Solve (5/3-3/11):[-8/3+6/7*(-frac{7}{6})^2-frac{12}{11}-(frac{5}{8}-1+frac{5}{4}):(-2+frac{1}{4})]

$$( \frac { 5 } { 3 } - \frac { 3 } { 11 } ) : [ - \frac { 8 } { 3 } + \frac { 6 } { 7 } \cdot ( - \frac { 7 } { 6 } ) ^ { 2 } - \frac { 12 } { 11 } - ( \frac { 5 } { 8 } - 1 + \frac { 5 } { 4 } ) : ( - 2 + \frac { 1 } { 4 } ) ]$$

Evaluate

$$-\frac{2}{3}\approx -0.666666667$$

Solution Steps

Least common multiple of 3 and 11 is 33. Convert \frac{5}{3} and \frac{3}{11} to fractions with denominator 33.

$$\frac{\frac{55}{33}-\frac{9}{33}}{-\frac{8}{3}+\frac{6}{7}\left(-\frac{7}{6}\right)^{2}-\frac{12}{11}-\frac{\frac{5}{8}-1+\frac{5}{4}}{-2+\frac{1}{4}}}$$

Since \frac{55}{33} and \frac{9}{33} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{55-9}{33}}{-\frac{8}{3}+\frac{6}{7}\left(-\frac{7}{6}\right)^{2}-\frac{12}{11}-\frac{\frac{5}{8}-1+\frac{5}{4}}{-2+\frac{1}{4}}}$$

Subtract 9 from 55 to get 46.

$$\frac{\frac{46}{33}}{-\frac{8}{3}+\frac{6}{7}\left(-\frac{7}{6}\right)^{2}-\frac{12}{11}-\frac{\frac{5}{8}-1+\frac{5}{4}}{-2+\frac{1}{4}}}$$

Calculate -\frac{7}{6} to the power of 2 and get \frac{49}{36}.

$$\frac{\frac{46}{33}}{-\frac{8}{3}+\frac{6}{7}\times \frac{49}{36}-\frac{12}{11}-\frac{\frac{5}{8}-1+\frac{5}{4}}{-2+\frac{1}{4}}}$$

Multiply \frac{6}{7} times \frac{49}{36} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{46}{33}}{-\frac{8}{3}+\frac{6\times 49}{7\times 36}-\frac{12}{11}-\frac{\frac{5}{8}-1+\frac{5}{4}}{-2+\frac{1}{4}}}$$

Do the multiplications in the fraction \frac{6\times 49}{7\times 36}.

$$\frac{\frac{46}{33}}{-\frac{8}{3}+\frac{294}{252}-\frac{12}{11}-\frac{\frac{5}{8}-1+\frac{5}{4}}{-2+\frac{1}{4}}}$$

Reduce the fraction \frac{294}{252} to lowest terms by extracting and canceling out 42.

$$\frac{\frac{46}{33}}{-\frac{8}{3}+\frac{7}{6}-\frac{12}{11}-\frac{\frac{5}{8}-1+\frac{5}{4}}{-2+\frac{1}{4}}}$$

Least common multiple of 3 and 6 is 6. Convert -\frac{8}{3} and \frac{7}{6} to fractions with denominator 6.

$$\frac{\frac{46}{33}}{-\frac{16}{6}+\frac{7}{6}-\frac{12}{11}-\frac{\frac{5}{8}-1+\frac{5}{4}}{-2+\frac{1}{4}}}$$

Since -\frac{16}{6} and \frac{7}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{46}{33}}{\frac{-16+7}{6}-\frac{12}{11}-\frac{\frac{5}{8}-1+\frac{5}{4}}{-2+\frac{1}{4}}}$$

Add -16 and 7 to get -9.

$$\frac{\frac{46}{33}}{\frac{-9}{6}-\frac{12}{11}-\frac{\frac{5}{8}-1+\frac{5}{4}}{-2+\frac{1}{4}}}$$

Reduce the fraction \frac{-9}{6} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{46}{33}}{-\frac{3}{2}-\frac{12}{11}-\frac{\frac{5}{8}-1+\frac{5}{4}}{-2+\frac{1}{4}}}$$

Least common multiple of 2 and 11 is 22. Convert -\frac{3}{2} and \frac{12}{11} to fractions with denominator 22.

$$\frac{\frac{46}{33}}{-\frac{33}{22}-\frac{24}{22}-\frac{\frac{5}{8}-1+\frac{5}{4}}{-2+\frac{1}{4}}}$$

Since -\frac{33}{22} and \frac{24}{22} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{46}{33}}{\frac{-33-24}{22}-\frac{\frac{5}{8}-1+\frac{5}{4}}{-2+\frac{1}{4}}}$$

Subtract 24 from -33 to get -57.

$$\frac{\frac{46}{33}}{-\frac{57}{22}-\frac{\frac{5}{8}-1+\frac{5}{4}}{-2+\frac{1}{4}}}$$

Convert 1 to fraction \frac{8}{8}.

$$\frac{\frac{46}{33}}{-\frac{57}{22}-\frac{\frac{5}{8}-\frac{8}{8}+\frac{5}{4}}{-2+\frac{1}{4}}}$$

Since \frac{5}{8} and \frac{8}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{46}{33}}{-\frac{57}{22}-\frac{\frac{5-8}{8}+\frac{5}{4}}{-2+\frac{1}{4}}}$$

Subtract 8 from 5 to get -3.

$$\frac{\frac{46}{33}}{-\frac{57}{22}-\frac{-\frac{3}{8}+\frac{5}{4}}{-2+\frac{1}{4}}}$$

Least common multiple of 8 and 4 is 8. Convert -\frac{3}{8} and \frac{5}{4} to fractions with denominator 8.

$$\frac{\frac{46}{33}}{-\frac{57}{22}-\frac{-\frac{3}{8}+\frac{10}{8}}{-2+\frac{1}{4}}}$$

Since -\frac{3}{8} and \frac{10}{8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{46}{33}}{-\frac{57}{22}-\frac{\frac{-3+10}{8}}{-2+\frac{1}{4}}}$$

Add -3 and 10 to get 7.

$$\frac{\frac{46}{33}}{-\frac{57}{22}-\frac{\frac{7}{8}}{-2+\frac{1}{4}}}$$

Convert -2 to fraction -\frac{8}{4}.

$$\frac{\frac{46}{33}}{-\frac{57}{22}-\frac{\frac{7}{8}}{-\frac{8}{4}+\frac{1}{4}}}$$

Since -\frac{8}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{46}{33}}{-\frac{57}{22}-\frac{\frac{7}{8}}{\frac{-8+1}{4}}}$$

Add -8 and 1 to get -7.

$$\frac{\frac{46}{33}}{-\frac{57}{22}-\frac{\frac{7}{8}}{-\frac{7}{4}}}$$

Divide \frac{7}{8} by -\frac{7}{4} by multiplying \frac{7}{8} by the reciprocal of -\frac{7}{4}.

$$\frac{\frac{46}{33}}{-\frac{57}{22}-\frac{7}{8}\left(-\frac{4}{7}\right)}$$

Multiply \frac{7}{8} times -\frac{4}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{46}{33}}{-\frac{57}{22}-\frac{7\left(-4\right)}{8\times 7}}$$

Cancel out 7 in both numerator and denominator.

$$\frac{\frac{46}{33}}{-\frac{57}{22}-\frac{-4}{8}}$$

Reduce the fraction \frac{-4}{8} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{46}{33}}{-\frac{57}{22}-\left(-\frac{1}{2}\right)}$$

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$\frac{\frac{46}{33}}{-\frac{57}{22}+\frac{1}{2}}$$

Least common multiple of 22 and 2 is 22. Convert -\frac{57}{22} and \frac{1}{2} to fractions with denominator 22.

$$\frac{\frac{46}{33}}{-\frac{57}{22}+\frac{11}{22}}$$

Since -\frac{57}{22} and \frac{11}{22} have the same denominator, add them by adding their numerators.

$$\frac{\frac{46}{33}}{\frac{-57+11}{22}}$$

Add -57 and 11 to get -46.

$$\frac{\frac{46}{33}}{\frac{-46}{22}}$$

Reduce the fraction \frac{-46}{22} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{46}{33}}{-\frac{23}{11}}$$

Divide \frac{46}{33} by -\frac{23}{11} by multiplying \frac{46}{33} by the reciprocal of -\frac{23}{11}.

$$\frac{46}{33}\left(-\frac{11}{23}\right)$$

Multiply \frac{46}{33} times -\frac{11}{23} by multiplying numerator times numerator and denominator times denominator.

$$\frac{46\left(-11\right)}{33\times 23}$$

Do the multiplications in the fraction \frac{46\left(-11\right)}{33\times 23}.

$$\frac{-506}{759}$$

Reduce the fraction \frac{-506}{759} to lowest terms by extracting and canceling out 253.

$$-\frac{2}{3}$$

Factor

$$-\frac{2}{3} = -0.6666666666666666$$