Solve {left(3/2right)}^2+3*3/2-2

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

Evaluate

$$\frac{19}{4}=4.75$$

Solution Steps

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

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

Express 3\times \frac{3}{2} as a single fraction.

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

Multiply 3 and 3 to get 9.

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

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

$$\frac{9}{4}+\frac{18}{4}-2$$

Since \frac{9}{4} and \frac{18}{4} have the same denominator, add them by adding their numerators.

$$\frac{9+18}{4}-2$$

Add 9 and 18 to get 27.

$$\frac{27}{4}-2$$

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

$$\frac{27}{4}-\frac{8}{4}$$

Since \frac{27}{4} and \frac{8}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-8}{4}$$

Subtract 8 from 27 to get 19.

$$\frac{19}{4}$$

Factor

$$\frac{19}{2 ^ {2}} = 4\frac{3}{4} = 4.75$$