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Question

Answer

$$-\dfrac{13}{4}+\dfrac{21}{8}=-\dfrac{5}{8}$$

Explanation
$$ \begin{aligned}-\frac{13}{4}+\frac{21}{8}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-\frac{5}{8}\end{aligned} $$
①

Add $ \dfrac{-13}{4} $ and $ \dfrac{21}{8} $ to get $ \dfrac{ \color{purple}{ -5 } }{ 8 }$.

To add fractions they must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 2 }$.

$$ \begin{aligned} \frac{-13}{4} + \frac{21}{8} & = \frac{ \left( -13 \right) \cdot \color{blue}{ 2 }}{ 4 \cdot \color{blue}{ 2 }} + \frac{ 21 }{ 8 } = \\[1ex] &=\frac{ \color{purple}{ -26 } }{ 8 } + \frac{ \color{purple}{ 21 } }{ 8 }=\frac{ \color{purple}{ -5 } }{ 8 } \end{aligned} $$
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