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

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

Evaluate

$$-\frac{8}{3}\approx -2.666666667$$

Solution Steps

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

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

Since \frac{3}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 3 to get 2.

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

Express \frac{\frac{2}{3}}{3} as a single fraction.

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

Multiply 3 and 3 to get 9.

$$1-\frac{1+\frac{2}{9}}{\frac{1}{3}}$$

Convert 1 to fraction \frac{9}{9}.

$$1-\frac{\frac{9}{9}+\frac{2}{9}}{\frac{1}{3}}$$

Since \frac{9}{9} and \frac{2}{9} have the same denominator, add them by adding their numerators.

$$1-\frac{\frac{9+2}{9}}{\frac{1}{3}}$$

Add 9 and 2 to get 11.

$$1-\frac{\frac{11}{9}}{\frac{1}{3}}$$

Divide \frac{11}{9} by \frac{1}{3} by multiplying \frac{11}{9} by the reciprocal of \frac{1}{3}.

$$1-\frac{11}{9}\times 3$$

Express \frac{11}{9}\times 3 as a single fraction.

$$1-\frac{11\times 3}{9}$$

Multiply 11 and 3 to get 33.

$$1-\frac{33}{9}$$

Reduce the fraction \frac{33}{9} to lowest terms by extracting and canceling out 3.

$$1-\frac{11}{3}$$

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

$$\frac{3}{3}-\frac{11}{3}$$

Since \frac{3}{3} and \frac{11}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-11}{3}$$

Subtract 11 from 3 to get -8.

$$-\frac{8}{3}$$

Factor

$$-\frac{8}{3} = -2\frac{2}{3} = -2.6666666666666665$$