Solve 3+1+1+frac{1/3/frac{1{3}}}{1/frac{1{3}}}

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

Evaluate

$$\frac{14}{3}\approx 4.666666667$$

Solution Steps

Convert 1 to fraction \frac{3}{3}.

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

Since \frac{3}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

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

Add 3 and 1 to get 4.

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

Divide \frac{4}{3} by \frac{1}{3} by multiplying \frac{4}{3} by the reciprocal of \frac{1}{3}.

$$3+\frac{1+\frac{4}{3}\times 3}{\frac{1}{\frac{1}{3}}}$$

Cancel out 3 and 3.

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

Add 1 and 4 to get 5.

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

Divide 1 by \frac{1}{3} by multiplying 1 by the reciprocal of \frac{1}{3}.

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

Multiply 1 and 3 to get 3.

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

Convert 3 to fraction \frac{9}{3}.

$$\frac{9}{3}+\frac{5}{3}$$

Since \frac{9}{3} and \frac{5}{3} have the same denominator, add them by adding their numerators.

$$\frac{9+5}{3}$$

Add 9 and 5 to get 14.

$$\frac{14}{3}$$

Factor

$$\frac{2 \cdot 7}{3} = 4\frac{2}{3} = 4.666666666666667$$