$$ (\frac{2}{5})^2 = \frac{ 2 }{ 5 }^{ 2 } \cdot 1 ^ { 2 } = \frac{ 2 }{ 5 }^{ 2 } 1 ^2 = \frac{ 2 }{ 5 }^{ 2 } \lvert 1 \rvert = \frac{4}{25} $$

Multiply $7$ by $ \dfrac{2}{5} $ to get $ \dfrac{14}{5} $.

Write $ 7 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

$$ \begin{aligned} 7 \cdot \frac{2}{5} = \frac{7}{\color{red}{1}} \cdot \frac{2}{5} = \frac{14}{5} \end{aligned} $$

Multiply $4$ by $ \dfrac{4}{25} $ to get $ \dfrac{16}{25} $.

Write $ 4 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

$$ \begin{aligned} 4 \cdot \frac{4}{25} = \frac{4}{\color{red}{1}} \cdot \frac{4}{25} = \frac{16}{25} \end{aligned} $$

Multiply $7$ by $ \dfrac{2}{5} $ to get $ \dfrac{14}{5} $.

Write $ 7 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

$$ \begin{aligned} 7 \cdot \frac{2}{5} = \frac{7}{\color{red}{1}} \cdot \frac{2}{5} = \frac{14}{5} \end{aligned} $$

Add $ \dfrac{16}{25} $ and $ \dfrac{14}{5} $ to get $ \dfrac{ \color{purple}{ 86 } }{ 25 }$.

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

$$ \begin{aligned} \frac{16}{25} + \frac{14}{5} & = \frac{ 16 }{ 25 } + \frac{ 14 \cdot \color{blue}{ 5 }}{ 5 \cdot \color{blue}{ 5 }} = \\[1ex] &=\frac{ \color{purple}{ 16 } }{ 25 } + \frac{ \color{purple}{ 70 } }{ 25 }=\frac{ \color{purple}{ 86 } }{ 25 } \end{aligned} $$

Add $ \dfrac{86}{25} $ and $ 6 $ to get $ \dfrac{ \color{purple}{ 236 } }{ 25 }$.

Step 1: Write $ 6 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add fractions they must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{25}$.

$$ \begin{aligned} \frac{86}{25} +6 & \xlongequal{\text{Step 1}} \frac{86}{25} + \frac{6}{\color{red}{1}} = \frac{ 86 }{ 25 } + \frac{ 6 \cdot \color{blue}{ 25 }}{ 1 \cdot \color{blue}{ 25 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 86 } }{ 25 } + \frac{ \color{purple}{ 150 } }{ 25 }=\frac{ \color{purple}{ 236 } }{ 25 } \end{aligned} $$

Multiply $ \dfrac{1}{4} $ by $ \dfrac{236}{25} $ to get $ \dfrac{59}{25} $.

Multiply numerators and denominators.

Step 2: Cancel down by $ \color{blue}{4} $

$$ \begin{aligned} \frac{1}{4} \cdot \frac{236}{25} & = \frac{236 : \color{blue}{4}}{100 : \color{blue}{4}}= \frac{59}{25} \end{aligned} $$

Subtract $4$ from $ \dfrac{59}{25} $ to get $ \dfrac{ \color{purple}{ -41 } }{ 25 }$.

Step 1: Write $ 4 $ 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 $\color{blue}{25}$.

$$ \begin{aligned} \frac{59}{25} -4 & \xlongequal{\text{Step 1}} \frac{59}{25} - \frac{4}{\color{red}{1}} = \frac{ 59 }{ 25 } - \frac{ 4 \cdot \color{blue}{ 25 }}{ 1 \cdot \color{blue}{ 25 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 59 } }{ 25 } - \frac{ \color{purple}{ 100 } }{ 25 }=\frac{ \color{purple}{ -41 } }{ 25 } \end{aligned} $$