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

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

Evaluate

$$\frac{46}{9}\approx 5.111111111$$

Solution Steps

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

$$\frac{4\left(\frac{4}{3}+1\right)}{3}+2$$

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

$$\frac{4\left(\frac{4}{3}+\frac{3}{3}\right)}{3}+2$$

Since \frac{4}{3} and \frac{3}{3} have the same denominator, add them by adding their numerators.

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

Add 4 and 3 to get 7.

$$\frac{4\times \frac{7}{3}}{3}+2$$

Express 4\times \frac{7}{3} as a single fraction.

$$\frac{\frac{4\times 7}{3}}{3}+2$$

Multiply 4 and 7 to get 28.

$$\frac{\frac{28}{3}}{3}+2$$

Express \frac{\frac{28}{3}}{3} as a single fraction.

$$\frac{28}{3\times 3}+2$$

Multiply 3 and 3 to get 9.

$$\frac{28}{9}+2$$

Convert 2 to fraction \frac{18}{9}.

$$\frac{28}{9}+\frac{18}{9}$$

Since \frac{28}{9} and \frac{18}{9} have the same denominator, add them by adding their numerators.

$$\frac{28+18}{9}$$

Add 28 and 18 to get 46.

$$\frac{46}{9}$$

Factor

$$\frac{2 \cdot 23}{3 ^ {2}} = 5\frac{1}{9} = 5.111111111111111$$