Solve -1^4*(-1/2)^2+[3/4+(-1/2)-7/8]div(-frac{7}{8})

$$- 1 ^ { 4 } \times ( - \frac { 1 } { 2 } ) ^ { 2 } + [ \frac { 3 } { 4 } + ( - \frac { 1 } { 2 } ) - \frac { 7 } { 8 } ] \div ( - \frac { 7 } { 8 } )$$

Evaluate

$$\frac{13}{28}\approx 0.464285714$$

Solution Steps

Calculate 1 to the power of 4 and get 1.

$$-\left(-\frac{1}{2}\right)^{2}+\frac{\frac{3}{4}-\frac{1}{2}-\frac{7}{8}}{-\frac{7}{8}}$$

Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$-\frac{1}{4}+\frac{\frac{3}{4}-\frac{1}{2}-\frac{7}{8}}{-\frac{7}{8}}$$

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

$$-\frac{1}{4}+\frac{\frac{3}{4}-\frac{2}{4}-\frac{7}{8}}{-\frac{7}{8}}$$

Since \frac{3}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{4}+\frac{\frac{3-2}{4}-\frac{7}{8}}{-\frac{7}{8}}$$

Subtract 2 from 3 to get 1.

$$-\frac{1}{4}+\frac{\frac{1}{4}-\frac{7}{8}}{-\frac{7}{8}}$$

Least common multiple of 4 and 8 is 8. Convert \frac{1}{4} and \frac{7}{8} to fractions with denominator 8.

$$-\frac{1}{4}+\frac{\frac{2}{8}-\frac{7}{8}}{-\frac{7}{8}}$$

Since \frac{2}{8} and \frac{7}{8} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{4}+\frac{\frac{2-7}{8}}{-\frac{7}{8}}$$

Subtract 7 from 2 to get -5.

$$-\frac{1}{4}+\frac{-\frac{5}{8}}{-\frac{7}{8}}$$

Divide -\frac{5}{8} by -\frac{7}{8} by multiplying -\frac{5}{8} by the reciprocal of -\frac{7}{8}.

$$-\frac{1}{4}-\frac{5}{8}\left(-\frac{8}{7}\right)$$

Multiply -\frac{5}{8} times -\frac{8}{7} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{1}{4}+\frac{-5\left(-8\right)}{8\times 7}$$

Do the multiplications in the fraction \frac{-5\left(-8\right)}{8\times 7}.

$$-\frac{1}{4}+\frac{40}{56}$$

Reduce the fraction \frac{40}{56} to lowest terms by extracting and canceling out 8.

$$-\frac{1}{4}+\frac{5}{7}$$

Least common multiple of 4 and 7 is 28. Convert -\frac{1}{4} and \frac{5}{7} to fractions with denominator 28.

$$-\frac{7}{28}+\frac{20}{28}$$

Since -\frac{7}{28} and \frac{20}{28} have the same denominator, add them by adding their numerators.

$$\frac{-7+20}{28}$$

Add -7 and 20 to get 13.

$$\frac{13}{28}$$

Factor

$$\frac{13}{2 ^ {2} \cdot 7} = 0.4642857142857143$$