Question
Answer
$$\dfrac{4}{9k^5}\cdot3\dfrac{k^3}{8}=\dfrac{12k^3}{72k^5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4}{9k^5}\cdot3\frac{k^3}{8}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4}{9k^5}\frac{3k^3}{8} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{12k^3}{72k^5}\end{aligned} $$ | |
| ① | Multiply $3$ by $ \dfrac{k^3}{8} $ to get $ \dfrac{ 3k^3 }{ 8 } $. Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 3 \cdot \frac{k^3}{8} & \xlongequal{\text{Step 1}} \frac{3}{\color{red}{1}} \cdot \frac{k^3}{8} \xlongequal{\text{Step 2}} \frac{ 3 \cdot k^3 }{ 1 \cdot 8 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3k^3 }{ 8 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{4}{9k^5} $ by $ \dfrac{3k^3}{8} $ to get $ \dfrac{ 12k^3 }{ 72k^5 } $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{4}{9k^5} \cdot \frac{3k^3}{8} & \xlongequal{\text{Step 1}} \frac{ 4 \cdot 3k^3 }{ 9k^5 \cdot 8 } \xlongequal{\text{Step 2}} \frac{ 12k^3 }{ 72k^5 } \end{aligned} $$ |
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