Solve 5/2left(-3/5+4/5-3/10-frac{4}{5}right)

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

Evaluate

$$-\frac{9}{4}=-2.25$$

Solution Steps

Since -\frac{3}{5} and \frac{4}{5} have the same denominator, add them by adding their numerators.

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

Add -3 and 4 to get 1.

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

Least common multiple of 5 and 10 is 10. Convert \frac{1}{5} and \frac{3}{10} to fractions with denominator 10.

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

Since \frac{2}{10} and \frac{3}{10} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 3 from 2 to get -1.

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

Least common multiple of 10 and 5 is 10. Convert -\frac{1}{10} and \frac{4}{5} to fractions with denominator 10.

$$\frac{5}{2}\left(-\frac{1}{10}-\frac{8}{10}\right)$$

Since -\frac{1}{10} and \frac{8}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{2}\times \frac{-1-8}{10}$$

Subtract 8 from -1 to get -9.

$$\frac{5}{2}\left(-\frac{9}{10}\right)$$

Multiply \frac{5}{2} times -\frac{9}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\left(-9\right)}{2\times 10}$$

Do the multiplications in the fraction \frac{5\left(-9\right)}{2\times 10}.

$$\frac{-45}{20}$$

Reduce the fraction \frac{-45}{20} to lowest terms by extracting and canceling out 5.

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

Factor

$$-\frac{9}{4} = -2\frac{1}{4} = -2.25$$