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Question

Answer

$$-\dfrac{6}{7}+\dfrac{3}{14}+\dfrac{1}{4}=-\dfrac{11}{28}$$

Explanation

Tap the blue circles to see an explanation.

$$ \begin{aligned}-\frac{6}{7}+\frac{3}{14}+\frac{1}{4}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-\frac{9}{14}+\frac{1}{4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-\frac{11}{28}\end{aligned} $$
①
Combine like terms
②

Add $ \dfrac{-9}{14} $ and $ \dfrac{1}{4} $ to get $ \dfrac{ \color{purple}{ -11 } }{ 28 }$.

To add fractions they must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ 2 }$ and the second by $\color{blue}{ 7 }$.

$$ \begin{aligned} \frac{-9}{14} + \frac{1}{4} & = \frac{ \left( -9 \right) \cdot \color{blue}{ 2 }}{ 14 \cdot \color{blue}{ 2 }} + \frac{ 1 \cdot \color{blue}{ 7 }}{ 4 \cdot \color{blue}{ 7 }} = \\[1ex] &=\frac{ \color{purple}{ -18 } }{ 28 } + \frac{ \color{purple}{ 7 } }{ 28 }=\frac{ \color{purple}{ -11 } }{ 28 } \end{aligned} $$
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