Solve 3+3+3+1/4/9/2

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

Evaluate

$$\frac{337}{72}\approx 4.680555556$$

Solution Steps

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

$$3+\frac{3+\frac{\frac{12}{4}+\frac{1}{4}}{9}}{2}$$

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

$$3+\frac{3+\frac{\frac{12+1}{4}}{9}}{2}$$

Add 12 and 1 to get 13.

$$3+\frac{3+\frac{\frac{13}{4}}{9}}{2}$$

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

$$3+\frac{3+\frac{13}{4\times 9}}{2}$$

Multiply 4 and 9 to get 36.

$$3+\frac{3+\frac{13}{36}}{2}$$

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

$$3+\frac{\frac{108}{36}+\frac{13}{36}}{2}$$

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

$$3+\frac{\frac{108+13}{36}}{2}$$

Add 108 and 13 to get 121.

$$3+\frac{\frac{121}{36}}{2}$$

Express \frac{\frac{121}{36}}{2} as a single fraction.

$$3+\frac{121}{36\times 2}$$

Multiply 36 and 2 to get 72.

$$3+\frac{121}{72}$$

Convert 3 to fraction \frac{216}{72}.

$$\frac{216}{72}+\frac{121}{72}$$

Since \frac{216}{72} and \frac{121}{72} have the same denominator, add them by adding their numerators.

$$\frac{216+121}{72}$$

Add 216 and 121 to get 337.

$$\frac{337}{72}$$

Factor

$$\frac{337}{2 ^ {3} \cdot 3 ^ {2}} = 4\frac{49}{72} = 4.680555555555555$$