Solve 2/2+2{3+frac{2/3+frac{2{3}}}*0.39}=?

$$\frac { 2 } { 2 + \frac { 2 } { 3 + \frac { 2 } { 3 + \frac { 2 } { 3 } } } \times 0.39 } = ?$$

Evaluate

$$\frac{100}{111}\approx 0.900900901$$

Solution Steps

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

$$\frac{2}{2+\frac{2}{3+\frac{2}{\frac{9}{3}+\frac{2}{3}}}\times 0.39}$$

Since \frac{9}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{2}{2+\frac{2}{3+\frac{2}{\frac{9+2}{3}}}\times 0.39}$$

Add 9 and 2 to get 11.

$$\frac{2}{2+\frac{2}{3+\frac{2}{\frac{11}{3}}}\times 0.39}$$

Divide 2 by \frac{11}{3} by multiplying 2 by the reciprocal of \frac{11}{3}.

$$\frac{2}{2+\frac{2}{3+2\times \frac{3}{11}}\times 0.39}$$

Express 2\times \frac{3}{11} as a single fraction.

$$\frac{2}{2+\frac{2}{3+\frac{2\times 3}{11}}\times 0.39}$$

Multiply 2 and 3 to get 6.

$$\frac{2}{2+\frac{2}{3+\frac{6}{11}}\times 0.39}$$

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

$$\frac{2}{2+\frac{2}{\frac{33}{11}+\frac{6}{11}}\times 0.39}$$

Since \frac{33}{11} and \frac{6}{11} have the same denominator, add them by adding their numerators.

$$\frac{2}{2+\frac{2}{\frac{33+6}{11}}\times 0.39}$$

Add 33 and 6 to get 39.

$$\frac{2}{2+\frac{2}{\frac{39}{11}}\times 0.39}$$

Divide 2 by \frac{39}{11} by multiplying 2 by the reciprocal of \frac{39}{11}.

$$\frac{2}{2+2\times \frac{11}{39}\times 0.39}$$

Express 2\times \frac{11}{39} as a single fraction.

$$\frac{2}{2+\frac{2\times 11}{39}\times 0.39}$$

Multiply 2 and 11 to get 22.

$$\frac{2}{2+\frac{22}{39}\times 0.39}$$

Convert decimal number 0.39 to fraction \frac{39}{100}.

$$\frac{2}{2+\frac{22}{39}\times \frac{39}{100}}$$

Multiply \frac{22}{39} times \frac{39}{100} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{2+\frac{22\times 39}{39\times 100}}$$

Cancel out 39 in both numerator and denominator.

$$\frac{2}{2+\frac{22}{100}}$$

Reduce the fraction \frac{22}{100} to lowest terms by extracting and canceling out 2.

$$\frac{2}{2+\frac{11}{50}}$$

Convert 2 to fraction \frac{100}{50}.

$$\frac{2}{\frac{100}{50}+\frac{11}{50}}$$

Since \frac{100}{50} and \frac{11}{50} have the same denominator, add them by adding their numerators.

$$\frac{2}{\frac{100+11}{50}}$$

Add 100 and 11 to get 111.

$$\frac{2}{\frac{111}{50}}$$

Divide 2 by \frac{111}{50} by multiplying 2 by the reciprocal of \frac{111}{50}.

$$2\times \frac{50}{111}$$

Express 2\times \frac{50}{111} as a single fraction.

$$\frac{2\times 50}{111}$$

Multiply 2 and 50 to get 100.

$$\frac{100}{111}$$

Factor

$$\frac{2 ^ {2} \cdot 5 ^ {2}}{3 \cdot 37} = 0.9009009009009009$$