Solve [(-2)^2-(-3/2)^2]-1/2

$$[ ( - 2 ) ^ { 2 } - ( - \frac { 3 } { 2 } ) ^ { 2 } ] - \frac { 1 } { 2 }$$

Evaluate

$$\frac{5}{4}=1.25$$

Solution Steps

Calculate -2 to the power of 2 and get 4.

$$4-\left(-\frac{3}{2}\right)^{2}-\frac{1}{2}$$

Calculate -\frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$4-\frac{9}{4}-\frac{1}{2}$$

Convert 4 to fraction \frac{16}{4}.

$$\frac{16}{4}-\frac{9}{4}-\frac{1}{2}$$

Since \frac{16}{4} and \frac{9}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-9}{4}-\frac{1}{2}$$

Subtract 9 from 16 to get 7.

$$\frac{7}{4}-\frac{1}{2}$$

Least common multiple of 4 and 2 is 4. Convert \frac{7}{4} and \frac{1}{2} to fractions with denominator 4.

$$\frac{7}{4}-\frac{2}{4}$$

Since \frac{7}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-2}{4}$$

Subtract 2 from 7 to get 5.

$$\frac{5}{4}$$

Factor

$$\frac{5}{2 ^ {2}} = 1\frac{1}{4} = 1.25$$