Solve 5/5+5{3+frac{5/5+5}}

$$\frac { 5 } { 5 + \frac { 5 } { 3 + \frac { 5 } { 5 + 5 } } }$$

Evaluate

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

Solution Steps

Add 5 and 5 to get 10.

$$\frac{5}{5+\frac{5}{3+\frac{5}{10}}}$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

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

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

$$\frac{5}{5+\frac{5}{\frac{6}{2}+\frac{1}{2}}}$$

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

$$\frac{5}{5+\frac{5}{\frac{6+1}{2}}}$$

Add 6 and 1 to get 7.

$$\frac{5}{5+\frac{5}{\frac{7}{2}}}$$

Divide 5 by \frac{7}{2} by multiplying 5 by the reciprocal of \frac{7}{2}.

$$\frac{5}{5+5\times \frac{2}{7}}$$

Express 5\times \frac{2}{7} as a single fraction.

$$\frac{5}{5+\frac{5\times 2}{7}}$$

Multiply 5 and 2 to get 10.

$$\frac{5}{5+\frac{10}{7}}$$

Convert 5 to fraction \frac{35}{7}.

$$\frac{5}{\frac{35}{7}+\frac{10}{7}}$$

Since \frac{35}{7} and \frac{10}{7} have the same denominator, add them by adding their numerators.

$$\frac{5}{\frac{35+10}{7}}$$

Add 35 and 10 to get 45.

$$\frac{5}{\frac{45}{7}}$$

Divide 5 by \frac{45}{7} by multiplying 5 by the reciprocal of \frac{45}{7}.

$$5\times \frac{7}{45}$$

Express 5\times \frac{7}{45} as a single fraction.

$$\frac{5\times 7}{45}$$

Multiply 5 and 7 to get 35.

$$\frac{35}{45}$$

Reduce the fraction \frac{35}{45} to lowest terms by extracting and canceling out 5.

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

Factor

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