Solve (1/6+2/3)(1-2/5)quad|(17/22+1)div(2-frac{9}{11})

$$( \frac { 1 } { 6 } + \frac { 2 } { 3 } ) ( 1 - \frac { 2 } { 5 } ) \quad | ( \frac { 17 } { 22 } + 1 ) \div ( 2 - \frac { 9 } { 11 } )$$

Evaluate

$$\frac{3}{4}=0.75$$

Solution Steps

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

$$\left(\frac{1}{6}+\frac{4}{6}\right)\left(1-\frac{2}{5}\right)|\frac{\frac{17}{22}+1}{2-\frac{9}{11}}|$$

Since \frac{1}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{1+4}{6}\left(1-\frac{2}{5}\right)|\frac{\frac{17}{22}+1}{2-\frac{9}{11}}|$$

Add 1 and 4 to get 5.

$$\frac{5}{6}\left(1-\frac{2}{5}\right)|\frac{\frac{17}{22}+1}{2-\frac{9}{11}}|$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{5}{6}\left(\frac{5}{5}-\frac{2}{5}\right)|\frac{\frac{17}{22}+1}{2-\frac{9}{11}}|$$

Since \frac{5}{5} and \frac{2}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{6}\times \frac{5-2}{5}|\frac{\frac{17}{22}+1}{2-\frac{9}{11}}|$$

Subtract 2 from 5 to get 3.

$$\frac{5}{6}\times \frac{3}{5}|\frac{\frac{17}{22}+1}{2-\frac{9}{11}}|$$

Multiply \frac{5}{6} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 3}{6\times 5}|\frac{\frac{17}{22}+1}{2-\frac{9}{11}}|$$

Cancel out 5 in both numerator and denominator.

$$\frac{3}{6}|\frac{\frac{17}{22}+1}{2-\frac{9}{11}}|$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{1}{2}|\frac{\frac{17}{22}+1}{2-\frac{9}{11}}|$$

Convert 1 to fraction \frac{22}{22}.

$$\frac{1}{2}|\frac{\frac{17}{22}+\frac{22}{22}}{2-\frac{9}{11}}|$$

Since \frac{17}{22} and \frac{22}{22} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}|\frac{\frac{17+22}{22}}{2-\frac{9}{11}}|$$

Add 17 and 22 to get 39.

$$\frac{1}{2}|\frac{\frac{39}{22}}{2-\frac{9}{11}}|$$

Convert 2 to fraction \frac{22}{11}.

$$\frac{1}{2}|\frac{\frac{39}{22}}{\frac{22}{11}-\frac{9}{11}}|$$

Since \frac{22}{11} and \frac{9}{11} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}|\frac{\frac{39}{22}}{\frac{22-9}{11}}|$$

Subtract 9 from 22 to get 13.

$$\frac{1}{2}|\frac{\frac{39}{22}}{\frac{13}{11}}|$$

Divide \frac{39}{22} by \frac{13}{11} by multiplying \frac{39}{22} by the reciprocal of \frac{13}{11}.

$$\frac{1}{2}|\frac{39}{22}\times \frac{11}{13}|$$

Multiply \frac{39}{22} times \frac{11}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}|\frac{39\times 11}{22\times 13}|$$

Do the multiplications in the fraction \frac{39\times 11}{22\times 13}.

$$\frac{1}{2}|\frac{429}{286}|$$

Reduce the fraction \frac{429}{286} to lowest terms by extracting and canceling out 143.

$$\frac{1}{2}|\frac{3}{2}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{3}{2} is \frac{3}{2}.

$$\frac{1}{2}\times \frac{3}{2}$$

Multiply \frac{1}{2} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 3}{2\times 2}$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 2}.

$$\frac{3}{4}$$

Factor

$$\frac{3}{2 ^ {2}} = 0.75$$