Multiply $50000$ by $ \dfrac{i}{101} $ to get $ \dfrac{ 50000i }{ 101 } $.

Step 1: Write $ 50000 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 50000 \cdot \frac{i}{101} & \xlongequal{\text{Step 1}} \frac{50000}{\color{red}{1}} \cdot \frac{i}{101} \xlongequal{\text{Step 2}} \frac{ 50000 \cdot i }{ 1 \cdot 101 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 50000i }{ 101 } \end{aligned} $$

Multiply $50000$ by $ \dfrac{i}{101} $ to get $ \dfrac{ 50000i }{ 101 } $.

Step 1: Write $ 50000 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 50000 \cdot \frac{i}{101} & \xlongequal{\text{Step 1}} \frac{50000}{\color{red}{1}} \cdot \frac{i}{101} \xlongequal{\text{Step 2}} \frac{ 50000 \cdot i }{ 1 \cdot 101 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 50000i }{ 101 } \end{aligned} $$

Add $ \dfrac{50000i}{101} $ and $ \dfrac{5000}{101} $ to get $ \dfrac{ 50000i + 5000 }{ \color{blue}{ 101 }}$.

To add expressions with the same denominators, we add the numerators and write the result over the common denominator.

$$ \begin{aligned} \frac{50000i}{101} + \frac{5000}{101} & = \frac{50000i}{\color{blue}{101}} + \frac{5000}{\color{blue}{101}} = \\[1ex] &=\frac{ 50000i + 5000 }{ \color{blue}{ 101 }} \end{aligned} $$

Add $ \dfrac{50000i}{101} $ and $ \dfrac{5000}{101} $ to get $ \dfrac{ 50000i + 5000 }{ \color{blue}{ 101 }}$.

To add expressions with the same denominators, we add the numerators and write the result over the common denominator.

$$ \begin{aligned} \frac{50000i}{101} + \frac{5000}{101} & = \frac{50000i}{\color{blue}{101}} + \frac{5000}{\color{blue}{101}} = \\[1ex] &=\frac{ 50000i + 5000 }{ \color{blue}{ 101 }} \end{aligned} $$

Add $ \dfrac{50000i}{101} $ and $ \dfrac{5000}{101} $ to get $ \dfrac{ 50000i + 5000 }{ \color{blue}{ 101 }}$.

To add expressions with the same denominators, we add the numerators and write the result over the common denominator.

$$ \begin{aligned} \frac{50000i}{101} + \frac{5000}{101} & = \frac{50000i}{\color{blue}{101}} + \frac{5000}{\color{blue}{101}} = \\[1ex] &=\frac{ 50000i + 5000 }{ \color{blue}{ 101 }} \end{aligned} $$

Add $ \dfrac{50000i+5000}{101} $ and $ 99i $ to get $ \dfrac{ \color{purple}{ 59999i+5000 } }{ 101 }$.

Step 1: Write $ 99i $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{101}$.

$$ \begin{aligned} \frac{50000i+5000}{101} +99i & \xlongequal{\text{Step 1}} \frac{50000i+5000}{101} + \frac{99i}{\color{red}{1}} = \frac{ 50000i+5000 }{ 101 } + \frac{ 99i \cdot \color{blue}{ 101 }}{ 1 \cdot \color{blue}{ 101 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 50000i+5000 } }{ 101 } + \frac{ \color{purple}{ 9999i } }{ 101 }=\frac{ \color{purple}{ 59999i+5000 } }{ 101 } \end{aligned} $$

Add $ \dfrac{50000i}{101} $ and $ \dfrac{5000}{101} $ to get $ \dfrac{ 50000i + 5000 }{ \color{blue}{ 101 }}$.

To add expressions with the same denominators, we add the numerators and write the result over the common denominator.

$$ \begin{aligned} \frac{50000i}{101} + \frac{5000}{101} & = \frac{50000i}{\color{blue}{101}} + \frac{5000}{\color{blue}{101}} = \\[1ex] &=\frac{ 50000i + 5000 }{ \color{blue}{ 101 }} \end{aligned} $$

Add $ \dfrac{59999i+5000}{101} $ and $ 84 $ to get $ \dfrac{ \color{purple}{ 59999i+13484 } }{ 101 }$.

Step 1: Write $ 84 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{101}$.

$$ \begin{aligned} \frac{59999i+5000}{101} +84 & \xlongequal{\text{Step 1}} \frac{59999i+5000}{101} + \frac{84}{\color{red}{1}} = \frac{ 59999i+5000 }{ 101 } + \frac{ 84 \cdot \color{blue}{ 101 }}{ 1 \cdot \color{blue}{ 101 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 59999i+5000 } }{ 101 } + \frac{ \color{purple}{ 8484 } }{ 101 }=\frac{ \color{purple}{ 59999i+13484 } }{ 101 } \end{aligned} $$

Divide $ \dfrac{50000i+5000}{101} $ by $ \dfrac{59999i+13484}{101} $ to get $ \dfrac{ 50000i+5000 }{ 59999i+13484 } $.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

Step 2: Cancel $ \color{red}{ 101 } $ in first and second fraction.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} \frac{ \frac{50000i+5000}{101} }{ \frac{\color{blue}{59999i+13484}}{\color{blue}{101}} } & \xlongequal{\text{Step 1}} \frac{50000i+5000}{101} \cdot \frac{\color{blue}{101}}{\color{blue}{59999i+13484}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{50000i+5000}{\color{red}{1}} \cdot \frac{\color{red}{1}}{59999i+13484} \xlongequal{\text{Step 3}} \frac{ \left( 50000i+5000 \right) \cdot 1 }{ 1 \cdot \left( 59999i+13484 \right) } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ 50000i+5000 }{ 59999i+13484 } \end{aligned} $$

Divide $ \, 5000+50000i \, $ by $ \, 13484+59999i \, $ to get $\,\, \dfrac{30370000+3705000i}{37442557} $.
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