Solve -12/5left(4/3-2/5+5/2-frac{4}{3}right)

$$- \frac{ 12 }{ 5 } \left( \frac{ 4 }{ 3 } - \frac{ 2 }{ 5 } + \frac{ 5 }{ 2 } - \frac{ 4 }{ 3 } \right)$$

Evaluate

$$-\frac{126}{25}=-5.04$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{4}{3} and \frac{2}{5} to fractions with denominator 15.

$$-\frac{12}{5}\left(\frac{20}{15}-\frac{6}{15}+\frac{5}{2}-\frac{4}{3}\right)$$

Since \frac{20}{15} and \frac{6}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{12}{5}\left(\frac{20-6}{15}+\frac{5}{2}-\frac{4}{3}\right)$$

Subtract 6 from 20 to get 14.

$$-\frac{12}{5}\left(\frac{14}{15}+\frac{5}{2}-\frac{4}{3}\right)$$

Least common multiple of 15 and 2 is 30. Convert \frac{14}{15} and \frac{5}{2} to fractions with denominator 30.

$$-\frac{12}{5}\left(\frac{28}{30}+\frac{75}{30}-\frac{4}{3}\right)$$

Since \frac{28}{30} and \frac{75}{30} have the same denominator, add them by adding their numerators.

$$-\frac{12}{5}\left(\frac{28+75}{30}-\frac{4}{3}\right)$$

Add 28 and 75 to get 103.

$$-\frac{12}{5}\left(\frac{103}{30}-\frac{4}{3}\right)$$

Least common multiple of 30 and 3 is 30. Convert \frac{103}{30} and \frac{4}{3} to fractions with denominator 30.

$$-\frac{12}{5}\left(\frac{103}{30}-\frac{40}{30}\right)$$

Since \frac{103}{30} and \frac{40}{30} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{12}{5}\times \frac{103-40}{30}$$

Subtract 40 from 103 to get 63.

$$-\frac{12}{5}\times \frac{63}{30}$$

Reduce the fraction \frac{63}{30} to lowest terms by extracting and canceling out 3.

$$-\frac{12}{5}\times \frac{21}{10}$$

Multiply -\frac{12}{5} times \frac{21}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-12\times 21}{5\times 10}$$

Do the multiplications in the fraction \frac{-12\times 21}{5\times 10}.

$$\frac{-252}{50}$$

Reduce the fraction \frac{-252}{50} to lowest terms by extracting and canceling out 2.

$$-\frac{126}{25}$$

Factor

$$-\frac{126}{25} = -5\frac{1}{25} = -5.04$$