Solve {[5/3-(-2/5)]-4/3div1/2}*(-frac{3}{5}+frac{7}{2})

$$\{ [ \frac { 5 } { 3 } - ( - \frac { 2 } { 5 } ) ] - \frac { 4 } { 3 } \div \frac { 1 } { 2 } \} \times ( - \frac { 3 } { 5 } + \frac { 7 } { 2 } )$$

Evaluate

$$-\frac{87}{50}=-1.74$$

Solution Steps

The opposite of -\frac{2}{5} is \frac{2}{5}.

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

Least common multiple of 3 and 5 is 15. Convert \frac{5}{3} and \frac{2}{5} to fractions with denominator 15.

$$\left(\frac{25}{15}+\frac{6}{15}-\frac{\frac{4}{3}}{\frac{1}{2}}\right)\left(-\frac{3}{5}+\frac{7}{2}\right)$$

Since \frac{25}{15} and \frac{6}{15} have the same denominator, add them by adding their numerators.

$$\left(\frac{25+6}{15}-\frac{\frac{4}{3}}{\frac{1}{2}}\right)\left(-\frac{3}{5}+\frac{7}{2}\right)$$

Add 25 and 6 to get 31.

$$\left(\frac{31}{15}-\frac{\frac{4}{3}}{\frac{1}{2}}\right)\left(-\frac{3}{5}+\frac{7}{2}\right)$$

Divide \frac{4}{3} by \frac{1}{2} by multiplying \frac{4}{3} by the reciprocal of \frac{1}{2}.

$$\left(\frac{31}{15}-\frac{4}{3}\times 2\right)\left(-\frac{3}{5}+\frac{7}{2}\right)$$

Express \frac{4}{3}\times 2 as a single fraction.

$$\left(\frac{31}{15}-\frac{4\times 2}{3}\right)\left(-\frac{3}{5}+\frac{7}{2}\right)$$

Multiply 4 and 2 to get 8.

$$\left(\frac{31}{15}-\frac{8}{3}\right)\left(-\frac{3}{5}+\frac{7}{2}\right)$$

Least common multiple of 15 and 3 is 15. Convert \frac{31}{15} and \frac{8}{3} to fractions with denominator 15.

$$\left(\frac{31}{15}-\frac{40}{15}\right)\left(-\frac{3}{5}+\frac{7}{2}\right)$$

Since \frac{31}{15} and \frac{40}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{31-40}{15}\left(-\frac{3}{5}+\frac{7}{2}\right)$$

Subtract 40 from 31 to get -9.

$$\frac{-9}{15}\left(-\frac{3}{5}+\frac{7}{2}\right)$$

Reduce the fraction \frac{-9}{15} to lowest terms by extracting and canceling out 3.

$$-\frac{3}{5}\left(-\frac{3}{5}+\frac{7}{2}\right)$$

Least common multiple of 5 and 2 is 10. Convert -\frac{3}{5} and \frac{7}{2} to fractions with denominator 10.

$$-\frac{3}{5}\left(-\frac{6}{10}+\frac{35}{10}\right)$$

Since -\frac{6}{10} and \frac{35}{10} have the same denominator, add them by adding their numerators.

$$-\frac{3}{5}\times \frac{-6+35}{10}$$

Add -6 and 35 to get 29.

$$-\frac{3}{5}\times \frac{29}{10}$$

Multiply -\frac{3}{5} times \frac{29}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3\times 29}{5\times 10}$$

Do the multiplications in the fraction \frac{-3\times 29}{5\times 10}.

$$\frac{-87}{50}$$

Fraction \frac{-87}{50} can be rewritten as -\frac{87}{50} by extracting the negative sign.

$$-\frac{87}{50}$$

Factor

$$-\frac{87}{50} = -1\frac{37}{50} = -1.74$$