Solve [5/2-1/(frac{1{2})^2}]+(3/2)^2

$$[ \frac { 5 } { 2 } - \frac { 1 } { ( \frac { 1 } { 2 } ) ^ { 2 } } ] + ( \frac { 3 } { 2 } ) ^ { 2 }$$

Evaluate

$$\frac{3}{4}=0.75$$

Solution Steps

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

$$\frac{5}{2}-\frac{1}{\frac{1}{4}}+\left(\frac{3}{2}\right)^{2}$$

Divide 1 by \frac{1}{4} by multiplying 1 by the reciprocal of \frac{1}{4}.

$$\frac{5}{2}-1\times 4+\left(\frac{3}{2}\right)^{2}$$

Multiply 1 and 4 to get 4.

$$\frac{5}{2}-4+\left(\frac{3}{2}\right)^{2}$$

Convert 4 to fraction \frac{8}{2}.

$$\frac{5}{2}-\frac{8}{2}+\left(\frac{3}{2}\right)^{2}$$

Since \frac{5}{2} and \frac{8}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-8}{2}+\left(\frac{3}{2}\right)^{2}$$

Subtract 8 from 5 to get -3.

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

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

$$-\frac{3}{2}+\frac{9}{4}$$

Least common multiple of 2 and 4 is 4. Convert -\frac{3}{2} and \frac{9}{4} to fractions with denominator 4.

$$-\frac{6}{4}+\frac{9}{4}$$

Since -\frac{6}{4} and \frac{9}{4} have the same denominator, add them by adding their numerators.

$$\frac{-6+9}{4}$$

Add -6 and 9 to get 3.

$$\frac{3}{4}$$

Factor

$$\frac{3}{2 ^ {2}} = 0.75$$