Solve (6/5-(-3/5+1/6+2/15)*(-frac{5}{4})]*(frac{2}{3}-frac{5}{6}+1)

$$( \frac { 6 } { 5 } - ( - \frac { 3 } { 5 } + \frac { 1 } { 6 } + \frac { 2 } { 15 } ) \cdot ( - \frac { 5 } { 4 } ) ] \cdot ( \frac { 2 } { 3 } - \frac { 5 } { 6 } + 1 )$$

Evaluate

$$\frac{11}{16}=0.6875$$

Solution Steps

Least common multiple of 5 and 6 is 30. Convert -\frac{3}{5} and \frac{1}{6} to fractions with denominator 30.

$$\left(\frac{6}{5}-\left(-\frac{18}{30}+\frac{5}{30}+\frac{2}{15}\right)\left(-\frac{5}{4}\right)\right)\left(\frac{2}{3}-\frac{5}{6}+1\right)$$

Since -\frac{18}{30} and \frac{5}{30} have the same denominator, add them by adding their numerators.

$$\left(\frac{6}{5}-\left(\frac{-18+5}{30}+\frac{2}{15}\right)\left(-\frac{5}{4}\right)\right)\left(\frac{2}{3}-\frac{5}{6}+1\right)$$

Add -18 and 5 to get -13.

$$\left(\frac{6}{5}-\left(-\frac{13}{30}+\frac{2}{15}\right)\left(-\frac{5}{4}\right)\right)\left(\frac{2}{3}-\frac{5}{6}+1\right)$$

Least common multiple of 30 and 15 is 30. Convert -\frac{13}{30} and \frac{2}{15} to fractions with denominator 30.

$$\left(\frac{6}{5}-\left(-\frac{13}{30}+\frac{4}{30}\right)\left(-\frac{5}{4}\right)\right)\left(\frac{2}{3}-\frac{5}{6}+1\right)$$

Since -\frac{13}{30} and \frac{4}{30} have the same denominator, add them by adding their numerators.

$$\left(\frac{6}{5}-\frac{-13+4}{30}\left(-\frac{5}{4}\right)\right)\left(\frac{2}{3}-\frac{5}{6}+1\right)$$

Add -13 and 4 to get -9.

$$\left(\frac{6}{5}-\frac{-9}{30}\left(-\frac{5}{4}\right)\right)\left(\frac{2}{3}-\frac{5}{6}+1\right)$$

Reduce the fraction \frac{-9}{30} to lowest terms by extracting and canceling out 3.

$$\left(\frac{6}{5}-\left(-\frac{3}{10}\left(-\frac{5}{4}\right)\right)\right)\left(\frac{2}{3}-\frac{5}{6}+1\right)$$

Multiply -\frac{3}{10} times -\frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\left(\frac{6}{5}-\frac{-3\left(-5\right)}{10\times 4}\right)\left(\frac{2}{3}-\frac{5}{6}+1\right)$$

Do the multiplications in the fraction \frac{-3\left(-5\right)}{10\times 4}.

$$\left(\frac{6}{5}-\frac{15}{40}\right)\left(\frac{2}{3}-\frac{5}{6}+1\right)$$

Reduce the fraction \frac{15}{40} to lowest terms by extracting and canceling out 5.

$$\left(\frac{6}{5}-\frac{3}{8}\right)\left(\frac{2}{3}-\frac{5}{6}+1\right)$$

Least common multiple of 5 and 8 is 40. Convert \frac{6}{5} and \frac{3}{8} to fractions with denominator 40.

$$\left(\frac{48}{40}-\frac{15}{40}\right)\left(\frac{2}{3}-\frac{5}{6}+1\right)$$

Since \frac{48}{40} and \frac{15}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{48-15}{40}\left(\frac{2}{3}-\frac{5}{6}+1\right)$$

Subtract 15 from 48 to get 33.

$$\frac{33}{40}\left(\frac{2}{3}-\frac{5}{6}+1\right)$$

Least common multiple of 3 and 6 is 6. Convert \frac{2}{3} and \frac{5}{6} to fractions with denominator 6.

$$\frac{33}{40}\left(\frac{4}{6}-\frac{5}{6}+1\right)$$

Since \frac{4}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{33}{40}\left(\frac{4-5}{6}+1\right)$$

Subtract 5 from 4 to get -1.

$$\frac{33}{40}\left(-\frac{1}{6}+1\right)$$

Convert 1 to fraction \frac{6}{6}.

$$\frac{33}{40}\left(-\frac{1}{6}+\frac{6}{6}\right)$$

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

$$\frac{33}{40}\times \frac{-1+6}{6}$$

Add -1 and 6 to get 5.

$$\frac{33}{40}\times \frac{5}{6}$$

Multiply \frac{33}{40} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{33\times 5}{40\times 6}$$

Do the multiplications in the fraction \frac{33\times 5}{40\times 6}.

$$\frac{165}{240}$$

Reduce the fraction \frac{165}{240} to lowest terms by extracting and canceling out 15.

$$\frac{11}{16}$$

Factor

$$\frac{11}{2 ^ {4}} = 0.6875$$