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

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

Evaluate

$$-\frac{13}{3}\approx -4.333333333$$

Solution Steps

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

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

Since \frac{10}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 5 from 10 to get 5.

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

Multiply \frac{3}{4} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{3\times 5}{4\times 6}.

$$\frac{2}{3}\left(-4+\frac{15}{24}-\frac{3}{4}\left(\frac{5}{2}-1\right)\right)-\frac{4}{3}$$

Reduce the fraction \frac{15}{24} to lowest terms by extracting and canceling out 3.

$$\frac{2}{3}\left(-4+\frac{5}{8}-\frac{3}{4}\left(\frac{5}{2}-1\right)\right)-\frac{4}{3}$$

Convert -4 to fraction -\frac{32}{8}.

$$\frac{2}{3}\left(-\frac{32}{8}+\frac{5}{8}-\frac{3}{4}\left(\frac{5}{2}-1\right)\right)-\frac{4}{3}$$

Since -\frac{32}{8} and \frac{5}{8} have the same denominator, add them by adding their numerators.

$$\frac{2}{3}\left(\frac{-32+5}{8}-\frac{3}{4}\left(\frac{5}{2}-1\right)\right)-\frac{4}{3}$$

Add -32 and 5 to get -27.

$$\frac{2}{3}\left(-\frac{27}{8}-\frac{3}{4}\left(\frac{5}{2}-1\right)\right)-\frac{4}{3}$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{2}{3}\left(-\frac{27}{8}-\frac{3}{4}\left(\frac{5}{2}-\frac{2}{2}\right)\right)-\frac{4}{3}$$

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

$$\frac{2}{3}\left(-\frac{27}{8}-\frac{3}{4}\times \frac{5-2}{2}\right)-\frac{4}{3}$$

Subtract 2 from 5 to get 3.

$$\frac{2}{3}\left(-\frac{27}{8}-\frac{3}{4}\times \frac{3}{2}\right)-\frac{4}{3}$$

Multiply \frac{3}{4} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}\left(-\frac{27}{8}-\frac{3\times 3}{4\times 2}\right)-\frac{4}{3}$$

Do the multiplications in the fraction \frac{3\times 3}{4\times 2}.

$$\frac{2}{3}\left(-\frac{27}{8}-\frac{9}{8}\right)-\frac{4}{3}$$

Since -\frac{27}{8} and \frac{9}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{3}\times \frac{-27-9}{8}-\frac{4}{3}$$

Subtract 9 from -27 to get -36.

$$\frac{2}{3}\times \frac{-36}{8}-\frac{4}{3}$$

Reduce the fraction \frac{-36}{8} to lowest terms by extracting and canceling out 4.

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

Multiply \frac{2}{3} times -\frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2 in both numerator and denominator.

$$\frac{-9}{3}-\frac{4}{3}$$

Divide -9 by 3 to get -3.

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

Convert -3 to fraction -\frac{9}{3}.

$$-\frac{9}{3}-\frac{4}{3}$$

Since -\frac{9}{3} and \frac{4}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-9-4}{3}$$

Subtract 4 from -9 to get -13.

$$-\frac{13}{3}$$

Factor

$$-\frac{13}{3} = -4\frac{1}{3} = -4.333333333333333$$