Answer
$$\frac{\frac{1}{10}+\frac{13}{4}}{\frac{3}{5}-\frac{1}{2}}=\frac{67}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\frac{1}{10}+\frac{13}{4}}{\frac{3}{5}-\frac{1}{2}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{\frac{67}{20}}{\frac{1}{10}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{67}{2}\end{aligned} $$ | |
| ① | Combine like terms |
| ② | Combine like terms |
| ③ | Divide $ \dfrac{67}{20} $ by $ \dfrac{1}{10} $ to get $ \dfrac{67}{2} $. Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction. Step 2: Multiply numerators and denominators. Step 3: Cancel down by $ \color{blue}{10} $ $$ \begin{aligned} \frac{ \frac{67}{20} }{ \frac{\color{blue}{1}}{\color{blue}{10}} } & \xlongequal{\text{Step 1}} \frac{67}{20} \cdot \frac{\color{blue}{10}}{\color{blue}{1}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{670 : \color{blue}{10}}{20 : \color{blue}{10}}= \frac{67}{2} \end{aligned} $$ |
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Simplify Rational Expressions