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

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

Evaluate

$$\frac{10}{11}\approx 0.909090909$$

Solution Steps

Add 5 and 5 to get 10.

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

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

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

Convert 5 to fraction \frac{10}{2}.

$$\frac{5}{\frac{10}{2}+\frac{1}{2}}$$

Since \frac{10}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{5}{\frac{10+1}{2}}$$

Add 10 and 1 to get 11.

$$\frac{5}{\frac{11}{2}}$$

Divide 5 by \frac{11}{2} by multiplying 5 by the reciprocal of \frac{11}{2}.

$$5\times \frac{2}{11}$$

Express 5\times \frac{2}{11} as a single fraction.

$$\frac{5\times 2}{11}$$

Multiply 5 and 2 to get 10.

$$\frac{10}{11}$$

Factor

$$\frac{2 \cdot 5}{11} = 0.9090909090909091$$