Solve 1/2-3/4+1/8/frac{1{2}+frac{3}{4}-frac{7}{8}}

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

Evaluate

$$-\frac{1}{3}\approx -0.333333333$$

Solution Steps

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

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

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

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

Subtract 3 from 2 to get -1.

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

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

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

Since -\frac{2}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

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

Add -2 and 1 to get -1.

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

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

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

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

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

Add 2 and 3 to get 5.

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

Least common multiple of 4 and 8 is 8. Convert \frac{5}{4} and \frac{7}{8} to fractions with denominator 8.

$$\frac{-\frac{1}{8}}{\frac{10}{8}-\frac{7}{8}}$$

Since \frac{10}{8} and \frac{7}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{1}{8}}{\frac{10-7}{8}}$$

Subtract 7 from 10 to get 3.

$$\frac{-\frac{1}{8}}{\frac{3}{8}}$$

Divide -\frac{1}{8} by \frac{3}{8} by multiplying -\frac{1}{8} by the reciprocal of \frac{3}{8}.

$$-\frac{1}{8}\times \frac{8}{3}$$

Multiply -\frac{1}{8} times \frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-8}{8\times 3}$$

Cancel out 8 in both numerator and denominator.

$$\frac{-1}{3}$$

Fraction \frac{-1}{3} can be rewritten as -\frac{1}{3} by extracting the negative sign.

$$-\frac{1}{3}$$

Factor

$$-\frac{1}{3} = -0.3333333333333333$$