Answer
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}45a^2\frac{b}{30}ab& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{45a^2b}{30}ab \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{45a^3b}{30}b \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{45a^3b^2}{30}\end{aligned} $$ | |
| ① | Multiply $45a^2$ by $ \dfrac{b}{30} $ to get $ \dfrac{ 45a^2b }{ 30 } $. Step 1: Write $ 45a^2 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 45a^2 \cdot \frac{b}{30} & \xlongequal{\text{Step 1}} \frac{45a^2}{\color{red}{1}} \cdot \frac{b}{30} \xlongequal{\text{Step 2}} \frac{ 45a^2 \cdot b }{ 1 \cdot 30 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 45a^2b }{ 30 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{45a^2b}{30} $ by $ a $ to get $ \dfrac{ 45a^3b }{ 30 } $. Step 1: Write $ a $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{45a^2b}{30} \cdot a & \xlongequal{\text{Step 1}} \frac{45a^2b}{30} \cdot \frac{a}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 45a^2b \cdot a }{ 30 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 45a^3b }{ 30 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{45a^3b}{30} $ by $ b $ to get $ \dfrac{ 45a^3b^2 }{ 30 } $. Step 1: Write $ b $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{45a^3b}{30} \cdot b & \xlongequal{\text{Step 1}} \frac{45a^3b}{30} \cdot \frac{b}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 45a^3b \cdot b }{ 30 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 45a^3b^2 }{ 30 } \end{aligned} $$ |