Question
Answer
$$12\cdot\dfrac{x^2}{15}x=\dfrac{12x^3}{15}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}12 \cdot \frac{x^2}{15}x& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{12x^2}{15}x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{12x^3}{15}\end{aligned} $$ | |
| ① | Multiply $12$ by $ \dfrac{x^2}{15} $ to get $ \dfrac{ 12x^2 }{ 15 } $. Step 1: Write $ 12 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 12 \cdot \frac{x^2}{15} & \xlongequal{\text{Step 1}} \frac{12}{\color{red}{1}} \cdot \frac{x^2}{15} \xlongequal{\text{Step 2}} \frac{ 12 \cdot x^2 }{ 1 \cdot 15 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 12x^2 }{ 15 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{12x^2}{15} $ by $ x $ to get $ \dfrac{ 12x^3 }{ 15 } $. 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. $$ \begin{aligned} \frac{12x^2}{15} \cdot x & \xlongequal{\text{Step 1}} \frac{12x^2}{15} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 12x^2 \cdot x }{ 15 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 12x^3 }{ 15 } \end{aligned} $$ |
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