Solve 1-[-2/5-(-1/2+3/4)]-2

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

Evaluate

$$-\frac{7}{20}=-0.35$$

Solution Steps

Least common multiple of 2 and 4 is 4. Convert -\frac{1}{2} and \frac{3}{4} to fractions with denominator 4.

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

Since -\frac{2}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

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

Add -2 and 3 to get 1.

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

Least common multiple of 5 and 4 is 20. Convert -\frac{2}{5} and \frac{1}{4} to fractions with denominator 20.

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

Since -\frac{8}{20} and \frac{5}{20} have the same denominator, subtract them by subtracting their numerators.

$$1-\frac{-8-5}{20}-2$$

Subtract 5 from -8 to get -13.

$$1-\left(-\frac{13}{20}\right)-2$$

The opposite of -\frac{13}{20} is \frac{13}{20}.

$$1+\frac{13}{20}-2$$

Convert 1 to fraction \frac{20}{20}.

$$\frac{20}{20}+\frac{13}{20}-2$$

Since \frac{20}{20} and \frac{13}{20} have the same denominator, add them by adding their numerators.

$$\frac{20+13}{20}-2$$

Add 20 and 13 to get 33.

$$\frac{33}{20}-2$$

Convert 2 to fraction \frac{40}{20}.

$$\frac{33}{20}-\frac{40}{20}$$

Since \frac{33}{20} and \frac{40}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{33-40}{20}$$

Subtract 40 from 33 to get -7.

$$-\frac{7}{20}$$

Factor

$$-\frac{7}{20} = -0.35$$