Solve -81/4-[-31/4-(-21/2)]

$$- 8 \frac { 1 } { 4 } - [ - 3 \frac { 1 } { 4 } - ( - 2 \frac { 1 } { 2 } ) ]$$

Evaluate

$$-\frac{15}{2}=-7.5$$

Solution Steps

Multiply 8 and 4 to get 32.

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

Add 32 and 1 to get 33.

$$-\frac{33}{4}-\left(-\frac{3\times 4+1}{4}-\left(-\frac{2\times 2+1}{2}\right)\right)$$

Multiply 3 and 4 to get 12.

$$-\frac{33}{4}-\left(-\frac{12+1}{4}-\left(-\frac{2\times 2+1}{2}\right)\right)$$

Add 12 and 1 to get 13.

$$-\frac{33}{4}-\left(-\frac{13}{4}-\left(-\frac{2\times 2+1}{2}\right)\right)$$

Multiply 2 and 2 to get 4.

$$-\frac{33}{4}-\left(-\frac{13}{4}-\left(-\frac{4+1}{2}\right)\right)$$

Add 4 and 1 to get 5.

$$-\frac{33}{4}-\left(-\frac{13}{4}-\left(-\frac{5}{2}\right)\right)$$

The opposite of -\frac{5}{2} is \frac{5}{2}.

$$-\frac{33}{4}-\left(-\frac{13}{4}+\frac{5}{2}\right)$$

Least common multiple of 4 and 2 is 4. Convert -\frac{13}{4} and \frac{5}{2} to fractions with denominator 4.

$$-\frac{33}{4}-\left(-\frac{13}{4}+\frac{10}{4}\right)$$

Since -\frac{13}{4} and \frac{10}{4} have the same denominator, add them by adding their numerators.

$$-\frac{33}{4}-\frac{-13+10}{4}$$

Add -13 and 10 to get -3.

$$-\frac{33}{4}-\left(-\frac{3}{4}\right)$$

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

$$-\frac{33}{4}+\frac{3}{4}$$

Since -\frac{33}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{-33+3}{4}$$

Add -33 and 3 to get -30.

$$\frac{-30}{4}$$

Reduce the fraction \frac{-30}{4} to lowest terms by extracting and canceling out 2.

$$-\frac{15}{2}$$

Factor

$$-\frac{15}{2} = -7\frac{1}{2} = -7.5$$