$$\dfrac{284928}{1000000}x+\dfrac{310406}{1000000}y+\dfrac{404666}{1000000}z=\dfrac{142464x+155203y+202333z}{500000}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{284928}{1000000}x+\frac{310406}{1000000}y+\frac{404666}{1000000}z& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 284928 : \color{orangered}{ 64 } }{ 1000000 : \color{orangered}{ 64 }} \cdot x + \frac{ 310406 : \color{orangered}{ 2 } }{ 1000000 : \color{orangered}{ 2 }} \cdot y + \frac{ 404666 : \color{orangered}{ 2 } }{ 1000000 : \color{orangered}{ 2 }} \cdot z \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{4452}{15625}x+\frac{155203}{500000}y+\frac{202333}{500000}z \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}\frac{4452x}{15625}+\frac{155203y}{500000}+\frac{202333z}{500000} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} \htmlClass{explanationCircle explanationCircle8}{\textcircled {8}} } }}}\frac{142464x+155203y}{500000}+\frac{202333z}{500000} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle9}{\textcircled {9}} } }}}\frac{142464x+155203y+202333z}{500000}\end{aligned} $$ | |
| ① | Divide both the top and bottom numbers by $ \color{orangered}{ 64 } $. |
| ② | Divide both the top and bottom numbers by $ \color{orangered}{ 2 } $. |
| ③ | Divide both the top and bottom numbers by $ \color{orangered}{ 2 } $. |
| ④ | Multiply $ \dfrac{4452}{15625} $ by $ x $ to get $ \dfrac{ 4452x }{ 15625 } $. 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. $$ \begin{aligned} \frac{4452}{15625} \cdot x & \xlongequal{\text{Step 1}} \frac{4452}{15625} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 4452 \cdot x }{ 15625 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4452x }{ 15625 } \end{aligned} $$ |
| ⑤ | Multiply $ \dfrac{155203}{500000} $ by $ y $ to get $ \dfrac{ 155203y }{ 500000 } $. 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. $$ \begin{aligned} \frac{155203}{500000} \cdot y & \xlongequal{\text{Step 1}} \frac{155203}{500000} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 155203 \cdot y }{ 500000 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 155203y }{ 500000 } \end{aligned} $$ |
| ⑥ | Multiply $ \dfrac{202333}{500000} $ by $ z $ to get $ \dfrac{ 202333z }{ 500000 } $. Step 1: Write $ z $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{202333}{500000} \cdot z & \xlongequal{\text{Step 1}} \frac{202333}{500000} \cdot \frac{z}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 202333 \cdot z }{ 500000 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 202333z }{ 500000 } \end{aligned} $$ |
| ⑦ | Add $ \dfrac{4452x}{15625} $ and $ \dfrac{155203y}{500000} $ to get $ \dfrac{ \color{purple}{ 142464x+155203y } }{ 500000 }$. To add raitonal expressions, both fractions must have the same denominator. |
| ⑧ | Multiply $ \dfrac{202333}{500000} $ by $ z $ to get $ \dfrac{ 202333z }{ 500000 } $. Step 1: Write $ z $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{202333}{500000} \cdot z & \xlongequal{\text{Step 1}} \frac{202333}{500000} \cdot \frac{z}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 202333 \cdot z }{ 500000 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 202333z }{ 500000 } \end{aligned} $$ |
| ⑨ | Add $ \dfrac{142464x+155203y}{500000} $ and $ \dfrac{202333z}{500000} $ to get $ \dfrac{ 142464x+155203y + 202333z }{ \color{blue}{ 500000 }}$. To add expressions with the same denominators, we add the numerators and write the result over the common denominator. $$ \begin{aligned} \frac{142464x+155203y}{500000} + \frac{202333z}{500000} & = \frac{142464x+155203y}{\color{blue}{500000}} + \frac{202333z}{\color{blue}{500000}} = \\[1ex] &=\frac{ 142464x+155203y + 202333z }{ \color{blue}{ 500000 }} \end{aligned} $$ |