$$\dfrac{284924}{1000000}x+\dfrac{310408}{1000000}y+\dfrac{404668}{1000000}z=\dfrac{71231x+77602y+101167z}{250000}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{284924}{1000000}x+\frac{310408}{1000000}y+\frac{404668}{1000000}z& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 284924 : \color{orangered}{ 4 } }{ 1000000 : \color{orangered}{ 4 }} \cdot x + \frac{ 310408 : \color{orangered}{ 8 } }{ 1000000 : \color{orangered}{ 8 }} \cdot y + \frac{ 404668 : \color{orangered}{ 4 } }{ 1000000 : \color{orangered}{ 4 }} \cdot z \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{71231}{250000}x+\frac{38801}{125000}y+\frac{101167}{250000}z \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}\frac{71231x}{250000}+\frac{38801y}{125000}+\frac{101167z}{250000} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} \htmlClass{explanationCircle explanationCircle8}{\textcircled {8}} } }}}\frac{71231x+77602y}{250000}+\frac{101167z}{250000} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle9}{\textcircled {9}} } }}}\frac{71231x+77602y+101167z}{250000}\end{aligned} $$ | |
| ① | Divide both the top and bottom numbers by $ \color{orangered}{ 4 } $. |
| ② | Divide both the top and bottom numbers by $ \color{orangered}{ 8 } $. |
| ③ | Divide both the top and bottom numbers by $ \color{orangered}{ 4 } $. |
| ④ | Multiply $ \dfrac{71231}{250000} $ by $ x $ to get $ \dfrac{ 71231x }{ 250000 } $. 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. $$ \begin{aligned} \frac{71231}{250000} \cdot x & \xlongequal{\text{Step 1}} \frac{71231}{250000} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 71231 \cdot x }{ 250000 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 71231x }{ 250000 } \end{aligned} $$ |
| ⑤ | Multiply $ \dfrac{38801}{125000} $ by $ y $ to get $ \dfrac{ 38801y }{ 125000 } $. 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. $$ \begin{aligned} \frac{38801}{125000} \cdot y & \xlongequal{\text{Step 1}} \frac{38801}{125000} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 38801 \cdot y }{ 125000 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 38801y }{ 125000 } \end{aligned} $$ |
| ⑥ | Multiply $ \dfrac{101167}{250000} $ by $ z $ to get $ \dfrac{ 101167z }{ 250000 } $. 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. $$ \begin{aligned} \frac{101167}{250000} \cdot z & \xlongequal{\text{Step 1}} \frac{101167}{250000} \cdot \frac{z}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 101167 \cdot z }{ 250000 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 101167z }{ 250000 } \end{aligned} $$ |
| ⑦ | Add $ \dfrac{71231x}{250000} $ and $ \dfrac{38801y}{125000} $ to get $ \dfrac{ \color{purple}{ 71231x+77602y } }{ 250000 }$. To add raitonal expressions, both fractions must have the same denominator. |
| ⑧ | Multiply $ \dfrac{101167}{250000} $ by $ z $ to get $ \dfrac{ 101167z }{ 250000 } $. 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. $$ \begin{aligned} \frac{101167}{250000} \cdot z & \xlongequal{\text{Step 1}} \frac{101167}{250000} \cdot \frac{z}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 101167 \cdot z }{ 250000 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 101167z }{ 250000 } \end{aligned} $$ |
| ⑨ | Add $ \dfrac{71231x+77602y}{250000} $ and $ \dfrac{101167z}{250000} $ to get $ \dfrac{ 71231x+77602y + 101167z }{ \color{blue}{ 250000 }}$. To add expressions with the same denominators, we add the numerators and write the result over the common denominator. $$ \begin{aligned} \frac{71231x+77602y}{250000} + \frac{101167z}{250000} & = \frac{71231x+77602y}{\color{blue}{250000}} + \frac{101167z}{\color{blue}{250000}} = \\[1ex] &=\frac{ 71231x+77602y + 101167z }{ \color{blue}{ 250000 }} \end{aligned} $$ |