Solve -1/2+1/frac{1{2}+8}

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

Evaluate

$$-\frac{13}{34}\approx -0.382352941$$

Solution Steps

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

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

Convert 8 to fraction \frac{16}{2}.

$$-\frac{1}{2}+\frac{1}{\frac{1}{2}+\frac{16}{2}}$$

Since \frac{1}{2} and \frac{16}{2} have the same denominator, add them by adding their numerators.

$$-\frac{1}{2}+\frac{1}{\frac{1+16}{2}}$$

Add 1 and 16 to get 17.

$$-\frac{1}{2}+\frac{1}{\frac{17}{2}}$$

Divide 1 by \frac{17}{2} by multiplying 1 by the reciprocal of \frac{17}{2}.

$$-\frac{1}{2}+1\times \frac{2}{17}$$

Multiply 1 and \frac{2}{17} to get \frac{2}{17}.

$$-\frac{1}{2}+\frac{2}{17}$$

Least common multiple of 2 and 17 is 34. Convert -\frac{1}{2} and \frac{2}{17} to fractions with denominator 34.

$$-\frac{17}{34}+\frac{4}{34}$$

Since -\frac{17}{34} and \frac{4}{34} have the same denominator, add them by adding their numerators.

$$\frac{-17+4}{34}$$

Add -17 and 4 to get -13.

$$-\frac{13}{34}$$

Factor

$$-\frac{13}{34} = -0.38235294117647056$$