Question
Answer
$$\dfrac{\dfrac{7^1}{2}-\dfrac{5^1}{2}}{\dfrac{7^1}{2}+\dfrac{5^1}{2}}=\dfrac{1}{6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\frac{7^1}{2}-\frac{5^1}{2}}{\frac{7^1}{2}+\frac{5^1}{2}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{(7^1-5^1)\cdot\frac{1}{2}}{(7^1+5^1)\cdot\frac{1}{2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}\frac{(7-5)\cdot\frac{1}{2}}{(7+5)\cdot\frac{1}{2}} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{2\cdot\frac{1}{2}}{12\cdot\frac{1}{2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} \htmlClass{explanationCircle explanationCircle8}{\textcircled {8}} } }}}\frac{1}{6}\end{aligned} $$ | |
| ① | Use the distributive property. |
| ② | Use the distributive property. |
| ③ | A polynomial raised to the power of one equals itself. |
| ④ | A polynomial raised to the power of one equals itself. |
| ⑤ | A polynomial raised to the power of one equals itself. |
| ⑥ | A polynomial raised to the power of one equals itself. |
| ⑦ | Multiply $2$ by $ \dfrac{1}{2} $ to get $ 1$. Step 1: Write $ 2 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Cancel $ \color{blue}{ 2 } $ in first and second fraction. Step 3: Multiply numerators and denominators. $$ \begin{aligned} 2 \cdot \frac{1}{2} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{1}{2} \xlongequal{\text{Step 2}} \frac{\color{blue}{1}}{1} \cdot \frac{1}{\color{blue}{1}} = \\[1ex] &= \frac{1}{1} =1 \end{aligned} $$ |
| ⑧ | Multiply $12$ by $ \dfrac{1}{2} $ to get $ 6$. Write $ 12 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Cancel down by $ \color{blue}{2} $ $$ \begin{aligned} 12 \cdot \frac{1}{2} & = \frac{12}{\color{red}{1}} \cdot \frac{1}{2} = \frac{12 : \color{blue}{2}}{2 : \color{blue}{2}} = \\[1ex] &= \frac{6}{1} =6 \end{aligned} $$ |
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