Solve 1+7/5(-5/2)^3+2div3/2-2(1/3-frac{3}{4})

$$1 + \frac { 7 } { 5 } ( - \frac { 5 } { 2 } ) ^ { 3 } + 2 \div \frac { 3 } { 2 } - 2 ( \frac { 1 } { 3 } - \frac { 3 } { 4 } )$$

Evaluate

$$-\frac{449}{24}\approx -18.708333333$$

Solution Steps

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

$$1+\frac{7}{5}\left(-\frac{125}{8}\right)+\frac{2}{\frac{3}{2}}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

Multiply \frac{7}{5} times -\frac{125}{8} by multiplying numerator times numerator and denominator times denominator.

$$1+\frac{7\left(-125\right)}{5\times 8}+\frac{2}{\frac{3}{2}}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

Do the multiplications in the fraction \frac{7\left(-125\right)}{5\times 8}.

$$1+\frac{-875}{40}+\frac{2}{\frac{3}{2}}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

Reduce the fraction \frac{-875}{40} to lowest terms by extracting and canceling out 5.

$$1-\frac{175}{8}+\frac{2}{\frac{3}{2}}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

Convert 1 to fraction \frac{8}{8}.

$$\frac{8}{8}-\frac{175}{8}+\frac{2}{\frac{3}{2}}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

Since \frac{8}{8} and \frac{175}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-175}{8}+\frac{2}{\frac{3}{2}}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

Subtract 175 from 8 to get -167.

$$-\frac{167}{8}+\frac{2}{\frac{3}{2}}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

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

$$-\frac{167}{8}+2\times \frac{2}{3}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

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

$$-\frac{167}{8}+\frac{2\times 2}{3}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

Multiply 2 and 2 to get 4.

$$-\frac{167}{8}+\frac{4}{3}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

Least common multiple of 8 and 3 is 24. Convert -\frac{167}{8} and \frac{4}{3} to fractions with denominator 24.

$$-\frac{501}{24}+\frac{32}{24}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

Since -\frac{501}{24} and \frac{32}{24} have the same denominator, add them by adding their numerators.

$$\frac{-501+32}{24}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

Add -501 and 32 to get -469.

$$-\frac{469}{24}-2\left(\frac{1}{3}-\frac{3}{4}\right)$$

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

$$-\frac{469}{24}-2\left(\frac{4}{12}-\frac{9}{12}\right)$$

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

$$-\frac{469}{24}-2\times \frac{4-9}{12}$$

Subtract 9 from 4 to get -5.

$$-\frac{469}{24}-2\left(-\frac{5}{12}\right)$$

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

$$-\frac{469}{24}-\frac{2\left(-5\right)}{12}$$

Multiply 2 and -5 to get -10.

$$-\frac{469}{24}-\frac{-10}{12}$$

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

$$-\frac{469}{24}-\left(-\frac{5}{6}\right)$$

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

$$-\frac{469}{24}+\frac{5}{6}$$

Least common multiple of 24 and 6 is 24. Convert -\frac{469}{24} and \frac{5}{6} to fractions with denominator 24.

$$-\frac{469}{24}+\frac{20}{24}$$

Since -\frac{469}{24} and \frac{20}{24} have the same denominator, add them by adding their numerators.

$$\frac{-469+20}{24}$$

Add -469 and 20 to get -449.

$$-\frac{449}{24}$$

Factor

$$-\frac{449}{24} = -18\frac{17}{24} = -18.708333333333332$$