Solve 5+{-1/2-2-[3/4-5/6+(-1+1/3)]+frac{5}{4}}+1

$$5 + \{ - \frac { 1 } { 2 } - 2 - [ \frac { 3 } { 4 } - \frac { 5 } { 6 } + ( - 1 + \frac { 1 } { 3 } ) ] + \frac { 5 } { 4 } \} + 1$$

Evaluate

$$\frac{11}{2}=5.5$$

Solution Steps

Convert 2 to fraction \frac{4}{2}.

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

Since -\frac{1}{2} and \frac{4}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 4 from -1 to get -5.

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

Least common multiple of 4 and 6 is 12. Convert \frac{3}{4} and \frac{5}{6} to fractions with denominator 12.

$$5+-\frac{5}{2}-\left(\frac{9}{12}-\frac{10}{12}-1+\frac{1}{3}\right)+\frac{5}{4}+1$$

Since \frac{9}{12} and \frac{10}{12} have the same denominator, subtract them by subtracting their numerators.

$$5+-\frac{5}{2}-\left(\frac{9-10}{12}-1+\frac{1}{3}\right)+\frac{5}{4}+1$$

Subtract 10 from 9 to get -1.

$$5+-\frac{5}{2}-\left(-\frac{1}{12}-1+\frac{1}{3}\right)+\frac{5}{4}+1$$

Convert 1 to fraction \frac{12}{12}.

$$5+-\frac{5}{2}-\left(-\frac{1}{12}-\frac{12}{12}+\frac{1}{3}\right)+\frac{5}{4}+1$$

Since -\frac{1}{12} and \frac{12}{12} have the same denominator, subtract them by subtracting their numerators.

$$5+-\frac{5}{2}-\left(\frac{-1-12}{12}+\frac{1}{3}\right)+\frac{5}{4}+1$$

Subtract 12 from -1 to get -13.

$$5+-\frac{5}{2}-\left(-\frac{13}{12}+\frac{1}{3}\right)+\frac{5}{4}+1$$

Least common multiple of 12 and 3 is 12. Convert -\frac{13}{12} and \frac{1}{3} to fractions with denominator 12.

$$5+-\frac{5}{2}-\left(-\frac{13}{12}+\frac{4}{12}\right)+\frac{5}{4}+1$$

Since -\frac{13}{12} and \frac{4}{12} have the same denominator, add them by adding their numerators.

$$5-\frac{5}{2}-\frac{-13+4}{12}+\frac{5}{4}+1$$

Add -13 and 4 to get -9.

$$5-\frac{5}{2}-\frac{-9}{12}+\frac{5}{4}+1$$

Reduce the fraction \frac{-9}{12} to lowest terms by extracting and canceling out 3.

$$5+-\frac{5}{2}-\left(-\frac{3}{4}\right)+\frac{5}{4}+1$$

The opposite of -\frac{3}{4} is \frac{3}{4}.

$$5-\frac{5}{2}+\frac{3}{4}+\frac{5}{4}+1$$

Least common multiple of 2 and 4 is 4. Convert -\frac{5}{2} and \frac{3}{4} to fractions with denominator 4.

$$5-\frac{10}{4}+\frac{3}{4}+\frac{5}{4}+1$$

Since -\frac{10}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$5+\frac{-10+3}{4}+\frac{5}{4}+1$$

Add -10 and 3 to get -7.

$$5-\frac{7}{4}+\frac{5}{4}+1$$

Convert 5 to fraction \frac{20}{4}.

$$\frac{20}{4}-\frac{7}{4}+\frac{5}{4}+1$$

Since \frac{20}{4} and \frac{7}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20-7}{4}+\frac{5}{4}+1$$

Subtract 7 from 20 to get 13.

$$\frac{13}{4}+\frac{5}{4}+1$$

Since \frac{13}{4} and \frac{5}{4} have the same denominator, add them by adding their numerators.

$$\frac{13+5}{4}+1$$

Add 13 and 5 to get 18.

$$\frac{18}{4}+1$$

Reduce the fraction \frac{18}{4} to lowest terms by extracting and canceling out 2.

$$\frac{9}{2}+1$$

Convert 1 to fraction \frac{2}{2}.

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

Since \frac{9}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

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

Add 9 and 2 to get 11.

$$\frac{11}{2}$$

Factor

$$\frac{11}{2} = 5\frac{1}{2} = 5.5$$