Solve 6-3/2-(11/12+1/4)-(1/2-frac{7}{6})

$$6- \frac{ 3 }{ 2 } -( \frac{ 11 }{ 12 } + \frac{ 1 }{ 4 } )-( \frac{ 1 }{ 2 } - \frac{ 7 }{ 6 } )$$

Evaluate

$$4$$

Solution Steps

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

$$\frac{12}{2}-\frac{3}{2}-\left(\frac{11}{12}+\frac{1}{4}\right)-\left(\frac{1}{2}-\frac{7}{6}\right)$$

Since \frac{12}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12-3}{2}-\left(\frac{11}{12}+\frac{1}{4}\right)-\left(\frac{1}{2}-\frac{7}{6}\right)$$

Subtract 3 from 12 to get 9.

$$\frac{9}{2}-\left(\frac{11}{12}+\frac{1}{4}\right)-\left(\frac{1}{2}-\frac{7}{6}\right)$$

Least common multiple of 12 and 4 is 12. Convert \frac{11}{12} and \frac{1}{4} to fractions with denominator 12.

$$\frac{9}{2}-\left(\frac{11}{12}+\frac{3}{12}\right)-\left(\frac{1}{2}-\frac{7}{6}\right)$$

Since \frac{11}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{9}{2}-\frac{11+3}{12}-\left(\frac{1}{2}-\frac{7}{6}\right)$$

Add 11 and 3 to get 14.

$$\frac{9}{2}-\frac{14}{12}-\left(\frac{1}{2}-\frac{7}{6}\right)$$

Reduce the fraction \frac{14}{12} to lowest terms by extracting and canceling out 2.

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

Least common multiple of 2 and 6 is 6. Convert \frac{9}{2} and \frac{7}{6} to fractions with denominator 6.

$$\frac{27}{6}-\frac{7}{6}-\left(\frac{1}{2}-\frac{7}{6}\right)$$

Since \frac{27}{6} and \frac{7}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-7}{6}-\left(\frac{1}{2}-\frac{7}{6}\right)$$

Subtract 7 from 27 to get 20.

$$\frac{20}{6}-\left(\frac{1}{2}-\frac{7}{6}\right)$$

Reduce the fraction \frac{20}{6} to lowest terms by extracting and canceling out 2.

$$\frac{10}{3}-\left(\frac{1}{2}-\frac{7}{6}\right)$$

Least common multiple of 2 and 6 is 6. Convert \frac{1}{2} and \frac{7}{6} to fractions with denominator 6.

$$\frac{10}{3}-\left(\frac{3}{6}-\frac{7}{6}\right)$$

Since \frac{3}{6} and \frac{7}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10}{3}-\frac{3-7}{6}$$

Subtract 7 from 3 to get -4.

$$\frac{10}{3}-\frac{-4}{6}$$

Reduce the fraction \frac{-4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{10}{3}-\left(-\frac{2}{3}\right)$$

The opposite of -\frac{2}{3} is \frac{2}{3}.

$$\frac{10}{3}+\frac{2}{3}$$

Since \frac{10}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{10+2}{3}$$

Add 10 and 2 to get 12.

$$\frac{12}{3}$$

Divide 12 by 3 to get 4.

$$4$$

Factor

$$2^{2}$$