Solve 1/2-3/frac{1{2}+1}

$$\frac { \frac { 1 } { 2 } - 3 } { \frac { 1 } { 2 } + 1 }$$

Evaluate

$$-\frac{5}{3}\approx -1.666666667$$

Solution Steps

Convert 3 to fraction \frac{6}{2}.

$$\frac{\frac{1}{2}-\frac{6}{2}}{\frac{1}{2}+1}$$

Since \frac{1}{2} and \frac{6}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1-6}{2}}{\frac{1}{2}+1}$$

Subtract 6 from 1 to get -5.

$$\frac{-\frac{5}{2}}{\frac{1}{2}+1}$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{-\frac{5}{2}}{\frac{1}{2}+\frac{2}{2}}$$

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

$$\frac{-\frac{5}{2}}{\frac{1+2}{2}}$$

Add 1 and 2 to get 3.

$$\frac{-\frac{5}{2}}{\frac{3}{2}}$$

Divide -\frac{5}{2} by \frac{3}{2} by multiplying -\frac{5}{2} by the reciprocal of \frac{3}{2}.

$$-\frac{5}{2}\times \frac{2}{3}$$

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

$$\frac{-5\times 2}{2\times 3}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-5}{3}$$

Fraction \frac{-5}{3} can be rewritten as -\frac{5}{3} by extracting the negative sign.

$$-\frac{5}{3}$$

Factor

$$-\frac{5}{3} = -1\frac{2}{3} = -1.6666666666666667$$