Solve 1-(1/3):(1/2-1)

$$1 - ( \frac { 1 } { 3 } ) : ( \frac { 1 } { 2 } - 1 )$$

Evaluate

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

Solution Steps

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

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

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

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

Subtract 2 from 1 to get -1.

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

Divide \frac{1}{3} by -\frac{1}{2} by multiplying \frac{1}{3} by the reciprocal of -\frac{1}{2}.

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

Multiply \frac{1}{3} and -2 to get \frac{-2}{3}.

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

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

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

The opposite of -\frac{2}{3} is \frac{2}{3}.

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

Convert 1 to fraction \frac{3}{3}.

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

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

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

Add 3 and 2 to get 5.

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

Factor

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