$$5\cdot\dfrac{i}{9}+\dfrac{6}{3}+8\dfrac{i}{3}-2\dfrac{i}{3}=\dfrac{23i+18}{9}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}5 \cdot \frac{i}{9}+\frac{6}{3}+8\frac{i}{3}-2\frac{i}{3}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{5i}{9} + \frac{ 6 : \color{orangered}{ 3 } }{ 3 : \color{orangered}{ 3 }} + \frac{8i}{3} - \frac{2i}{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}\frac{5i}{9}+\frac{2}{1}+\frac{8i}{3}-\frac{2i}{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle8}{\textcircled {8}} \htmlClass{explanationCircle explanationCircle9}{\textcircled {9}} \htmlClass{explanationCircle explanationCircle10}{\textcircled {10}} \htmlClass{explanationCircle explanationCircle11}{\textcircled {11}} } }}}\frac{5i}{9}+2+\frac{8i}{3}-\frac{2i}{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle12}{\textcircled {12}} \htmlClass{explanationCircle explanationCircle13}{\textcircled {13}} \htmlClass{explanationCircle explanationCircle14}{\textcircled {14}} } }}}\frac{5i+18}{9}+\frac{8i}{3}-\frac{2i}{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle15}{\textcircled {15}} \htmlClass{explanationCircle explanationCircle16}{\textcircled {16}} } }}}\frac{29i+18}{9}-\frac{2i}{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle17}{\textcircled {17}} } }}}\frac{23i+18}{9}\end{aligned} $$ | |
| ① | Multiply $5$ by $ \dfrac{i}{9} $ to get $ \dfrac{ 5i }{ 9 } $. Step 1: Write $ 5 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 5 \cdot \frac{i}{9} & \xlongequal{\text{Step 1}} \frac{5}{\color{red}{1}} \cdot \frac{i}{9} \xlongequal{\text{Step 2}} \frac{ 5 \cdot i }{ 1 \cdot 9 } \xlongequal{\text{Step 3}} \frac{ 5i }{ 9 } \end{aligned} $$ |
| ② | Divide both the top and bottom numbers by $ \color{orangered}{ 3 } $. |
| ③ | Multiply $8$ by $ \dfrac{i}{3} $ to get $ \dfrac{ 8i }{ 3 } $. Step 1: Write $ 8 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 8 \cdot \frac{i}{3} & \xlongequal{\text{Step 1}} \frac{8}{\color{red}{1}} \cdot \frac{i}{3} \xlongequal{\text{Step 2}} \frac{ 8 \cdot i }{ 1 \cdot 3 } \xlongequal{\text{Step 3}} \frac{ 8i }{ 3 } \end{aligned} $$ |
| ④ | Multiply $2$ by $ \dfrac{i}{3} $ to get $ \dfrac{ 2i }{ 3 } $. 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. $$ \begin{aligned} 2 \cdot \frac{i}{3} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{i}{3} \xlongequal{\text{Step 2}} \frac{ 2 \cdot i }{ 1 \cdot 3 } \xlongequal{\text{Step 3}} \frac{ 2i }{ 3 } \end{aligned} $$ |
| ⑤ | Multiply $5$ by $ \dfrac{i}{9} $ to get $ \dfrac{ 5i }{ 9 } $. Step 1: Write $ 5 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 5 \cdot \frac{i}{9} & \xlongequal{\text{Step 1}} \frac{5}{\color{red}{1}} \cdot \frac{i}{9} \xlongequal{\text{Step 2}} \frac{ 5 \cdot i }{ 1 \cdot 9 } \xlongequal{\text{Step 3}} \frac{ 5i }{ 9 } \end{aligned} $$ |
| ⑥ | Multiply $8$ by $ \dfrac{i}{3} $ to get $ \dfrac{ 8i }{ 3 } $. Step 1: Write $ 8 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 8 \cdot \frac{i}{3} & \xlongequal{\text{Step 1}} \frac{8}{\color{red}{1}} \cdot \frac{i}{3} \xlongequal{\text{Step 2}} \frac{ 8 \cdot i }{ 1 \cdot 3 } \xlongequal{\text{Step 3}} \frac{ 8i }{ 3 } \end{aligned} $$ |
| ⑦ | Multiply $2$ by $ \dfrac{i}{3} $ to get $ \dfrac{ 2i }{ 3 } $. 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. $$ \begin{aligned} 2 \cdot \frac{i}{3} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{i}{3} \xlongequal{\text{Step 2}} \frac{ 2 \cdot i }{ 1 \cdot 3 } \xlongequal{\text{Step 3}} \frac{ 2i }{ 3 } \end{aligned} $$ |
| ⑧ | Multiply $5$ by $ \dfrac{i}{9} $ to get $ \dfrac{ 5i }{ 9 } $. Step 1: Write $ 5 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 5 \cdot \frac{i}{9} & \xlongequal{\text{Step 1}} \frac{5}{\color{red}{1}} \cdot \frac{i}{9} \xlongequal{\text{Step 2}} \frac{ 5 \cdot i }{ 1 \cdot 9 } \xlongequal{\text{Step 3}} \frac{ 5i }{ 9 } \end{aligned} $$ |
| ⑨ | Remove 1 from denominator. |
| ⑩ | Multiply $8$ by $ \dfrac{i}{3} $ to get $ \dfrac{ 8i }{ 3 } $. Step 1: Write $ 8 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 8 \cdot \frac{i}{3} & \xlongequal{\text{Step 1}} \frac{8}{\color{red}{1}} \cdot \frac{i}{3} \xlongequal{\text{Step 2}} \frac{ 8 \cdot i }{ 1 \cdot 3 } \xlongequal{\text{Step 3}} \frac{ 8i }{ 3 } \end{aligned} $$ |
| ⑪ | Multiply $2$ by $ \dfrac{i}{3} $ to get $ \dfrac{ 2i }{ 3 } $. 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. $$ \begin{aligned} 2 \cdot \frac{i}{3} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{i}{3} \xlongequal{\text{Step 2}} \frac{ 2 \cdot i }{ 1 \cdot 3 } \xlongequal{\text{Step 3}} \frac{ 2i }{ 3 } \end{aligned} $$ |
| ⑫ | Add $ \dfrac{5i}{9} $ and $ 2 $ to get $ \dfrac{ \color{purple}{ 5i+18 } }{ 9 }$. Step 1: Write $ 2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: To add raitonal expressions, both fractions must have the same denominator. |
| ⑬ | Multiply $8$ by $ \dfrac{i}{3} $ to get $ \dfrac{ 8i }{ 3 } $. Step 1: Write $ 8 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 8 \cdot \frac{i}{3} & \xlongequal{\text{Step 1}} \frac{8}{\color{red}{1}} \cdot \frac{i}{3} \xlongequal{\text{Step 2}} \frac{ 8 \cdot i }{ 1 \cdot 3 } \xlongequal{\text{Step 3}} \frac{ 8i }{ 3 } \end{aligned} $$ |
| ⑭ | Multiply $2$ by $ \dfrac{i}{3} $ to get $ \dfrac{ 2i }{ 3 } $. 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. $$ \begin{aligned} 2 \cdot \frac{i}{3} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{i}{3} \xlongequal{\text{Step 2}} \frac{ 2 \cdot i }{ 1 \cdot 3 } \xlongequal{\text{Step 3}} \frac{ 2i }{ 3 } \end{aligned} $$ |
| ⑮ | Add $ \dfrac{5i+18}{9} $ and $ \dfrac{8i}{3} $ to get $ \dfrac{ \color{purple}{ 29i+18 } }{ 9 }$. To add raitonal expressions, both fractions must have the same denominator. |
| ⑯ | Multiply $2$ by $ \dfrac{i}{3} $ to get $ \dfrac{ 2i }{ 3 } $. 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. $$ \begin{aligned} 2 \cdot \frac{i}{3} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{i}{3} \xlongequal{\text{Step 2}} \frac{ 2 \cdot i }{ 1 \cdot 3 } \xlongequal{\text{Step 3}} \frac{ 2i }{ 3 } \end{aligned} $$ |
| ⑰ | Subtract $ \dfrac{2i}{3} $ from $ \dfrac{29i+18}{9} $ to get $ \dfrac{ \color{purple}{ 23i+18 } }{ 9 }$. To subtract raitonal expressions, both fractions must have the same denominator. |