Solve -2^2-15/4div(-5)+|-1/4|+1/8*(-2)+(2/3-2frac{3}{4})*24-(-1)^2018

$$- 2 ^ { 2 } - \frac { 15 } { 4 } \div ( - 5 ) + | - \frac { 1 } { 4 } | + \frac { 1 } { 8 } \times ( - 2 ) + ( \frac { 2 } { 3 } - 2 \frac { 3 } { 4 } ) \times 24 - ( - 1 ) ^ { 2018 }$$

Evaluate

$$-\frac{217}{4}=-54.25$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$-4-\frac{\frac{15}{4}}{-5}+|-\frac{1}{4}|+\frac{1}{8}\left(-2\right)+\left(\frac{2}{3}-\frac{2\times 4+3}{4}\right)\times 24-\left(-1\right)^{2018}$$

Express \frac{\frac{15}{4}}{-5} as a single fraction.

$$-4-\frac{15}{4\left(-5\right)}+|-\frac{1}{4}|+\frac{1}{8}\left(-2\right)+\left(\frac{2}{3}-\frac{2\times 4+3}{4}\right)\times 24-\left(-1\right)^{2018}$$

Multiply 4 and -5 to get -20.

$$-4-\frac{15}{-20}+|-\frac{1}{4}|+\frac{1}{8}\left(-2\right)+\left(\frac{2}{3}-\frac{2\times 4+3}{4}\right)\times 24-\left(-1\right)^{2018}$$

Reduce the fraction \frac{15}{-20} to lowest terms by extracting and canceling out 5.

$$-4-\left(-\frac{3}{4}\right)+|-\frac{1}{4}|+\frac{1}{8}\left(-2\right)+\left(\frac{2}{3}-\frac{2\times 4+3}{4}\right)\times 24-\left(-1\right)^{2018}$$

The opposite of -\frac{3}{4} is \frac{3}{4}.

$$-4+\frac{3}{4}+|-\frac{1}{4}|+\frac{1}{8}\left(-2\right)+\left(\frac{2}{3}-\frac{2\times 4+3}{4}\right)\times 24-\left(-1\right)^{2018}$$

Convert -4 to fraction -\frac{16}{4}.

$$-\frac{16}{4}+\frac{3}{4}+|-\frac{1}{4}|+\frac{1}{8}\left(-2\right)+\left(\frac{2}{3}-\frac{2\times 4+3}{4}\right)\times 24-\left(-1\right)^{2018}$$

Since -\frac{16}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{-16+3}{4}+|-\frac{1}{4}|+\frac{1}{8}\left(-2\right)+\left(\frac{2}{3}-\frac{2\times 4+3}{4}\right)\times 24-\left(-1\right)^{2018}$$

Add -16 and 3 to get -13.

$$-\frac{13}{4}+|-\frac{1}{4}|+\frac{1}{8}\left(-2\right)+\left(\frac{2}{3}-\frac{2\times 4+3}{4}\right)\times 24-\left(-1\right)^{2018}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{1}{4} is \frac{1}{4}.

$$-\frac{13}{4}+\frac{1}{4}+\frac{1}{8}\left(-2\right)+\left(\frac{2}{3}-\frac{2\times 4+3}{4}\right)\times 24-\left(-1\right)^{2018}$$

Since -\frac{13}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{-13+1}{4}+\frac{1}{8}\left(-2\right)+\left(\frac{2}{3}-\frac{2\times 4+3}{4}\right)\times 24-\left(-1\right)^{2018}$$

Add -13 and 1 to get -12.

$$\frac{-12}{4}+\frac{1}{8}\left(-2\right)+\left(\frac{2}{3}-\frac{2\times 4+3}{4}\right)\times 24-\left(-1\right)^{2018}$$

Divide -12 by 4 to get -3.

$$-3+\frac{1}{8}\left(-2\right)+\left(\frac{2}{3}-\frac{2\times 4+3}{4}\right)\times 24-\left(-1\right)^{2018}$$

Multiply \frac{1}{8} and -2 to get \frac{-2}{8}.

$$-3+\frac{-2}{8}+\left(\frac{2}{3}-\frac{2\times 4+3}{4}\right)\times 24-\left(-1\right)^{2018}$$

Reduce the fraction \frac{-2}{8} to lowest terms by extracting and canceling out 2.

$$-3-\frac{1}{4}+\left(\frac{2}{3}-\frac{2\times 4+3}{4}\right)\times 24-\left(-1\right)^{2018}$$

Convert -3 to fraction -\frac{12}{4}.

$$-\frac{12}{4}-\frac{1}{4}+\left(\frac{2}{3}-\frac{2\times 4+3}{4}\right)\times 24-\left(-1\right)^{2018}$$

Since -\frac{12}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-12-1}{4}+\left(\frac{2}{3}-\frac{2\times 4+3}{4}\right)\times 24-\left(-1\right)^{2018}$$

Subtract 1 from -12 to get -13.

$$-\frac{13}{4}+\left(\frac{2}{3}-\frac{2\times 4+3}{4}\right)\times 24-\left(-1\right)^{2018}$$

Multiply 2 and 4 to get 8.

$$-\frac{13}{4}+\left(\frac{2}{3}-\frac{8+3}{4}\right)\times 24-\left(-1\right)^{2018}$$

Add 8 and 3 to get 11.

$$-\frac{13}{4}+\left(\frac{2}{3}-\frac{11}{4}\right)\times 24-\left(-1\right)^{2018}$$

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{11}{4} to fractions with denominator 12.

$$-\frac{13}{4}+\left(\frac{8}{12}-\frac{33}{12}\right)\times 24-\left(-1\right)^{2018}$$

Since \frac{8}{12} and \frac{33}{12} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{13}{4}+\frac{8-33}{12}\times 24-\left(-1\right)^{2018}$$

Subtract 33 from 8 to get -25.

$$-\frac{13}{4}-\frac{25}{12}\times 24-\left(-1\right)^{2018}$$

Express -\frac{25}{12}\times 24 as a single fraction.

$$-\frac{13}{4}+\frac{-25\times 24}{12}-\left(-1\right)^{2018}$$

Multiply -25 and 24 to get -600.

$$-\frac{13}{4}+\frac{-600}{12}-\left(-1\right)^{2018}$$

Divide -600 by 12 to get -50.

$$-\frac{13}{4}-50-\left(-1\right)^{2018}$$

Convert 50 to fraction \frac{200}{4}.

$$-\frac{13}{4}-\frac{200}{4}-\left(-1\right)^{2018}$$

Since -\frac{13}{4} and \frac{200}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-13-200}{4}-\left(-1\right)^{2018}$$

Subtract 200 from -13 to get -213.

$$-\frac{213}{4}-\left(-1\right)^{2018}$$

Calculate -1 to the power of 2018 and get 1.

$$-\frac{213}{4}-1$$

Convert 1 to fraction \frac{4}{4}.

$$-\frac{213}{4}-\frac{4}{4}$$

Since -\frac{213}{4} and \frac{4}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-213-4}{4}$$

Subtract 4 from -213 to get -217.

$$-\frac{217}{4}$$

Factor

$$-\frac{217}{4} = -54\frac{1}{4} = -54.25$$