Solve 92/3+992/3+9992/3

$$9 \frac { 2 } { 3 } + 99 \frac { 2 } { 3 } + 999 \frac { 2 } { 3 }$$

Evaluate

$$\frac{3161}{3}\approx 1053.666666667$$

Solution Steps

Multiply 9 and 3 to get 27.

$$\frac{27+2}{3}+9\times \frac{9\times 3+2}{3}+99\times \frac{9\times 3+2}{3}$$

Add 27 and 2 to get 29.

$$\frac{29}{3}+9\times \frac{9\times 3+2}{3}+99\times \frac{9\times 3+2}{3}$$

Multiply 9 and 3 to get 27.

$$\frac{29}{3}+9\times \frac{27+2}{3}+99\times \frac{9\times 3+2}{3}$$

Add 27 and 2 to get 29.

$$\frac{29}{3}+9\times \frac{29}{3}+99\times \frac{9\times 3+2}{3}$$

Express 9\times \frac{29}{3} as a single fraction.

$$\frac{29}{3}+\frac{9\times 29}{3}+99\times \frac{9\times 3+2}{3}$$

Multiply 9 and 29 to get 261.

$$\frac{29}{3}+\frac{261}{3}+99\times \frac{9\times 3+2}{3}$$

Since \frac{29}{3} and \frac{261}{3} have the same denominator, add them by adding their numerators.

$$\frac{29+261}{3}+99\times \frac{9\times 3+2}{3}$$

Add 29 and 261 to get 290.

$$\frac{290}{3}+99\times \frac{9\times 3+2}{3}$$

Multiply 9 and 3 to get 27.

$$\frac{290}{3}+99\times \frac{27+2}{3}$$

Add 27 and 2 to get 29.

$$\frac{290}{3}+99\times \frac{29}{3}$$

Express 99\times \frac{29}{3} as a single fraction.

$$\frac{290}{3}+\frac{99\times 29}{3}$$

Multiply 99 and 29 to get 2871.

$$\frac{290}{3}+\frac{2871}{3}$$

Since \frac{290}{3} and \frac{2871}{3} have the same denominator, add them by adding their numerators.

$$\frac{290+2871}{3}$$

Add 290 and 2871 to get 3161.

$$\frac{3161}{3}$$

Factor

$$\frac{29 \cdot 109}{3} = 1053\frac{2}{3} = 1053.6666666666667$$