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Question

Answer

$$\dfrac{4}{3}+\dfrac{3}{5}+(-\dfrac{2}{5})+(-\dfrac{11}{5})=-\dfrac{10}{15}$$

Explanation

Tap the blue circles to see an explanation.

$$ \begin{aligned}\frac{4}{3}+\frac{3}{5}+(-\frac{2}{5})+(-\frac{11}{5})& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{23}{15}+(-\frac{11}{5}) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-\frac{10}{15}\end{aligned} $$
①
Combine like terms
②

Add $ \dfrac{23}{15} $ and $ \dfrac{-11}{5} $ to get $ \dfrac{ \color{purple}{ -10 } }{ 15 }$.

To add fractions they must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{3}$.

$$ \begin{aligned} \frac{23}{15} + \frac{-11}{5} & = \frac{ 23 }{ 15 } + \frac{ \left( -11 \right) \cdot \color{blue}{ 3 }}{ 5 \cdot \color{blue}{ 3 }} = \\[1ex] &=\frac{ \color{purple}{ 23 } }{ 15 } + \frac{ \color{purple}{ -33 } }{ 15 }=\frac{ \color{purple}{ -10 } }{ 15 } \end{aligned} $$
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