Solve 3/2(2/3)^2+3/2(1)^2+3/2(-1)^2

$$\frac { 3 } { 2 } ( 2 / 3 ) ^ { 2 } + \frac { 3 } { 2 } ( 1 ) ^ { 2 } + \frac { 3 } { 2 } ( - 1 ) ^ { 2 }$$

Evaluate

$$\frac{11}{3}\approx 3.666666667$$

Solution Steps

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

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

Multiply \frac{3}{2} times \frac{4}{9} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{3\times 4}{2\times 9}.

$$\frac{12}{18}+\frac{3}{2}\times 1^{2}+\frac{3}{2}\left(-1\right)^{2}$$

Reduce the fraction \frac{12}{18} to lowest terms by extracting and canceling out 6.

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

Calculate 1 to the power of 2 and get 1.

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

Multiply \frac{3}{2} and 1 to get \frac{3}{2}.

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

Least common multiple of 3 and 2 is 6. Convert \frac{2}{3} and \frac{3}{2} to fractions with denominator 6.

$$\frac{4}{6}+\frac{9}{6}+\frac{3}{2}\left(-1\right)^{2}$$

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

$$\frac{4+9}{6}+\frac{3}{2}\left(-1\right)^{2}$$

Add 4 and 9 to get 13.

$$\frac{13}{6}+\frac{3}{2}\left(-1\right)^{2}$$

Calculate -1 to the power of 2 and get 1.

$$\frac{13}{6}+\frac{3}{2}\times 1$$

Multiply \frac{3}{2} and 1 to get \frac{3}{2}.

$$\frac{13}{6}+\frac{3}{2}$$

Least common multiple of 6 and 2 is 6. Convert \frac{13}{6} and \frac{3}{2} to fractions with denominator 6.

$$\frac{13}{6}+\frac{9}{6}$$

Since \frac{13}{6} and \frac{9}{6} have the same denominator, add them by adding their numerators.

$$\frac{13+9}{6}$$

Add 13 and 9 to get 22.

$$\frac{22}{6}$$

Reduce the fraction \frac{22}{6} to lowest terms by extracting and canceling out 2.

$$\frac{11}{3}$$

Factor

$$\frac{11}{3} = 3\frac{2}{3} = 3.6666666666666665$$