$$x^4-x^3+13\cdot\dfrac{x^2}{100}-13\dfrac{x}{100}=\dfrac{100x^4-100x^3+13x^2-13x}{100}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}x^4-x^3+13 \cdot \frac{x^2}{100}-13\frac{x}{100}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^4-x^3+\frac{13x^2}{100}-\frac{13x}{100} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{100x^4-100x^3+13x^2}{100}-\frac{13x}{100} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{100x^4-100x^3+13x^2-13x}{100}\end{aligned} $$ | |
| ① | Multiply $13$ by $ \dfrac{x^2}{100} $ to get $ \dfrac{ 13x^2 }{ 100 } $. Step 1: Write $ 13 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 13 \cdot \frac{x^2}{100} & \xlongequal{\text{Step 1}} \frac{13}{\color{red}{1}} \cdot \frac{x^2}{100} \xlongequal{\text{Step 2}} \frac{ 13 \cdot x^2 }{ 1 \cdot 100 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 13x^2 }{ 100 } \end{aligned} $$ |
| ② | Multiply $13$ by $ \dfrac{x}{100} $ to get $ \dfrac{ 13x }{ 100 } $. Step 1: Write $ 13 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 13 \cdot \frac{x}{100} & \xlongequal{\text{Step 1}} \frac{13}{\color{red}{1}} \cdot \frac{x}{100} \xlongequal{\text{Step 2}} \frac{ 13 \cdot x }{ 1 \cdot 100 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 13x }{ 100 } \end{aligned} $$ |
| ③ | Add $x^4-x^3$ and $ \dfrac{13x^2}{100} $ to get $ \dfrac{ \color{purple}{ 100x^4-100x^3+13x^2 } }{ 100 }$. Step 1: Write $ x^4-x^3 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: To add raitonal expressions, both fractions must have the same denominator. |
| ④ | Multiply $13$ by $ \dfrac{x}{100} $ to get $ \dfrac{ 13x }{ 100 } $. Step 1: Write $ 13 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 13 \cdot \frac{x}{100} & \xlongequal{\text{Step 1}} \frac{13}{\color{red}{1}} \cdot \frac{x}{100} \xlongequal{\text{Step 2}} \frac{ 13 \cdot x }{ 1 \cdot 100 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 13x }{ 100 } \end{aligned} $$ |
| ⑤ | Subtract $ \dfrac{13x}{100} $ from $ \dfrac{100x^4-100x^3+13x^2}{100} $ to get $ \dfrac{ 100x^4-100x^3+13x^2 - 13x }{ \color{blue}{ 100 }}$. To subtract expressions with the same denominators, we subtract the numerators and write the result over the common denominator. $$ \begin{aligned} \frac{100x^4-100x^3+13x^2}{100} - \frac{13x}{100} & = \frac{100x^4-100x^3+13x^2}{\color{blue}{100}} - \frac{13x}{\color{blue}{100}} = \\[1ex] &=\frac{ 100x^4-100x^3+13x^2 - 13x }{ \color{blue}{ 100 }} \end{aligned} $$ |