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Answer

$$\frac{9}{45}-\frac{45}{45}=-\frac{4}{5}$$

Explanation

Tap the blue circles to see an explanation.

$$ \begin{aligned}\frac{9}{45}-\frac{45}{45}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{ 9 : \color{orangered}{ 9 } }{ 45 : \color{orangered}{ 9 }} - \frac{ 45 : \color{orangered}{ 45 } }{ 45 : \color{orangered}{ 45 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{1}{5}-\frac{1}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{1}{5}-1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-\frac{4}{5}\end{aligned} $$
①
Divide both the top and bottom numbers by $ \color{orangered}{ 9 } $.
②
Divide both the top and bottom numbers by $ \color{orangered}{ 45 } $.
③
Remove 1 from denominator.
④

Subtract $1$ from $ \dfrac{1}{5} $ to get $ \dfrac{ \color{purple}{ -4 } }{ 5 }$.

Step 1: Write $ 1 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To subtract fractions they must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{5}$.

$$ \begin{aligned} \frac{1}{5} -1 & \xlongequal{\text{Step 1}} \frac{1}{5} - \frac{1}{\color{red}{1}} = \frac{ 1 }{ 5 } - \frac{ 1 \cdot \color{blue}{ 5 }}{ 1 \cdot \color{blue}{ 5 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 1 } }{ 5 } - \frac{ \color{purple}{ 5 } }{ 5 }=\frac{ \color{purple}{ -4 } }{ 5 } \end{aligned} $$
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