Solve 1+2/3+frac{4{5+6}}

$$1 + \frac { 2 } { 3 + \frac { 4 } { 5 + 6 } }$$

Evaluate

$$\frac{59}{37}\approx 1.594594595$$

Solution Steps

Add 5 and 6 to get 11.

$$1+\frac{2}{3+\frac{4}{11}}$$

Convert 3 to fraction \frac{33}{11}.

$$1+\frac{2}{\frac{33}{11}+\frac{4}{11}}$$

Since \frac{33}{11} and \frac{4}{11} have the same denominator, add them by adding their numerators.

$$1+\frac{2}{\frac{33+4}{11}}$$

Add 33 and 4 to get 37.

$$1+\frac{2}{\frac{37}{11}}$$

Divide 2 by \frac{37}{11} by multiplying 2 by the reciprocal of \frac{37}{11}.

$$1+2\times \frac{11}{37}$$

Express 2\times \frac{11}{37} as a single fraction.

$$1+\frac{2\times 11}{37}$$

Multiply 2 and 11 to get 22.

$$1+\frac{22}{37}$$

Convert 1 to fraction \frac{37}{37}.

$$\frac{37}{37}+\frac{22}{37}$$

Since \frac{37}{37} and \frac{22}{37} have the same denominator, add them by adding their numerators.

$$\frac{37+22}{37}$$

Add 37 and 22 to get 59.

$$\frac{59}{37}$$

Factor

$$\frac{59}{37} = 1\frac{22}{37} = 1.5945945945945945$$