Calculate: 2

Evaluate: $2$

Reduce the fraction $\frac{6}{4}$ to lowest terms by extracting and canceling out $2$.

$$\left(2-\frac{3}{2}\right)^{2}+\left(4+\frac{1}{2}-\frac{2}{3}\right)\times \left(\frac{12}{23}\right)-\left(1-\frac{1}{2}\right)^{2}$$

Subtract $\frac{3}{2}$ from $2$ to get $\frac{1}{2}$.

$$\left(\frac{1}{2}\right)^{2}+\left(4+\frac{1}{2}-\frac{2}{3}\right)\times \left(\frac{12}{23}\right)-\left(1-\frac{1}{2}\right)^{2}$$

Calculate $\frac{1}{2}$ to the power of $2$ and get $\frac{1}{4}$.

$$\frac{1}{4}+\left(4+\frac{1}{2}-\frac{2}{3}\right)\times \left(\frac{12}{23}\right)-\left(1-\frac{1}{2}\right)^{2}$$

Add $4$ and $\frac{1}{2}$ to get $\frac{9}{2}$.

$$\frac{1}{4}+\left(\frac{9}{2}-\frac{2}{3}\right)\times \left(\frac{12}{23}\right)-\left(1-\frac{1}{2}\right)^{2}$$

Subtract $\frac{2}{3}$ from $\frac{9}{2}$ to get $\frac{23}{6}$.

$$\frac{1}{4}+\frac{23}{6}\times \left(\frac{12}{23}\right)-\left(1-\frac{1}{2}\right)^{2}$$

Multiply $\frac{23}{6}$ and $\frac{12}{23}$ to get $2$.

$$\frac{1}{4}+2-\left(1-\frac{1}{2}\right)^{2}$$

Add $\frac{1}{4}$ and $2$ to get $\frac{9}{4}$.

$$\frac{9}{4}-\left(1-\frac{1}{2}\right)^{2}$$

Subtract $\frac{1}{2}$ from $1$ to get $\frac{1}{2}$.

$$\frac{9}{4}-\left(\frac{1}{2}\right)^{2}$$

Calculate $\frac{1}{2}$ to the power of $2$ and get $\frac{1}{4}$.

$$\frac{9}{4}-\frac{1}{4}$$

Subtract $\frac{1}{4}$ from $\frac{9}{4}$ to get $2$.

$$2$$