Solve 3+3+3+1/4/9/frac{2{2}}

$$3+ \frac{ 3+ \frac{ 3+ \frac{ 1 }{ 4 } }{ 9 } }{ \frac{ 2 }{ 2 } }$$

Evaluate

$$\frac{229}{36}\approx 6.361111111$$

Solution Steps

Divide 2 by 2 to get 1.

$$3+\frac{3+\frac{3+\frac{1}{4}}{9}}{1}$$

Convert 3 to fraction \frac{12}{4}.

$$3+\frac{3+\frac{\frac{12}{4}+\frac{1}{4}}{9}}{1}$$

Since \frac{12}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$3+\frac{3+\frac{\frac{12+1}{4}}{9}}{1}$$

Add 12 and 1 to get 13.

$$3+\frac{3+\frac{\frac{13}{4}}{9}}{1}$$

Express \frac{\frac{13}{4}}{9} as a single fraction.

$$3+\frac{3+\frac{13}{4\times 9}}{1}$$

Multiply 4 and 9 to get 36.

$$3+\frac{3+\frac{13}{36}}{1}$$

Convert 3 to fraction \frac{108}{36}.

$$3+\frac{\frac{108}{36}+\frac{13}{36}}{1}$$

Since \frac{108}{36} and \frac{13}{36} have the same denominator, add them by adding their numerators.

$$3+\frac{\frac{108+13}{36}}{1}$$

Add 108 and 13 to get 121.

$$3+\frac{\frac{121}{36}}{1}$$

Anything divided by one gives itself.

$$3+\frac{121}{36}$$

Convert 3 to fraction \frac{108}{36}.

$$\frac{108}{36}+\frac{121}{36}$$

Since \frac{108}{36} and \frac{121}{36} have the same denominator, add them by adding their numerators.

$$\frac{108+121}{36}$$

Add 108 and 121 to get 229.

$$\frac{229}{36}$$

Factor

$$\frac{229}{2 ^ {2} \cdot 3 ^ {2}} = 6\frac{13}{36} = 6.361111111111111$$