Solve |-3|1/4(-21/2)|-(-81/4)

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

Evaluate

$$-\frac{495}{32}=-15.46875$$

Solution Steps

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -3 is 3.

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

Multiply 3 and \frac{1}{4} to get \frac{3}{4}.

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

Multiply 2 and 2 to get 4.

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

Add 4 and 1 to get 5.

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

Multiply \frac{3}{4} times -\frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{3\left(-5\right)}{4\times 2}.

$$\frac{-15}{8}|-\left(-\frac{8\times 4+1}{4}\right)|$$

Fraction \frac{-15}{8} can be rewritten as -\frac{15}{8} by extracting the negative sign.

$$-\frac{15}{8}|-\left(-\frac{8\times 4+1}{4}\right)|$$

Multiply 8 and 4 to get 32.

$$-\frac{15}{8}|-\left(-\frac{32+1}{4}\right)|$$

Add 32 and 1 to get 33.

$$-\frac{15}{8}|-\left(-\frac{33}{4}\right)|$$

The opposite of -\frac{33}{4} is \frac{33}{4}.

$$-\frac{15}{8}|\frac{33}{4}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{33}{4} is \frac{33}{4}.

$$-\frac{15}{8}\times \frac{33}{4}$$

Multiply -\frac{15}{8} times \frac{33}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-15\times 33}{8\times 4}$$

Do the multiplications in the fraction \frac{-15\times 33}{8\times 4}.

$$\frac{-495}{32}$$

Fraction \frac{-495}{32} can be rewritten as -\frac{495}{32} by extracting the negative sign.

$$-\frac{495}{32}$$

Factor

$$-\frac{495}{32} = -15\frac{15}{32} = -15.46875$$