$$\dfrac{28493}{100001}x+\dfrac{31041}{100001}y+40467\dfrac{z}{100001}=\dfrac{28493x+31041y+40467z}{100001}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{28493}{100001}x+\frac{31041}{100001}y+40467\frac{z}{100001}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{28493x}{100001}+\frac{31041y}{100001}+\frac{40467z}{100001} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{28493x+31041y}{100001}+\frac{40467z}{100001} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}\frac{28493x+31041y+40467z}{100001}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{28493}{100001} $ by $ x $ to get $ \dfrac{ 28493x }{ 100001 } $. 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. $$ \begin{aligned} \frac{28493}{100001} \cdot x & \xlongequal{\text{Step 1}} \frac{28493}{100001} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 28493 \cdot x }{ 100001 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 28493x }{ 100001 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{31041}{100001} $ by $ y $ to get $ \dfrac{ 31041y }{ 100001 } $. 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. $$ \begin{aligned} \frac{31041}{100001} \cdot y & \xlongequal{\text{Step 1}} \frac{31041}{100001} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 31041 \cdot y }{ 100001 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 31041y }{ 100001 } \end{aligned} $$ |
| ③ | Multiply $40467$ by $ \dfrac{z}{100001} $ to get $ \dfrac{ 40467z }{ 100001 } $. Step 1: Write $ 40467 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 40467 \cdot \frac{z}{100001} & \xlongequal{\text{Step 1}} \frac{40467}{\color{red}{1}} \cdot \frac{z}{100001} \xlongequal{\text{Step 2}} \frac{ 40467 \cdot z }{ 1 \cdot 100001 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 40467z }{ 100001 } \end{aligned} $$ |
| ④ | Add $ \dfrac{28493x}{100001} $ and $ \dfrac{31041y}{100001} $ to get $ \dfrac{ 28493x + 31041y }{ \color{blue}{ 100001 }}$. To add expressions with the same denominators, we add the numerators and write the result over the common denominator. $$ \begin{aligned} \frac{28493x}{100001} + \frac{31041y}{100001} & = \frac{28493x}{\color{blue}{100001}} + \frac{31041y}{\color{blue}{100001}} = \\[1ex] &=\frac{ 28493x + 31041y }{ \color{blue}{ 100001 }} \end{aligned} $$ |
| ⑤ | Multiply $40467$ by $ \dfrac{z}{100001} $ to get $ \dfrac{ 40467z }{ 100001 } $. Step 1: Write $ 40467 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 40467 \cdot \frac{z}{100001} & \xlongequal{\text{Step 1}} \frac{40467}{\color{red}{1}} \cdot \frac{z}{100001} \xlongequal{\text{Step 2}} \frac{ 40467 \cdot z }{ 1 \cdot 100001 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 40467z }{ 100001 } \end{aligned} $$ |
| ⑥ | Add $ \dfrac{28493x+31041y}{100001} $ and $ \dfrac{40467z}{100001} $ to get $ \dfrac{ 28493x+31041y + 40467z }{ \color{blue}{ 100001 }}$. To add expressions with the same denominators, we add the numerators and write the result over the common denominator. $$ \begin{aligned} \frac{28493x+31041y}{100001} + \frac{40467z}{100001} & = \frac{28493x+31041y}{\color{blue}{100001}} + \frac{40467z}{\color{blue}{100001}} = \\[1ex] &=\frac{ 28493x+31041y + 40467z }{ \color{blue}{ 100001 }} \end{aligned} $$ |