Solve [3/4div(-5/2)]-[(31/2)(-23/5)]

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

Evaluate

$$\frac{44}{5}=8.8$$

Solution Steps

Divide \frac{3}{4} by -\frac{5}{2} by multiplying \frac{3}{4} by the reciprocal of -\frac{5}{2}.

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

Multiply \frac{3}{4} times -\frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{3\left(-2\right)}{4\times 5}.

$$\frac{-6}{20}-\frac{3\times 2+1}{2}\left(-\frac{2\times 5+3}{5}\right)$$

Reduce the fraction \frac{-6}{20} to lowest terms by extracting and canceling out 2.

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

Multiply 3 and 2 to get 6.

$$-\frac{3}{10}-\frac{6+1}{2}\left(-\frac{2\times 5+3}{5}\right)$$

Add 6 and 1 to get 7.

$$-\frac{3}{10}-\frac{7}{2}\left(-\frac{2\times 5+3}{5}\right)$$

Multiply 2 and 5 to get 10.

$$-\frac{3}{10}-\frac{7}{2}\left(-\frac{10+3}{5}\right)$$

Add 10 and 3 to get 13.

$$-\frac{3}{10}-\frac{7}{2}\left(-\frac{13}{5}\right)$$

Multiply \frac{7}{2} times -\frac{13}{5} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{3}{10}-\frac{7\left(-13\right)}{2\times 5}$$

Do the multiplications in the fraction \frac{7\left(-13\right)}{2\times 5}.

$$-\frac{3}{10}-\frac{-91}{10}$$

Fraction \frac{-91}{10} can be rewritten as -\frac{91}{10} by extracting the negative sign.

$$-\frac{3}{10}-\left(-\frac{91}{10}\right)$$

The opposite of -\frac{91}{10} is \frac{91}{10}.

$$-\frac{3}{10}+\frac{91}{10}$$

Since -\frac{3}{10} and \frac{91}{10} have the same denominator, add them by adding their numerators.

$$\frac{-3+91}{10}$$

Add -3 and 91 to get 88.

$$\frac{88}{10}$$

Reduce the fraction \frac{88}{10} to lowest terms by extracting and canceling out 2.

$$\frac{44}{5}$$

Factor

$$\frac{2 ^ {2} \cdot 11}{5} = 8\frac{4}{5} = 8.8$$