Solve (9/4+7/2)*[2/5-(1/2+frac{4}{5})]

$$( \frac { 9 } { 4 } + \frac { 7 } { 2 } ) \cdot [ \frac { 2 } { 5 } - ( \frac { 1 } { 2 } + \frac { 4 } { 5 } ) ]$$

Evaluate

$$-\frac{207}{40}=-5.175$$

Solution Steps

Least common multiple of 4 and 2 is 4. Convert \frac{9}{4} and \frac{7}{2} to fractions with denominator 4.

$$\left(\frac{9}{4}+\frac{14}{4}\right)\left(\frac{2}{5}-\left(\frac{1}{2}+\frac{4}{5}\right)\right)$$

Since \frac{9}{4} and \frac{14}{4} have the same denominator, add them by adding their numerators.

$$\frac{9+14}{4}\left(\frac{2}{5}-\left(\frac{1}{2}+\frac{4}{5}\right)\right)$$

Add 9 and 14 to get 23.

$$\frac{23}{4}\left(\frac{2}{5}-\left(\frac{1}{2}+\frac{4}{5}\right)\right)$$

Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{4}{5} to fractions with denominator 10.

$$\frac{23}{4}\left(\frac{2}{5}-\left(\frac{5}{10}+\frac{8}{10}\right)\right)$$

Since \frac{5}{10} and \frac{8}{10} have the same denominator, add them by adding their numerators.

$$\frac{23}{4}\left(\frac{2}{5}-\frac{5+8}{10}\right)$$

Add 5 and 8 to get 13.

$$\frac{23}{4}\left(\frac{2}{5}-\frac{13}{10}\right)$$

Least common multiple of 5 and 10 is 10. Convert \frac{2}{5} and \frac{13}{10} to fractions with denominator 10.

$$\frac{23}{4}\left(\frac{4}{10}-\frac{13}{10}\right)$$

Since \frac{4}{10} and \frac{13}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{23}{4}\times \frac{4-13}{10}$$

Subtract 13 from 4 to get -9.

$$\frac{23}{4}\left(-\frac{9}{10}\right)$$

Multiply \frac{23}{4} times -\frac{9}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{23\left(-9\right)}{4\times 10}$$

Do the multiplications in the fraction \frac{23\left(-9\right)}{4\times 10}.

$$\frac{-207}{40}$$

Fraction \frac{-207}{40} can be rewritten as -\frac{207}{40} by extracting the negative sign.

$$-\frac{207}{40}$$

Factor

$$-\frac{207}{40} = -5\frac{7}{40} = -5.175$$