Solve 1+4/5(-5/2)^3+2:3/2-2(1/3-frac{3}{4})

$$1 + \frac { 4 } { 5 } ( - \frac { 5 } { 2 } ) ^ { 3 } + 2 : \frac { 3 } { 2 } - 2 ( \frac { 1 } { 3 } - \frac { 3 } { 4 } )$$

Evaluate

$$-\frac{28}{3}\approx -9.333333333$$

Solution Steps

Calculate -\frac{5}{2} to the power of 3 and get -\frac{125}{8}.

$$1+\frac{4}{5}\left(-\frac{125}{8}\right)+\frac{2}{\frac{3}{2}}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

Multiply \frac{4}{5} times -\frac{125}{8} by multiplying numerator times numerator and denominator times denominator.

$$1+\frac{4\left(-125\right)}{5\times 8}+\frac{2}{\frac{3}{2}}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

Do the multiplications in the fraction \frac{4\left(-125\right)}{5\times 8}.

$$1+\frac{-500}{40}+\frac{2}{\frac{3}{2}}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

Reduce the fraction \frac{-500}{40} to lowest terms by extracting and canceling out 20.

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

Convert 1 to fraction \frac{2}{2}.

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

Since \frac{2}{2} and \frac{25}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 25 from 2 to get -23.

$$-\frac{23}{2}+\frac{2}{\frac{3}{2}}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

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

$$-\frac{23}{2}+2\times \frac{2}{3}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

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

$$-\frac{23}{2}+\frac{2\times 2}{3}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

Multiply 2 and 2 to get 4.

$$-\frac{23}{2}+\frac{4}{3}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

Least common multiple of 2 and 3 is 6. Convert -\frac{23}{2} and \frac{4}{3} to fractions with denominator 6.

$$-\frac{69}{6}+\frac{8}{6}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

Since -\frac{69}{6} and \frac{8}{6} have the same denominator, add them by adding their numerators.

$$\frac{-69+8}{6}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

Add -69 and 8 to get -61.

$$-\frac{61}{6}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

Least common multiple of 3 and 4 is 12. Convert \frac{1}{3} and \frac{3}{4} to fractions with denominator 12.

$$-\frac{61}{6}-2\left(\frac{4}{12}-\frac{9}{12}\right)$$

Since \frac{4}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{61}{6}-2\times \frac{4-9}{12}$$

Subtract 9 from 4 to get -5.

$$-\frac{61}{6}-2\left(-\frac{5}{12}\right)$$

Express 2\left(-\frac{5}{12}\right) as a single fraction.

$$-\frac{61}{6}-\frac{2\left(-5\right)}{12}$$

Multiply 2 and -5 to get -10.

$$-\frac{61}{6}-\frac{-10}{12}$$

Reduce the fraction \frac{-10}{12} to lowest terms by extracting and canceling out 2.

$$-\frac{61}{6}-\left(-\frac{5}{6}\right)$$

The opposite of -\frac{5}{6} is \frac{5}{6}.

$$-\frac{61}{6}+\frac{5}{6}$$

Since -\frac{61}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$\frac{-61+5}{6}$$

Add -61 and 5 to get -56.

$$\frac{-56}{6}$$

Reduce the fraction \frac{-56}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{28}{3}$$

Factor

$$-\frac{28}{3} = -9\frac{1}{3} = -9.333333333333334$$