$$\dfrac{25}{16}x^2y+x\dfrac{y}{32}y^5=\dfrac{xy^6+50x^2y}{32}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{25}{16}x^2y+x\frac{y}{32}y^5& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{25x^2}{16}y+\frac{xy}{32}y^5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{25x^2y}{16}+\frac{xy^6}{32} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{xy^6+50x^2y}{32}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{25}{16} $ by $ x^2 $ to get $ \dfrac{ 25x^2 }{ 16 } $. Step 1: Write $ x^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{25}{16} \cdot x^2 & \xlongequal{\text{Step 1}} \frac{25}{16} \cdot \frac{x^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 25 \cdot x^2 }{ 16 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 25x^2 }{ 16 } \end{aligned} $$ |
| ② | Multiply $x$ by $ \dfrac{y}{32} $ to get $ \dfrac{ xy }{ 32 } $. 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. $$ \begin{aligned} x \cdot \frac{y}{32} & \xlongequal{\text{Step 1}} \frac{x}{\color{red}{1}} \cdot \frac{y}{32} \xlongequal{\text{Step 2}} \frac{ x \cdot y }{ 1 \cdot 32 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ xy }{ 32 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{25x^2}{16} $ by $ y $ to get $ \dfrac{ 25x^2y }{ 16 } $. Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{25x^2}{16} \cdot y & \xlongequal{\text{Step 1}} \frac{25x^2}{16} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 25x^2 \cdot y }{ 16 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 25x^2y }{ 16 } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{xy}{32} $ by $ y^5 $ to get $ \dfrac{ xy^6 }{ 32 } $. Step 1: Write $ y^5 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{xy}{32} \cdot y^5 & \xlongequal{\text{Step 1}} \frac{xy}{32} \cdot \frac{y^5}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ xy \cdot y^5 }{ 32 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ xy^6 }{ 32 } \end{aligned} $$ |
| ⑤ | Add $ \dfrac{25x^2y}{16} $ and $ \dfrac{xy^6}{32} $ to get $ \dfrac{ \color{purple}{ xy^6+50x^2y } }{ 32 }$. To add raitonal expressions, both fractions must have the same denominator. |