Solve +[1/4+(1-1/3)-1/6]*(11/3-frac{6}{3})}+(1+frac{2}{5}-frac{1}{3})*[(2-frac{1}{3}):(frac{3}{5}+1)]

$$+ [ \frac { 1 } { 4 } + ( 1 - \frac { 1 } { 3 } ) - \frac { 1 } { 6 } ] \cdot ( \frac { 11 } { 3 } - \frac { 6 } { 3 } ) \} + ( 1 + \frac { 2 } { 5 } - \frac { 1 } { 3 } ) \cdot [ ( 2 - \frac { 1 } { 3 } ) : ( \frac { 3 } { 5 } + 1 ) ]$$

Evaluate

$$\frac{5}{4}=1.25$$

Solution Steps

Convert 1 to fraction \frac{4}{4}.

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

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

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

Add 1 and 4 to get 5.

$$\left(\frac{5}{4}-\frac{1}{3}-\frac{1}{6}\right)\left(\frac{11}{3}-\frac{6}{3}\right)$$

Least common multiple of 4 and 3 is 12. Convert \frac{5}{4} and \frac{1}{3} to fractions with denominator 12.

$$\left(\frac{15}{12}-\frac{4}{12}-\frac{1}{6}\right)\left(\frac{11}{3}-\frac{6}{3}\right)$$

Since \frac{15}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{15-4}{12}-\frac{1}{6}\right)\left(\frac{11}{3}-\frac{6}{3}\right)$$

Subtract 4 from 15 to get 11.

$$\left(\frac{11}{12}-\frac{1}{6}\right)\left(\frac{11}{3}-\frac{6}{3}\right)$$

Least common multiple of 12 and 6 is 12. Convert \frac{11}{12} and \frac{1}{6} to fractions with denominator 12.

$$\left(\frac{11}{12}-\frac{2}{12}\right)\left(\frac{11}{3}-\frac{6}{3}\right)$$

Since \frac{11}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11-2}{12}\left(\frac{11}{3}-\frac{6}{3}\right)$$

Subtract 2 from 11 to get 9.

$$\frac{9}{12}\left(\frac{11}{3}-\frac{6}{3}\right)$$

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

$$\frac{3}{4}\left(\frac{11}{3}-\frac{6}{3}\right)$$

Since \frac{11}{3} and \frac{6}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{4}\times \frac{11-6}{3}$$

Subtract 6 from 11 to get 5.

$$\frac{3}{4}\times \frac{5}{3}$$

Multiply \frac{3}{4} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 5}{4\times 3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{5}{4}$$

Factor

$$\frac{5}{2 ^ {2}} = 1\frac{1}{4} = 1.25$$