Solve {q-[8-(1/3+1/4)*6]}div[8-(1/3+1/2)*6]

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

Evaluate

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

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{1}{3} and \frac{1}{4} to fractions with denominator 12.

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

Since \frac{4}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

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

Add 4 and 3 to get 7.

$$\frac{q-\left(8-\frac{7}{12}\times 6\right)}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}$$

Express \frac{7}{12}\times 6 as a single fraction.

$$\frac{q-\left(8-\frac{7\times 6}{12}\right)}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}$$

Multiply 7 and 6 to get 42.

$$\frac{q-\left(8-\frac{42}{12}\right)}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}$$

Reduce the fraction \frac{42}{12} to lowest terms by extracting and canceling out 6.

$$\frac{q-\left(8-\frac{7}{2}\right)}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}$$

Convert 8 to fraction \frac{16}{2}.

$$\frac{q-\left(\frac{16}{2}-\frac{7}{2}\right)}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}$$

Since \frac{16}{2} and \frac{7}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{q-\frac{16-7}{2}}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}$$

Subtract 7 from 16 to get 9.

$$\frac{q-\frac{9}{2}}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}$$

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

$$\frac{q-\frac{9}{2}}{8-\left(\frac{2}{6}+\frac{3}{6}\right)\times 6}$$

Since \frac{2}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

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

Add 2 and 3 to get 5.

$$\frac{q-\frac{9}{2}}{8-\frac{5}{6}\times 6}$$

Cancel out 6 and 6.

$$\frac{q-\frac{9}{2}}{8-5}$$

Subtract 5 from 8 to get 3.

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

Expand

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

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{1}{3} and \frac{1}{4} to fractions with denominator 12.

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

Since \frac{4}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

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

Add 4 and 3 to get 7.

$$\frac{q-\left(8-\frac{7}{12}\times 6\right)}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}$$

Express \frac{7}{12}\times 6 as a single fraction.

$$\frac{q-\left(8-\frac{7\times 6}{12}\right)}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}$$

Multiply 7 and 6 to get 42.

$$\frac{q-\left(8-\frac{42}{12}\right)}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}$$

Reduce the fraction \frac{42}{12} to lowest terms by extracting and canceling out 6.

$$\frac{q-\left(8-\frac{7}{2}\right)}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}$$

Convert 8 to fraction \frac{16}{2}.

$$\frac{q-\left(\frac{16}{2}-\frac{7}{2}\right)}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}$$

Since \frac{16}{2} and \frac{7}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{q-\frac{16-7}{2}}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}$$

Subtract 7 from 16 to get 9.

$$\frac{q-\frac{9}{2}}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}$$

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

$$\frac{q-\frac{9}{2}}{8-\left(\frac{2}{6}+\frac{3}{6}\right)\times 6}$$

Since \frac{2}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

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

Add 2 and 3 to get 5.

$$\frac{q-\frac{9}{2}}{8-\frac{5}{6}\times 6}$$

Cancel out 6 and 6.

$$\frac{q-\frac{9}{2}}{8-5}$$

Subtract 5 from 8 to get 3.

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