Solve 6/6-2{2-frac{2/3}}

$$\frac { 6 } { 6 - \frac { 2 } { 2 - \frac { 2 } { 3 } } }$$

Evaluate

$$\frac{4}{3}\approx 1.333333333$$

Solution Steps

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

$$\frac{6}{6-\frac{2}{\frac{6}{3}-\frac{2}{3}}}$$

Since \frac{6}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6}{6-\frac{2}{\frac{6-2}{3}}}$$

Subtract 2 from 6 to get 4.

$$\frac{6}{6-\frac{2}{\frac{4}{3}}}$$

Divide 2 by \frac{4}{3} by multiplying 2 by the reciprocal of \frac{4}{3}.

$$\frac{6}{6-2\times \frac{3}{4}}$$

Express 2\times \frac{3}{4} as a single fraction.

$$\frac{6}{6-\frac{2\times 3}{4}}$$

Multiply 2 and 3 to get 6.

$$\frac{6}{6-\frac{6}{4}}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{6}{6-\frac{3}{2}}$$

Convert 6 to fraction \frac{12}{2}.

$$\frac{6}{\frac{12}{2}-\frac{3}{2}}$$

Since \frac{12}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6}{\frac{12-3}{2}}$$

Subtract 3 from 12 to get 9.

$$\frac{6}{\frac{9}{2}}$$

Divide 6 by \frac{9}{2} by multiplying 6 by the reciprocal of \frac{9}{2}.

$$6\times \frac{2}{9}$$

Express 6\times \frac{2}{9} as a single fraction.

$$\frac{6\times 2}{9}$$

Multiply 6 and 2 to get 12.

$$\frac{12}{9}$$

Reduce the fraction \frac{12}{9} to lowest terms by extracting and canceling out 3.

$$\frac{4}{3}$$

Factor

$$\frac{2 ^ {2}}{3} = 1\frac{1}{3} = 1.3333333333333333$$