Solve (8/2-32/8-5+3/2+1/4)*(-frac{3}{4})

$$( \frac { 8 } { 2 } - 3 \frac { 2 } { 8 } - 5 + \frac { 3 } { 2 } + \frac { 1 } { 4 } ) \cdot ( - \frac { 3 } { 4 } )$$

Evaluate

$$\frac{15}{8}=1.875$$

Solution Steps

Divide 8 by 2 to get 4.

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

Multiply 3 and 8 to get 24.

$$\left(4-\frac{24+2}{8}-5+\frac{3}{2}+\frac{1}{4}\right)\left(-\frac{3}{4}\right)$$

Add 24 and 2 to get 26.

$$\left(4-\frac{26}{8}-5+\frac{3}{2}+\frac{1}{4}\right)\left(-\frac{3}{4}\right)$$

Reduce the fraction \frac{26}{8} to lowest terms by extracting and canceling out 2.

$$\left(4-\frac{13}{4}-5+\frac{3}{2}+\frac{1}{4}\right)\left(-\frac{3}{4}\right)$$

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

$$\left(\frac{16}{4}-\frac{13}{4}-5+\frac{3}{2}+\frac{1}{4}\right)\left(-\frac{3}{4}\right)$$

Since \frac{16}{4} and \frac{13}{4} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{16-13}{4}-5+\frac{3}{2}+\frac{1}{4}\right)\left(-\frac{3}{4}\right)$$

Subtract 13 from 16 to get 3.

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

Convert 5 to fraction \frac{20}{4}.

$$\left(\frac{3}{4}-\frac{20}{4}+\frac{3}{2}+\frac{1}{4}\right)\left(-\frac{3}{4}\right)$$

Since \frac{3}{4} and \frac{20}{4} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{3-20}{4}+\frac{3}{2}+\frac{1}{4}\right)\left(-\frac{3}{4}\right)$$

Subtract 20 from 3 to get -17.

$$\left(-\frac{17}{4}+\frac{3}{2}+\frac{1}{4}\right)\left(-\frac{3}{4}\right)$$

Least common multiple of 4 and 2 is 4. Convert -\frac{17}{4} and \frac{3}{2} to fractions with denominator 4.

$$\left(-\frac{17}{4}+\frac{6}{4}+\frac{1}{4}\right)\left(-\frac{3}{4}\right)$$

Since -\frac{17}{4} and \frac{6}{4} have the same denominator, add them by adding their numerators.

$$\left(\frac{-17+6}{4}+\frac{1}{4}\right)\left(-\frac{3}{4}\right)$$

Add -17 and 6 to get -11.

$$\left(-\frac{11}{4}+\frac{1}{4}\right)\left(-\frac{3}{4}\right)$$

Since -\frac{11}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{-11+1}{4}\left(-\frac{3}{4}\right)$$

Add -11 and 1 to get -10.

$$\frac{-10}{4}\left(-\frac{3}{4}\right)$$

Reduce the fraction \frac{-10}{4} to lowest terms by extracting and canceling out 2.

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

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

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

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

$$\frac{15}{8}$$

Factor

$$\frac{3 \cdot 5}{2 ^ {3}} = 1\frac{7}{8} = 1.875$$