Solve -3/4(2/9-2/6)+[1/2-(frac{2}{5}+frac{2}{4})]-(frac{3}{2}-frac{3}{4})

$$- \frac { 3 } { 4 } ( \frac { 2 } { 9 } - \frac { 2 } { 6 } ) + [ \frac { 1 } { 2 } - ( \frac { 2 } { 5 } + \frac { 2 } { 4 } ) ] - ( \frac { 3 } { 2 } - \frac { 3 } { 4 } )$$

Evaluate

$$-\frac{16}{15}\approx -1.066666667$$

Solution Steps

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

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

Least common multiple of 9 and 3 is 9. Convert \frac{2}{9} and \frac{1}{3} to fractions with denominator 9.

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

Since \frac{2}{9} and \frac{3}{9} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 3 from 2 to get -1.

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

Multiply -\frac{3}{4} times -\frac{1}{9} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-3\left(-1\right)}{4\times 9}.

$$\frac{3}{36}+\frac{1}{2}-\left(\frac{2}{5}+\frac{2}{4}\right)-\left(\frac{3}{2}-\frac{3}{4}\right)$$

Reduce the fraction \frac{3}{36} to lowest terms by extracting and canceling out 3.

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

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

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

Least common multiple of 5 and 2 is 10. Convert \frac{2}{5} and \frac{1}{2} to fractions with denominator 10.

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

Since \frac{4}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

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

Add 4 and 5 to get 9.

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

Least common multiple of 2 and 10 is 10. Convert \frac{1}{2} and \frac{9}{10} to fractions with denominator 10.

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

Since \frac{5}{10} and \frac{9}{10} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 9 from 5 to get -4.

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

Reduce the fraction \frac{-4}{10} to lowest terms by extracting and canceling out 2.

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

Least common multiple of 12 and 5 is 60. Convert \frac{1}{12} and \frac{2}{5} to fractions with denominator 60.

$$\frac{5}{60}-\frac{24}{60}-\left(\frac{3}{2}-\frac{3}{4}\right)$$

Since \frac{5}{60} and \frac{24}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-24}{60}-\left(\frac{3}{2}-\frac{3}{4}\right)$$

Subtract 24 from 5 to get -19.

$$-\frac{19}{60}-\left(\frac{3}{2}-\frac{3}{4}\right)$$

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

$$-\frac{19}{60}-\left(\frac{6}{4}-\frac{3}{4}\right)$$

Since \frac{6}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{19}{60}-\frac{6-3}{4}$$

Subtract 3 from 6 to get 3.

$$-\frac{19}{60}-\frac{3}{4}$$

Least common multiple of 60 and 4 is 60. Convert -\frac{19}{60} and \frac{3}{4} to fractions with denominator 60.

$$-\frac{19}{60}-\frac{45}{60}$$

Since -\frac{19}{60} and \frac{45}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-19-45}{60}$$

Subtract 45 from -19 to get -64.

$$\frac{-64}{60}$$

Reduce the fraction \frac{-64}{60} to lowest terms by extracting and canceling out 4.

$$-\frac{16}{15}$$

Factor

$$-\frac{16}{15} = -1\frac{1}{15} = -1.0666666666666667$$