$$\dfrac{284928}{1000000}x+\dfrac{310406}{1000000}y+404666\dfrac{z}{1000000}=\dfrac{284928x+310406y+404666z}{1000000}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{284928}{1000000}x+\frac{310406}{1000000}y+404666\frac{z}{1000000}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 284928 : \color{orangered}{ 64 } }{ 1000000 : \color{orangered}{ 64 }} \cdot x + \frac{ 310406 : \color{orangered}{ 2 } }{ 1000000 : \color{orangered}{ 2 }} \cdot y + \frac{404666z}{1000000} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{4452}{15625}x+\frac{155203}{500000}y+\frac{404666z}{1000000} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}\frac{4452x}{15625}+\frac{155203y}{500000}+\frac{404666z}{1000000} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle8}{\textcircled {8}} \htmlClass{explanationCircle explanationCircle9}{\textcircled {9}} } }}}\frac{142464x+155203y}{500000}+\frac{404666z}{1000000} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle10}{\textcircled {10}} } }}}\frac{284928x+310406y+404666z}{1000000}\end{aligned} $$ | |
| 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 | Multiply $404666$ by $ \dfrac{z}{1000000} $ to get $ \dfrac{ 404666z }{ 1000000 } $. Step 1: Write $ 404666 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 404666 \cdot \frac{z}{1000000} & \xlongequal{\text{Step 1}} \frac{404666}{\color{red}{1}} \cdot \frac{z}{1000000} \xlongequal{\text{Step 2}} \frac{ 404666 \cdot z }{ 1 \cdot 1000000 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 404666z }{ 1000000 } \end{aligned} $$ |
| ④ | Multiply $404666$ by $ \dfrac{z}{1000000} $ to get $ \dfrac{ 404666z }{ 1000000 } $. Step 1: Write $ 404666 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 404666 \cdot \frac{z}{1000000} & \xlongequal{\text{Step 1}} \frac{404666}{\color{red}{1}} \cdot \frac{z}{1000000} \xlongequal{\text{Step 2}} \frac{ 404666 \cdot z }{ 1 \cdot 1000000 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 404666z }{ 1000000 } \end{aligned} $$ |
| ⑤ | 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. $$ \begin{aligned} \frac{4452}{15625} \cdot x & \xlongequal{\text{Step 1}} \frac{4452}{15625} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 4452 \cdot x }{ 15625 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4452x }{ 15625 } \end{aligned} $$ |
| ⑥ | 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. $$ \begin{aligned} \frac{155203}{500000} \cdot y & \xlongequal{\text{Step 1}} \frac{155203}{500000} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 155203 \cdot y }{ 500000 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 155203y }{ 500000 } \end{aligned} $$ |
| ⑦ | Multiply $404666$ by $ \dfrac{z}{1000000} $ to get $ \dfrac{ 404666z }{ 1000000 } $. Step 1: Write $ 404666 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 404666 \cdot \frac{z}{1000000} & \xlongequal{\text{Step 1}} \frac{404666}{\color{red}{1}} \cdot \frac{z}{1000000} \xlongequal{\text{Step 2}} \frac{ 404666 \cdot z }{ 1 \cdot 1000000 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 404666z }{ 1000000 } \end{aligned} $$ |
| ⑧ | 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. |
| ⑨ | Multiply $404666$ by $ \dfrac{z}{1000000} $ to get $ \dfrac{ 404666z }{ 1000000 } $. Step 1: Write $ 404666 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 404666 \cdot \frac{z}{1000000} & \xlongequal{\text{Step 1}} \frac{404666}{\color{red}{1}} \cdot \frac{z}{1000000} \xlongequal{\text{Step 2}} \frac{ 404666 \cdot z }{ 1 \cdot 1000000 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 404666z }{ 1000000 } \end{aligned} $$ |
| ⑩ | Add $ \dfrac{142464x+155203y}{500000} $ and $ \dfrac{404666z}{1000000} $ to get $ \dfrac{ \color{purple}{ 284928x+310406y+404666z } }{ 1000000 }$. To add raitonal expressions, both fractions must have the same denominator. |