Question
Answer
$$7\cdot\dfrac{x^3}{8}\cdot4\dfrac{x^2}{5}=\dfrac{28x^5}{40}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}7 \cdot \frac{x^3}{8}\cdot4\frac{x^2}{5}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{7x^3}{8}\frac{4x^2}{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{28x^5}{40}\end{aligned} $$ | |
| ① | Multiply $7$ by $ \dfrac{x^3}{8} $ to get $ \dfrac{ 7x^3 }{ 8 } $. Step 1: Write $ 7 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 7 \cdot \frac{x^3}{8} & \xlongequal{\text{Step 1}} \frac{7}{\color{red}{1}} \cdot \frac{x^3}{8} \xlongequal{\text{Step 2}} \frac{ 7 \cdot x^3 }{ 1 \cdot 8 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 7x^3 }{ 8 } \end{aligned} $$ |
| ② | Multiply $4$ by $ \dfrac{x^2}{5} $ to get $ \dfrac{ 4x^2 }{ 5 } $. Step 1: Write $ 4 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 4 \cdot \frac{x^2}{5} & \xlongequal{\text{Step 1}} \frac{4}{\color{red}{1}} \cdot \frac{x^2}{5} \xlongequal{\text{Step 2}} \frac{ 4 \cdot x^2 }{ 1 \cdot 5 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4x^2 }{ 5 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{7x^3}{8} $ by $ \dfrac{4x^2}{5} $ to get $ \dfrac{ 28x^5 }{ 40 } $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{7x^3}{8} \cdot \frac{4x^2}{5} \xlongequal{\text{Step 1}} \frac{ 7x^3 \cdot 4x^2 }{ 8 \cdot 5 } \xlongequal{\text{Step 2}} \frac{ 28x^5 }{ 40 } \end{aligned} $$ |
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