Solve 9/2+(2/3)^2-(2/8+5/4)=

$$\frac { 9 } { 2 } + ( \frac { 2 } { 3 } ) ^ { 2 } - ( \frac { 2 } { 8 } + \frac { 5 } { 4 } ) =$$

Evaluate

$$\frac{31}{9}\approx 3.444444444$$

Solution Steps

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

$$\frac{9}{2}+\frac{4}{9}-\left(\frac{2}{8}+\frac{5}{4}\right)$$

Least common multiple of 2 and 9 is 18. Convert \frac{9}{2} and \frac{4}{9} to fractions with denominator 18.

$$\frac{81}{18}+\frac{8}{18}-\left(\frac{2}{8}+\frac{5}{4}\right)$$

Since \frac{81}{18} and \frac{8}{18} have the same denominator, add them by adding their numerators.

$$\frac{81+8}{18}-\left(\frac{2}{8}+\frac{5}{4}\right)$$

Add 81 and 8 to get 89.

$$\frac{89}{18}-\left(\frac{2}{8}+\frac{5}{4}\right)$$

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$\frac{89}{18}-\left(\frac{1}{4}+\frac{5}{4}\right)$$

Since \frac{1}{4} and \frac{5}{4} have the same denominator, add them by adding their numerators.

$$\frac{89}{18}-\frac{1+5}{4}$$

Add 1 and 5 to get 6.

$$\frac{89}{18}-\frac{6}{4}$$

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

$$\frac{89}{18}-\frac{3}{2}$$

Least common multiple of 18 and 2 is 18. Convert \frac{89}{18} and \frac{3}{2} to fractions with denominator 18.

$$\frac{89}{18}-\frac{27}{18}$$

Since \frac{89}{18} and \frac{27}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{89-27}{18}$$

Subtract 27 from 89 to get 62.

$$\frac{62}{18}$$

Reduce the fraction \frac{62}{18} to lowest terms by extracting and canceling out 2.

$$\frac{31}{9}$$

Factor

$$\frac{31}{3 ^ {2}} = 3\frac{4}{9} = 3.4444444444444446$$