Solve 71/2-[31/4div{3/4-1/3(frac{2}{3}-frac{1}{6}+frac{1}{8})}]

$$7 \frac { 1 } { 2 } - [ 3 \frac { 1 } { 4 } \div \{ \frac { 3 } { 4 } - \frac { 1 } { 3 } ( \frac { 2 } { 3 } - \frac { 1 } { 6 } + \frac { 1 } { 8 } ) \} ]$$

Evaluate

$$\frac{3}{2}=1.5$$

Solution Steps

Multiply 7 and 2 to get 14.

$$\frac{14+1}{2}-\frac{\frac{3\times 4+1}{4}}{\frac{3}{4}-\frac{1}{3}\left(\frac{2}{3}-\frac{1}{6}+\frac{1}{8}\right)}$$

Add 14 and 1 to get 15.

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

Multiply 3 and 4 to get 12.

$$\frac{15}{2}-\frac{\frac{12+1}{4}}{\frac{3}{4}-\frac{1}{3}\left(\frac{2}{3}-\frac{1}{6}+\frac{1}{8}\right)}$$

Add 12 and 1 to get 13.

$$\frac{15}{2}-\frac{\frac{13}{4}}{\frac{3}{4}-\frac{1}{3}\left(\frac{2}{3}-\frac{1}{6}+\frac{1}{8}\right)}$$

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

$$\frac{15}{2}-\frac{\frac{13}{4}}{\frac{3}{4}-\frac{1}{3}\left(\frac{4}{6}-\frac{1}{6}+\frac{1}{8}\right)}$$

Since \frac{4}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15}{2}-\frac{\frac{13}{4}}{\frac{3}{4}-\frac{1}{3}\left(\frac{4-1}{6}+\frac{1}{8}\right)}$$

Subtract 1 from 4 to get 3.

$$\frac{15}{2}-\frac{\frac{13}{4}}{\frac{3}{4}-\frac{1}{3}\left(\frac{3}{6}+\frac{1}{8}\right)}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{15}{2}-\frac{\frac{13}{4}}{\frac{3}{4}-\frac{1}{3}\left(\frac{1}{2}+\frac{1}{8}\right)}$$

Least common multiple of 2 and 8 is 8. Convert \frac{1}{2} and \frac{1}{8} to fractions with denominator 8.

$$\frac{15}{2}-\frac{\frac{13}{4}}{\frac{3}{4}-\frac{1}{3}\left(\frac{4}{8}+\frac{1}{8}\right)}$$

Since \frac{4}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

$$\frac{15}{2}-\frac{\frac{13}{4}}{\frac{3}{4}-\frac{1}{3}\times \frac{4+1}{8}}$$

Add 4 and 1 to get 5.

$$\frac{15}{2}-\frac{\frac{13}{4}}{\frac{3}{4}-\frac{1}{3}\times \frac{5}{8}}$$

Multiply \frac{1}{3} times \frac{5}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15}{2}-\frac{\frac{13}{4}}{\frac{3}{4}-\frac{1\times 5}{3\times 8}}$$

Do the multiplications in the fraction \frac{1\times 5}{3\times 8}.

$$\frac{15}{2}-\frac{\frac{13}{4}}{\frac{3}{4}-\frac{5}{24}}$$

Least common multiple of 4 and 24 is 24. Convert \frac{3}{4} and \frac{5}{24} to fractions with denominator 24.

$$\frac{15}{2}-\frac{\frac{13}{4}}{\frac{18}{24}-\frac{5}{24}}$$

Since \frac{18}{24} and \frac{5}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15}{2}-\frac{\frac{13}{4}}{\frac{18-5}{24}}$$

Subtract 5 from 18 to get 13.

$$\frac{15}{2}-\frac{\frac{13}{4}}{\frac{13}{24}}$$

Divide \frac{13}{4} by \frac{13}{24} by multiplying \frac{13}{4} by the reciprocal of \frac{13}{24}.

$$\frac{15}{2}-\frac{13}{4}\times \frac{24}{13}$$

Multiply \frac{13}{4} times \frac{24}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15}{2}-\frac{13\times 24}{4\times 13}$$

Cancel out 13 in both numerator and denominator.

$$\frac{15}{2}-\frac{24}{4}$$

Divide 24 by 4 to get 6.

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

Convert 6 to fraction \frac{12}{2}.

$$\frac{15}{2}-\frac{12}{2}$$

Since \frac{15}{2} and \frac{12}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-12}{2}$$

Subtract 12 from 15 to get 3.

$$\frac{3}{2}$$

Factor

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$