Solve 9-[8-(1/3+1/4)*6]}div[8-(1/3+1/2)*6]

$$9 - [ 8 - ( \frac { 1 } { 3 } + \frac { 1 } { 4 } ) \times 6 ] \} \div [ 8 - ( \frac { 1 } { 3 } + \frac { 1 } { 2 } ) \times 6 ]$$

Evaluate

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

Solution Steps

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

$$9-\left(8-\left(\frac{4}{12}+\frac{3}{12}\right)\times 6\right)$$

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

$$9-\left(8-\frac{4+3}{12}\times 6\right)$$

Add 4 and 3 to get 7.

$$9-\left(8-\frac{7}{12}\times 6\right)$$

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

$$9-\left(8-\frac{7\times 6}{12}\right)$$

Multiply 7 and 6 to get 42.

$$9-\left(8-\frac{42}{12}\right)$$

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

$$9-\left(8-\frac{7}{2}\right)$$

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

$$9-\left(\frac{16}{2}-\frac{7}{2}\right)$$

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

$$9-\frac{16-7}{2}$$

Subtract 7 from 16 to get 9.

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

Convert 9 to fraction \frac{18}{2}.

$$\frac{18}{2}-\frac{9}{2}$$

Since \frac{18}{2} and \frac{9}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{18-9}{2}$$

Subtract 9 from 18 to get 9.

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

Factor

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