Solve (1-2/3):(2+1/3)-1/5

$$( 1 - \frac { 2 } { 3 } ) : ( 2 + \frac { 1 } { 3 } ) - \frac { 1 } { 5 }$$

Evaluate

$$-\frac{2}{35}\approx -0.057142857$$

Solution Steps

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

$$\frac{\frac{3}{3}-\frac{2}{3}}{2+\frac{1}{3}}-\frac{1}{5}$$

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

$$\frac{\frac{3-2}{3}}{2+\frac{1}{3}}-\frac{1}{5}$$

Subtract 2 from 3 to get 1.

$$\frac{\frac{1}{3}}{2+\frac{1}{3}}-\frac{1}{5}$$

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

$$\frac{\frac{1}{3}}{\frac{6}{3}+\frac{1}{3}}-\frac{1}{5}$$

Since \frac{6}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{3}}{\frac{6+1}{3}}-\frac{1}{5}$$

Add 6 and 1 to get 7.

$$\frac{\frac{1}{3}}{\frac{7}{3}}-\frac{1}{5}$$

Divide \frac{1}{3} by \frac{7}{3} by multiplying \frac{1}{3} by the reciprocal of \frac{7}{3}.

$$\frac{1}{3}\times \frac{3}{7}-\frac{1}{5}$$

Multiply \frac{1}{3} times \frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 3}{3\times 7}-\frac{1}{5}$$

Cancel out 3 in both numerator and denominator.

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

Least common multiple of 7 and 5 is 35. Convert \frac{1}{7} and \frac{1}{5} to fractions with denominator 35.

$$\frac{5}{35}-\frac{7}{35}$$

Since \frac{5}{35} and \frac{7}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-7}{35}$$

Subtract 7 from 5 to get -2.

$$-\frac{2}{35}$$

Factor

$$-\frac{2}{35} = -0.05714285714285714$$