Solve [(6/8+4/2-3/12)+(3/4*frac{8}{6}*frac{9}{2}-frac{6}{12})]+[frac{6}{8}]

$$[ ( \frac { 6 } { 8 } + \frac { 4 } { 2 } - \frac { 3 } { 12 } ) + ( \frac { 3 } { 4 } \times \frac { 8 } { 6 } \times \frac { 9 } { 2 } - \frac { 6 } { 12 } ) ] + [ \frac { 6 } { 8 } ]$$

Evaluate

$$\frac{29}{4}=7.25$$

Solution Steps

Reduce the fraction \frac{6}{8} to lowest terms by extracting and canceling out 2.

$$\frac{3}{4}+\frac{4}{2}-\frac{3}{12}+\frac{3}{4}\times \frac{8}{6}\times \frac{9}{2}-\frac{6}{12}+\frac{6}{8}$$

Divide 4 by 2 to get 2.

$$\frac{3}{4}+2-\frac{3}{12}+\frac{3}{4}\times \frac{8}{6}\times \frac{9}{2}-\frac{6}{12}+\frac{6}{8}$$

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

$$\frac{3}{4}+\frac{8}{4}-\frac{3}{12}+\frac{3}{4}\times \frac{8}{6}\times \frac{9}{2}-\frac{6}{12}+\frac{6}{8}$$

Since \frac{3}{4} and \frac{8}{4} have the same denominator, add them by adding their numerators.

$$\frac{3+8}{4}-\frac{3}{12}+\frac{3}{4}\times \frac{8}{6}\times \frac{9}{2}-\frac{6}{12}+\frac{6}{8}$$

Add 3 and 8 to get 11.

$$\frac{11}{4}-\frac{3}{12}+\frac{3}{4}\times \frac{8}{6}\times \frac{9}{2}-\frac{6}{12}+\frac{6}{8}$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$\frac{11}{4}-\frac{1}{4}+\frac{3}{4}\times \frac{8}{6}\times \frac{9}{2}-\frac{6}{12}+\frac{6}{8}$$

Since \frac{11}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11-1}{4}+\frac{3}{4}\times \frac{8}{6}\times \frac{9}{2}-\frac{6}{12}+\frac{6}{8}$$

Subtract 1 from 11 to get 10.

$$\frac{10}{4}+\frac{3}{4}\times \frac{8}{6}\times \frac{9}{2}-\frac{6}{12}+\frac{6}{8}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$\frac{5}{2}+\frac{3}{4}\times \frac{8}{6}\times \frac{9}{2}-\frac{6}{12}+\frac{6}{8}$$

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$\frac{5}{2}+\frac{3}{4}\times \frac{4}{3}\times \frac{9}{2}-\frac{6}{12}+\frac{6}{8}$$

Cancel out \frac{3}{4} and its reciprocal \frac{4}{3}.

$$\frac{5}{2}+\frac{9}{2}-\frac{6}{12}+\frac{6}{8}$$

Since \frac{5}{2} and \frac{9}{2} have the same denominator, add them by adding their numerators.

$$\frac{5+9}{2}-\frac{6}{12}+\frac{6}{8}$$

Add 5 and 9 to get 14.

$$\frac{14}{2}-\frac{6}{12}+\frac{6}{8}$$

Divide 14 by 2 to get 7.

$$7-\frac{6}{12}+\frac{6}{8}$$

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

$$7-\frac{1}{2}+\frac{6}{8}$$

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

$$\frac{14}{2}-\frac{1}{2}+\frac{6}{8}$$

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

$$\frac{14-1}{2}+\frac{6}{8}$$

Subtract 1 from 14 to get 13.

$$\frac{13}{2}+\frac{6}{8}$$

Reduce the fraction \frac{6}{8} to lowest terms by extracting and canceling out 2.

$$\frac{13}{2}+\frac{3}{4}$$

Least common multiple of 2 and 4 is 4. Convert \frac{13}{2} and \frac{3}{4} to fractions with denominator 4.

$$\frac{26}{4}+\frac{3}{4}$$

Since \frac{26}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{26+3}{4}$$

Add 26 and 3 to get 29.

$$\frac{29}{4}$$

Factor

$$\frac{29}{2 ^ {2}} = 7\frac{1}{4} = 7.25$$