Solve 2-3[1/2-5/3*(3/2-1/3)+5div(frac{2}{5}divfrac{4}{5})]

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

Evaluate

$$-\frac{71}{3}\approx -23.666666667$$

Solution Steps

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

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

Since \frac{9}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 9 to get 7.

$$2-3\left(\frac{1}{2}-\frac{5}{3}\times \frac{7}{6}+\frac{5}{\frac{\frac{2}{5}}{\frac{4}{5}}}\right)$$

Multiply \frac{5}{3} times \frac{7}{6} by multiplying numerator times numerator and denominator times denominator.

$$2-3\left(\frac{1}{2}-\frac{5\times 7}{3\times 6}+\frac{5}{\frac{\frac{2}{5}}{\frac{4}{5}}}\right)$$

Do the multiplications in the fraction \frac{5\times 7}{3\times 6}.

$$2-3\left(\frac{1}{2}-\frac{35}{18}+\frac{5}{\frac{\frac{2}{5}}{\frac{4}{5}}}\right)$$

Least common multiple of 2 and 18 is 18. Convert \frac{1}{2} and \frac{35}{18} to fractions with denominator 18.

$$2-3\left(\frac{9}{18}-\frac{35}{18}+\frac{5}{\frac{\frac{2}{5}}{\frac{4}{5}}}\right)$$

Since \frac{9}{18} and \frac{35}{18} have the same denominator, subtract them by subtracting their numerators.

$$2-3\left(\frac{9-35}{18}+\frac{5}{\frac{\frac{2}{5}}{\frac{4}{5}}}\right)$$

Subtract 35 from 9 to get -26.

$$2-3\left(\frac{-26}{18}+\frac{5}{\frac{\frac{2}{5}}{\frac{4}{5}}}\right)$$

Reduce the fraction \frac{-26}{18} to lowest terms by extracting and canceling out 2.

$$2-3\left(-\frac{13}{9}+\frac{5}{\frac{\frac{2}{5}}{\frac{4}{5}}}\right)$$

Divide 5 by \frac{\frac{2}{5}}{\frac{4}{5}} by multiplying 5 by the reciprocal of \frac{\frac{2}{5}}{\frac{4}{5}}.

$$2-3\left(-\frac{13}{9}+\frac{5\times \frac{4}{5}}{\frac{2}{5}}\right)$$

Cancel out 5 and 5.

$$2-3\left(-\frac{13}{9}+\frac{4}{\frac{2}{5}}\right)$$

Divide 4 by \frac{2}{5} by multiplying 4 by the reciprocal of \frac{2}{5}.

$$2-3\left(-\frac{13}{9}+4\times \frac{5}{2}\right)$$

Express 4\times \frac{5}{2} as a single fraction.

$$2-3\left(-\frac{13}{9}+\frac{4\times 5}{2}\right)$$

Multiply 4 and 5 to get 20.

$$2-3\left(-\frac{13}{9}+\frac{20}{2}\right)$$

Divide 20 by 2 to get 10.

$$2-3\left(-\frac{13}{9}+10\right)$$

Convert 10 to fraction \frac{90}{9}.

$$2-3\left(-\frac{13}{9}+\frac{90}{9}\right)$$

Since -\frac{13}{9} and \frac{90}{9} have the same denominator, add them by adding their numerators.

$$2-3\times \frac{-13+90}{9}$$

Add -13 and 90 to get 77.

$$2-3\times \frac{77}{9}$$

Express 3\times \frac{77}{9} as a single fraction.

$$2-\frac{3\times 77}{9}$$

Multiply 3 and 77 to get 231.

$$2-\frac{231}{9}$$

Reduce the fraction \frac{231}{9} to lowest terms by extracting and canceling out 3.

$$2-\frac{77}{3}$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{6}{3}-\frac{77}{3}$$

Since \frac{6}{3} and \frac{77}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-77}{3}$$

Subtract 77 from 6 to get -71.

$$-\frac{71}{3}$$

Factor

$$-\frac{71}{3} = -23\frac{2}{3} = -23.666666666666668$$