Question
Answer
$$-1-6\cdot\dfrac{i}{2}i=2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-1-6 \cdot \frac{i}{2}i& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-1-\frac{6i}{2}i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-1-\frac{6i^2}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-1-\frac{-6}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-1-(-\frac{6}{2}) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-1 - \left(- \, \frac{ 6 : \color{orangered}{ 2 } }{ 2 : \color{orangered}{ 2 }}\right) \xlongequal{ } \\[1 em] & \xlongequal{ }-1-(-\frac{3}{1}) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}-1-(-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}-1+3 \xlongequal{ } \\[1 em] & \xlongequal{ }2\end{aligned} $$ | |
| ① | Multiply $6$ by $ \dfrac{i}{2} $ to get $ \dfrac{ 6i }{ 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. $$ \begin{aligned} 6 \cdot \frac{i}{2} & \xlongequal{\text{Step 1}} \frac{6}{\color{red}{1}} \cdot \frac{i}{2} \xlongequal{\text{Step 2}} \frac{ 6 \cdot i }{ 1 \cdot 2 } \xlongequal{\text{Step 3}} \frac{ 6i }{ 2 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{6i}{2} $ by $ i $ to get $ \dfrac{ 6i^2 }{ 2 } $. Step 1: Write $ i $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{6i}{2} \cdot i & \xlongequal{\text{Step 1}} \frac{6i}{2} \cdot \frac{i}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 6i \cdot i }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 6i^2 }{ 2 } \end{aligned} $$ |
| ③ | $$ 6i^2 = 6 \cdot (-1) = -6 $$ |
| ④ | Place minus sign in front of the fraction. |
| ⑤ | Divide both the top and bottom numbers by $ \color{orangered}{ 2 } $. |
| ⑥ | Remove 1 from denominator. |
| ⑦ | $ - \, ( \, -3 \, ) = 3 $ |
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