Solve 2/3+92/3+992/3+9992/3=

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

Evaluate

$$\frac{3163}{3}\approx 1054.333333333$$

Solution Steps

Multiply 9 and 3 to get 27.

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

Add 27 and 2 to get 29.

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

Since \frac{2}{3} and \frac{29}{3} have the same denominator, add them by adding their numerators.

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

Add 2 and 29 to get 31.

$$\frac{31}{3}+9\times \frac{9\times 3+2}{3}+99\times \frac{9\times 3+2}{3}$$

Multiply 9 and 3 to get 27.

$$\frac{31}{3}+9\times \frac{27+2}{3}+99\times \frac{9\times 3+2}{3}$$

Add 27 and 2 to get 29.

$$\frac{31}{3}+9\times \frac{29}{3}+99\times \frac{9\times 3+2}{3}$$

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

$$\frac{31}{3}+\frac{9\times 29}{3}+99\times \frac{9\times 3+2}{3}$$

Multiply 9 and 29 to get 261.

$$\frac{31}{3}+\frac{261}{3}+99\times \frac{9\times 3+2}{3}$$

Since \frac{31}{3} and \frac{261}{3} have the same denominator, add them by adding their numerators.

$$\frac{31+261}{3}+99\times \frac{9\times 3+2}{3}$$

Add 31 and 261 to get 292.

$$\frac{292}{3}+99\times \frac{9\times 3+2}{3}$$

Multiply 9 and 3 to get 27.

$$\frac{292}{3}+99\times \frac{27+2}{3}$$

Add 27 and 2 to get 29.

$$\frac{292}{3}+99\times \frac{29}{3}$$

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

$$\frac{292}{3}+\frac{99\times 29}{3}$$

Multiply 99 and 29 to get 2871.

$$\frac{292}{3}+\frac{2871}{3}$$

Since \frac{292}{3} and \frac{2871}{3} have the same denominator, add them by adding their numerators.

$$\frac{292+2871}{3}$$

Add 292 and 2871 to get 3163.

$$\frac{3163}{3}$$

Factor

$$\frac{3163}{3} = 1054\frac{1}{3} = 1054.3333333333333$$