ a \cdot x }{ 2 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ ax }{ 2 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{ax}{2} $ by $ 6 $ to get $ \dfrac{ 6ax }{ 2 } $. Step 1: Write $ 6 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{ax}{2} \cdot 6 & \xlongequal{\text{Step 1}} \frac{ax}{2} \cdot \frac{6}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ ax \cdot 6 }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 6ax }{ 2 } \end{aligned} $$ |