Solve 9-3/1+6{1+frac{2/3}}

$$9- \frac{ 3 }{ 1+ \frac{ 6 }{ 1+ \frac{ 2 }{ 3 } } }$$

Evaluate

$$\frac{192}{23}\approx 8.347826087$$

Solution Steps

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

$$9-\frac{3}{1+\frac{6}{\frac{3}{3}+\frac{2}{3}}}$$

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

$$9-\frac{3}{1+\frac{6}{\frac{3+2}{3}}}$$

Add 3 and 2 to get 5.

$$9-\frac{3}{1+\frac{6}{\frac{5}{3}}}$$

Divide 6 by \frac{5}{3} by multiplying 6 by the reciprocal of \frac{5}{3}.

$$9-\frac{3}{1+6\times \frac{3}{5}}$$

Express 6\times \frac{3}{5} as a single fraction.

$$9-\frac{3}{1+\frac{6\times 3}{5}}$$

Multiply 6 and 3 to get 18.

$$9-\frac{3}{1+\frac{18}{5}}$$

Convert 1 to fraction \frac{5}{5}.

$$9-\frac{3}{\frac{5}{5}+\frac{18}{5}}$$

Since \frac{5}{5} and \frac{18}{5} have the same denominator, add them by adding their numerators.

$$9-\frac{3}{\frac{5+18}{5}}$$

Add 5 and 18 to get 23.

$$9-\frac{3}{\frac{23}{5}}$$

Divide 3 by \frac{23}{5} by multiplying 3 by the reciprocal of \frac{23}{5}.

$$9-3\times \frac{5}{23}$$

Express 3\times \frac{5}{23} as a single fraction.

$$9-\frac{3\times 5}{23}$$

Multiply 3 and 5 to get 15.

$$9-\frac{15}{23}$$

Convert 9 to fraction \frac{207}{23}.

$$\frac{207}{23}-\frac{15}{23}$$

Since \frac{207}{23} and \frac{15}{23} have the same denominator, subtract them by subtracting their numerators.

$$\frac{207-15}{23}$$

Subtract 15 from 207 to get 192.

$$\frac{192}{23}$$

Factor

$$\frac{2 ^ {6} \cdot 3}{23} = 8\frac{8}{23} = 8.347826086956522$$