$$\dfrac{2}{5}x^2+3\dfrac{y}{10}x=\dfrac{4x^2+3xy}{10}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2}{5}x^2+3\frac{y}{10}x& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{2x^2}{5}+\frac{3y}{10}x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{2x^2}{5}+\frac{3xy}{10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{4x^2+3xy}{10}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{2}{5} $ by $ x^2 $ to get $ \dfrac{ 2x^2 }{ 5 } $. 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. $$ \begin{aligned} \frac{2}{5} \cdot x^2 & \xlongequal{\text{Step 1}} \frac{2}{5} \cdot \frac{x^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 2 \cdot x^2 }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2x^2 }{ 5 } \end{aligned} $$ |
| ② | Multiply $3$ by $ \dfrac{y}{10} $ to get $ \dfrac{ 3y }{ 10 } $. 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. $$ \begin{aligned} 3 \cdot \frac{y}{10} & \xlongequal{\text{Step 1}} \frac{3}{\color{red}{1}} \cdot \frac{y}{10} \xlongequal{\text{Step 2}} \frac{ 3 \cdot y }{ 1 \cdot 10 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3y }{ 10 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{2}{5} $ by $ x^2 $ to get $ \dfrac{ 2x^2 }{ 5 } $. 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. $$ \begin{aligned} \frac{2}{5} \cdot x^2 & \xlongequal{\text{Step 1}} \frac{2}{5} \cdot \frac{x^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 2 \cdot x^2 }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2x^2 }{ 5 } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{3y}{10} $ by $ x $ to get $ \dfrac{ 3xy }{ 10 } $. 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. $$ \begin{aligned} \frac{3y}{10} \cdot x & \xlongequal{\text{Step 1}} \frac{3y}{10} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 3y \cdot x }{ 10 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3xy }{ 10 } \end{aligned} $$ |
| ⑤ | Add $ \dfrac{2x^2}{5} $ and $ \dfrac{3xy}{10} $ to get $ \dfrac{ \color{purple}{ 4x^2+3xy } }{ 10 }$. To add raitonal expressions, both fractions must have the same denominator. |