$$2\cdot\dfrac{i}{15}+4\dfrac{i}{5}=\dfrac{14i}{15}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2 \cdot \frac{i}{15}+4\frac{i}{5}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{2i}{15}+\frac{4i}{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{14i}{15}\end{aligned} $$ | |
| ① | Multiply $2$ by $ \dfrac{i}{15} $ to get $ \dfrac{ 2i }{ 15 } $. Step 1: Write $ 2 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 2 \cdot \frac{i}{15} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{i}{15} \xlongequal{\text{Step 2}} \frac{ 2 \cdot i }{ 1 \cdot 15 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2i }{ 15 } \end{aligned} $$ |
| ② | Multiply $4$ by $ \dfrac{i}{5} $ to get $ \dfrac{ 4i }{ 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. $$ \begin{aligned} 4 \cdot \frac{i}{5} & \xlongequal{\text{Step 1}} \frac{4}{\color{red}{1}} \cdot \frac{i}{5} \xlongequal{\text{Step 2}} \frac{ 4 \cdot i }{ 1 \cdot 5 } \xlongequal{\text{Step 3}} \frac{ 4i }{ 5 } \end{aligned} $$ |
| ③ | Add $ \dfrac{2i}{15} $ and $ \dfrac{4i}{5} $ to get $ \dfrac{ \color{purple}{ 14i } }{ 15 }$. To add raitonal expressions, both fractions must have the same denominator. |