Solve 3/3+3{3+frac{3/3+3}}

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

Evaluate

$$\frac{7}{9}\approx 0.777777778$$

Solution Steps

Add 3 and 3 to get 6.

$$\frac{3}{3+\frac{3}{3+\frac{3}{6}}}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

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

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

$$\frac{3}{3+\frac{3}{\frac{6}{2}+\frac{1}{2}}}$$

Since \frac{6}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{3}{3+\frac{3}{\frac{6+1}{2}}}$$

Add 6 and 1 to get 7.

$$\frac{3}{3+\frac{3}{\frac{7}{2}}}$$

Divide 3 by \frac{7}{2} by multiplying 3 by the reciprocal of \frac{7}{2}.

$$\frac{3}{3+3\times \frac{2}{7}}$$

Express 3\times \frac{2}{7} as a single fraction.

$$\frac{3}{3+\frac{3\times 2}{7}}$$

Multiply 3 and 2 to get 6.

$$\frac{3}{3+\frac{6}{7}}$$

Convert 3 to fraction \frac{21}{7}.

$$\frac{3}{\frac{21}{7}+\frac{6}{7}}$$

Since \frac{21}{7} and \frac{6}{7} have the same denominator, add them by adding their numerators.

$$\frac{3}{\frac{21+6}{7}}$$

Add 21 and 6 to get 27.

$$\frac{3}{\frac{27}{7}}$$

Divide 3 by \frac{27}{7} by multiplying 3 by the reciprocal of \frac{27}{7}.

$$3\times \frac{7}{27}$$

Express 3\times \frac{7}{27} as a single fraction.

$$\frac{3\times 7}{27}$$

Multiply 3 and 7 to get 21.

$$\frac{21}{27}$$

Reduce the fraction \frac{21}{27} to lowest terms by extracting and canceling out 3.

$$\frac{7}{9}$$

Factor

$$\frac{7}{3 ^ {2}} = 0.7777777777777778$$