Solve |-21/2|+5/8*(-2)^2div(-1)^2019

$$| - 2 \frac { 1 } { 2 } | + \frac { 5 } { 8 } \times ( - 2 ) ^ { 2 } \div ( - 1 ) ^ { 2019 }$$

Evaluate

$$0$$

Solution Steps

Multiply 2 and 2 to get 4.

$$|-\frac{4+1}{2}|+\frac{\frac{5}{8}\left(-2\right)^{2}}{\left(-1\right)^{2019}}$$

Add 4 and 1 to get 5.

$$|-\frac{5}{2}|+\frac{\frac{5}{8}\left(-2\right)^{2}}{\left(-1\right)^{2019}}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{5}{2} is \frac{5}{2}.

$$\frac{5}{2}+\frac{\frac{5}{8}\left(-2\right)^{2}}{\left(-1\right)^{2019}}$$

Calculate -2 to the power of 2 and get 4.

$$\frac{5}{2}+\frac{\frac{5}{8}\times 4}{\left(-1\right)^{2019}}$$

Express \frac{5}{8}\times 4 as a single fraction.

$$\frac{5}{2}+\frac{\frac{5\times 4}{8}}{\left(-1\right)^{2019}}$$

Multiply 5 and 4 to get 20.

$$\frac{5}{2}+\frac{\frac{20}{8}}{\left(-1\right)^{2019}}$$

Reduce the fraction \frac{20}{8} to lowest terms by extracting and canceling out 4.

$$\frac{5}{2}+\frac{\frac{5}{2}}{\left(-1\right)^{2019}}$$

Calculate -1 to the power of 2019 and get -1.

$$\frac{5}{2}+\frac{\frac{5}{2}}{-1}$$

Express \frac{\frac{5}{2}}{-1} as a single fraction.

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

Multiply 2 and -1 to get -2.

$$\frac{5}{2}+\frac{5}{-2}$$

Fraction \frac{5}{-2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$\frac{5}{2}-\frac{5}{2}$$

Subtract \frac{5}{2} from \frac{5}{2} to get 0.

$$0$$

Factor

$$0$$