Question
Answer
$$\dfrac{1}{6}i(-5i)=\dfrac{5}{6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{1}{6}i(-5i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{i}{6}(-5i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-\frac{5i^2}{6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{5}{6}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{1}{6} $ by $ i $ to get $ \dfrac{ i }{ 6 } $. 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. $$ \begin{aligned} \frac{1}{6} \cdot i & \xlongequal{\text{Step 1}} \frac{1}{6} \cdot \frac{i}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot i }{ 6 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ i }{ 6 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{i}{6} $ by $ -5i $ to get $ \dfrac{ -5i^2 }{ 6 } $. Step 1: Write $ -5i $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{i}{6} \cdot -5i & \xlongequal{\text{Step 1}} \frac{i}{6} \cdot \frac{-5i}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ i \cdot \left( -5i \right) }{ 6 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -5i^2 }{ 6 } \end{aligned} $$ |
| ③ | $$ -5i^2 = -5 \cdot (-1) = 5 $$ |
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