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Question

Answer

$$\dfrac{3}{12y}+\dfrac{9}{24}=\dfrac{36y+24}{96y}$$

Explanation

Tap the blue circles to see an explanation.

$$ \begin{aligned}\frac{3}{12y}+\frac{9}{24}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3}{12y} + \frac{ 9 : \color{orangered}{ 3 } }{ 24 : \color{orangered}{ 3 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{3}{12y}+\frac{3}{8} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{36y+24}{96y}\end{aligned} $$
①
Divide both the top and bottom numbers by $ \color{orangered}{ 3 } $.
②

Add $ \dfrac{3}{12y} $ and $ \dfrac{3}{8} $ to get $ \dfrac{ \color{purple}{ 36y+24 } }{ 96y }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ 8 }$ and the second by $\color{blue}{ 12y }$.

$$ \begin{aligned} \frac{3}{12y} + \frac{3}{8} & = \frac{ 3 \cdot \color{blue}{ 8 }}{ 12y \cdot \color{blue}{ 8 }} + \frac{ 3 \cdot \color{blue}{ 12y }}{ 8 \cdot \color{blue}{ 12y }} = \\[1ex] &=\frac{ \color{purple}{ 24 } }{ 96y } + \frac{ \color{purple}{ 36y } }{ 96y }=\frac{ \color{purple}{ 36y+24 } }{ 96y } \end{aligned} $$
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