Solve 9-(6/7+7)+[2-1/2-(7-1/2)]+3

$$9 - ( \frac { 6 } { 7 } + 7 ) + [ 2 - \frac { 1 } { 2 } - ( 7 - \frac { 1 } { 2 } ) ] + 3$$

Evaluate

$$-\frac{6}{7}\approx -0.857142857$$

Solution Steps

Convert 7 to fraction \frac{49}{7}.

$$9-\left(\frac{6}{7}+\frac{49}{7}\right)+2-\frac{1}{2}-\left(7-\frac{1}{2}\right)+3$$

Since \frac{6}{7} and \frac{49}{7} have the same denominator, add them by adding their numerators.

$$9-\frac{6+49}{7}+2-\frac{1}{2}-\left(7-\frac{1}{2}\right)+3$$

Add 6 and 49 to get 55.

$$9-\frac{55}{7}+2-\frac{1}{2}-\left(7-\frac{1}{2}\right)+3$$

Convert 9 to fraction \frac{63}{7}.

$$\frac{63}{7}-\frac{55}{7}+2-\frac{1}{2}-\left(7-\frac{1}{2}\right)+3$$

Since \frac{63}{7} and \frac{55}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{63-55}{7}+2-\frac{1}{2}-\left(7-\frac{1}{2}\right)+3$$

Subtract 55 from 63 to get 8.

$$\frac{8}{7}+2-\frac{1}{2}-\left(7-\frac{1}{2}\right)+3$$

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

$$\frac{8}{7}+\frac{4}{2}-\frac{1}{2}-\left(7-\frac{1}{2}\right)+3$$

Since \frac{4}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8}{7}+\frac{4-1}{2}-\left(7-\frac{1}{2}\right)+3$$

Subtract 1 from 4 to get 3.

$$\frac{8}{7}+\frac{3}{2}-\left(7-\frac{1}{2}\right)+3$$

Convert 7 to fraction \frac{14}{2}.

$$\frac{8}{7}+\frac{3}{2}-\left(\frac{14}{2}-\frac{1}{2}\right)+3$$

Since \frac{14}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8}{7}+\frac{3}{2}-\frac{14-1}{2}+3$$

Subtract 1 from 14 to get 13.

$$\frac{8}{7}+\frac{3}{2}-\frac{13}{2}+3$$

Since \frac{3}{2} and \frac{13}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8}{7}+\frac{3-13}{2}+3$$

Subtract 13 from 3 to get -10.

$$\frac{8}{7}+\frac{-10}{2}+3$$

Divide -10 by 2 to get -5.

$$\frac{8}{7}-5+3$$

Convert 5 to fraction \frac{35}{7}.

$$\frac{8}{7}-\frac{35}{7}+3$$

Since \frac{8}{7} and \frac{35}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-35}{7}+3$$

Subtract 35 from 8 to get -27.

$$-\frac{27}{7}+3$$

Convert 3 to fraction \frac{21}{7}.

$$-\frac{27}{7}+\frac{21}{7}$$

Since -\frac{27}{7} and \frac{21}{7} have the same denominator, add them by adding their numerators.

$$\frac{-27+21}{7}$$

Add -27 and 21 to get -6.

$$-\frac{6}{7}$$

Factor

$$-\frac{6}{7} = -0.8571428571428571$$