Solve 2(1/3)-1/2(frac{1{3})+1}=

$$\frac { 2 ( \frac { 1 } { 3 } ) - 1 } { 2 ( \frac { 1 } { 3 } ) + 1 } =$$

Evaluate

$$-\frac{1}{5}=-0.2$$

Solution Steps

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

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

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

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

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

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

Subtract 3 from 2 to get -1.

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

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

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

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

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

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

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

Add 2 and 3 to get 5.

$$\frac{-\frac{1}{3}}{\frac{5}{3}}$$

Divide -\frac{1}{3} by \frac{5}{3} by multiplying -\frac{1}{3} by the reciprocal of \frac{5}{3}.

$$-\frac{1}{3}\times \frac{3}{5}$$

Multiply -\frac{1}{3} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 3 in both numerator and denominator.

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

Fraction \frac{-1}{5} can be rewritten as -\frac{1}{5} by extracting the negative sign.

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

Factor

$$-\frac{1}{5} = -0.2$$