Solve 71/2-[21/4div{11/4-1/2(frac{3}{2}-frac{1}{3}-frac{1}{6})}]

$$7 \frac { 1 } { 2 } - [ 2 \frac { 1 } { 4 } \div \{ 1 \frac { 1 } { 4 } - \frac { 1 } { 2 } ( \frac { 3 } { 2 } - \frac { 1 } { 3 } - \frac { 1 } { 6 } ) \} ]$$

Evaluate

$$\frac{9}{2}=4.5$$

Solution Steps

Multiply 7 and 2 to get 14.

$$\frac{14+1}{2}-\frac{\frac{2\times 4+1}{4}}{\frac{1\times 4+1}{4}-\frac{1}{2}\left(\frac{3}{2}-\frac{1}{3}-\frac{1}{6}\right)}$$

Add 14 and 1 to get 15.

$$\frac{15}{2}-\frac{\frac{2\times 4+1}{4}}{\frac{1\times 4+1}{4}-\frac{1}{2}\left(\frac{3}{2}-\frac{1}{3}-\frac{1}{6}\right)}$$

Multiply 2 and 4 to get 8.

$$\frac{15}{2}-\frac{\frac{8+1}{4}}{\frac{1\times 4+1}{4}-\frac{1}{2}\left(\frac{3}{2}-\frac{1}{3}-\frac{1}{6}\right)}$$

Add 8 and 1 to get 9.

$$\frac{15}{2}-\frac{\frac{9}{4}}{\frac{1\times 4+1}{4}-\frac{1}{2}\left(\frac{3}{2}-\frac{1}{3}-\frac{1}{6}\right)}$$

Multiply 1 and 4 to get 4.

$$\frac{15}{2}-\frac{\frac{9}{4}}{\frac{4+1}{4}-\frac{1}{2}\left(\frac{3}{2}-\frac{1}{3}-\frac{1}{6}\right)}$$

Add 4 and 1 to get 5.

$$\frac{15}{2}-\frac{\frac{9}{4}}{\frac{5}{4}-\frac{1}{2}\left(\frac{3}{2}-\frac{1}{3}-\frac{1}{6}\right)}$$

Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{15}{2}-\frac{\frac{9}{4}}{\frac{5}{4}-\frac{1}{2}\left(\frac{9}{6}-\frac{2}{6}-\frac{1}{6}\right)}$$

Since \frac{9}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15}{2}-\frac{\frac{9}{4}}{\frac{5}{4}-\frac{1}{2}\left(\frac{9-2}{6}-\frac{1}{6}\right)}$$

Subtract 2 from 9 to get 7.

$$\frac{15}{2}-\frac{\frac{9}{4}}{\frac{5}{4}-\frac{1}{2}\left(\frac{7}{6}-\frac{1}{6}\right)}$$

Since \frac{7}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15}{2}-\frac{\frac{9}{4}}{\frac{5}{4}-\frac{1}{2}\times \frac{7-1}{6}}$$

Subtract 1 from 7 to get 6.

$$\frac{15}{2}-\frac{\frac{9}{4}}{\frac{5}{4}-\frac{1}{2}\times \frac{6}{6}}$$

Divide 6 by 6 to get 1.

$$\frac{15}{2}-\frac{\frac{9}{4}}{\frac{5}{4}-\frac{1}{2}\times 1}$$

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

$$\frac{15}{2}-\frac{\frac{9}{4}}{\frac{5}{4}-\frac{1}{2}}$$

Least common multiple of 4 and 2 is 4. Convert \frac{5}{4} and \frac{1}{2} to fractions with denominator 4.

$$\frac{15}{2}-\frac{\frac{9}{4}}{\frac{5}{4}-\frac{2}{4}}$$

Since \frac{5}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15}{2}-\frac{\frac{9}{4}}{\frac{5-2}{4}}$$

Subtract 2 from 5 to get 3.

$$\frac{15}{2}-\frac{\frac{9}{4}}{\frac{3}{4}}$$

Divide \frac{9}{4} by \frac{3}{4} by multiplying \frac{9}{4} by the reciprocal of \frac{3}{4}.

$$\frac{15}{2}-\frac{9}{4}\times \frac{4}{3}$$

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

$$\frac{15}{2}-\frac{9\times 4}{4\times 3}$$

Cancel out 4 in both numerator and denominator.

$$\frac{15}{2}-\frac{9}{3}$$

Divide 9 by 3 to get 3.

$$\frac{15}{2}-3$$

Convert 3 to fraction \frac{6}{2}.

$$\frac{15}{2}-\frac{6}{2}$$

Since \frac{15}{2} and \frac{6}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-6}{2}$$

Subtract 6 from 15 to get 9.

$$\frac{9}{2}$$

Factor

$$\frac{3 ^ {2}}{2} = 4\frac{1}{2} = 4.5$$