Solve 2/3+{1/9+[3/4-1/2]-(-frac{1}{2})^0}+3-(1frac{2}{3}):5

$$\frac { 2 } { 3 } + \{ \frac { 1 } { 9 } + [ \frac { 3 } { 4 } - \frac { 1 } { 2 } ] - ( - \frac { 1 } { 2 } ) ^ { 0 } \} + 3 - ( 1 \frac { 2 } { 3 } ) : 5$$

Evaluate

$$\frac{97}{36}\approx 2.694444444$$

Solution Steps

Add \frac{1}{9} and \frac{3}{4} to get \frac{31}{36}.

$$\frac{2}{3}+\frac{31}{36}-\frac{1}{2}-\left(-\frac{1}{2}\right)^{0}+3-\frac{\frac{1\times 3+2}{3}}{5}$$

Subtract \frac{1}{2} from \frac{31}{36} to get \frac{13}{36}.

$$\frac{2}{3}+\frac{13}{36}-\left(-\frac{1}{2}\right)^{0}+3-\frac{\frac{1\times 3+2}{3}}{5}$$

Calculate -\frac{1}{2} to the power of 0 and get 1.

$$\frac{2}{3}+\frac{13}{36}-1+3-\frac{\frac{1\times 3+2}{3}}{5}$$

Subtract 1 from \frac{13}{36} to get -\frac{23}{36}.

$$\frac{2}{3}-\frac{23}{36}+3-\frac{\frac{1\times 3+2}{3}}{5}$$

Subtract \frac{23}{36} from \frac{2}{3} to get \frac{1}{36}.

$$\frac{1}{36}+3-\frac{\frac{1\times 3+2}{3}}{5}$$

Add \frac{1}{36} and 3 to get \frac{109}{36}.

$$\frac{109}{36}-\frac{\frac{1\times 3+2}{3}}{5}$$

Express \frac{\frac{1\times 3+2}{3}}{5} as a single fraction.

$$\frac{109}{36}-\frac{1\times 3+2}{3\times 5}$$

Multiply 1 and 3 to get 3.

$$\frac{109}{36}-\frac{3+2}{3\times 5}$$

Add 3 and 2 to get 5.

$$\frac{109}{36}-\frac{5}{3\times 5}$$

Multiply 3 and 5 to get 15.

$$\frac{109}{36}-\frac{5}{15}$$

Reduce the fraction \frac{5}{15} to lowest terms by extracting and canceling out 5.

$$\frac{109}{36}-\frac{1}{3}$$

Subtract \frac{1}{3} from \frac{109}{36} to get \frac{97}{36}.

$$\frac{97}{36}$$

Factor

$$\frac{97}{2 ^ {2} \cdot 3 ^ {2}} = 2\frac{25}{36} = 2.6944444444444446$$