Solve 45/11+(89/11-57/11)-38/11+1frac{3}{11}

$$4 \frac { 5 } { 11 } + ( 8 \frac { 9 } { 11 } - 5 \frac { 7 } { 11 } ) - 3 \frac { 8 } { 11 } + 1 \frac { 3 } { 11 }$$

Evaluate

$$\frac{57}{11}\approx 5.181818182$$

Solution Steps

Multiply 4 and 11 to get 44.

$$\frac{44+5}{11}+\frac{8\times 11+9}{11}-\frac{5\times 11+7}{11}-\frac{3\times 11+8}{11}+\frac{1\times 11+3}{11}$$

Add 44 and 5 to get 49.

$$\frac{49}{11}+\frac{8\times 11+9}{11}-\frac{5\times 11+7}{11}-\frac{3\times 11+8}{11}+\frac{1\times 11+3}{11}$$

Multiply 8 and 11 to get 88.

$$\frac{49}{11}+\frac{88+9}{11}-\frac{5\times 11+7}{11}-\frac{3\times 11+8}{11}+\frac{1\times 11+3}{11}$$

Add 88 and 9 to get 97.

$$\frac{49}{11}+\frac{97}{11}-\frac{5\times 11+7}{11}-\frac{3\times 11+8}{11}+\frac{1\times 11+3}{11}$$

Since \frac{49}{11} and \frac{97}{11} have the same denominator, add them by adding their numerators.

$$\frac{49+97}{11}-\frac{5\times 11+7}{11}-\frac{3\times 11+8}{11}+\frac{1\times 11+3}{11}$$

Add 49 and 97 to get 146.

$$\frac{146}{11}-\frac{5\times 11+7}{11}-\frac{3\times 11+8}{11}+\frac{1\times 11+3}{11}$$

Multiply 5 and 11 to get 55.

$$\frac{146}{11}-\frac{55+7}{11}-\frac{3\times 11+8}{11}+\frac{1\times 11+3}{11}$$

Add 55 and 7 to get 62.

$$\frac{146}{11}-\frac{62}{11}-\frac{3\times 11+8}{11}+\frac{1\times 11+3}{11}$$

Since \frac{146}{11} and \frac{62}{11} have the same denominator, subtract them by subtracting their numerators.

$$\frac{146-62}{11}-\frac{3\times 11+8}{11}+\frac{1\times 11+3}{11}$$

Subtract 62 from 146 to get 84.

$$\frac{84}{11}-\frac{3\times 11+8}{11}+\frac{1\times 11+3}{11}$$

Multiply 3 and 11 to get 33.

$$\frac{84}{11}-\frac{33+8}{11}+\frac{1\times 11+3}{11}$$

Add 33 and 8 to get 41.

$$\frac{84}{11}-\frac{41}{11}+\frac{1\times 11+3}{11}$$

Since \frac{84}{11} and \frac{41}{11} have the same denominator, subtract them by subtracting their numerators.

$$\frac{84-41}{11}+\frac{1\times 11+3}{11}$$

Subtract 41 from 84 to get 43.

$$\frac{43}{11}+\frac{1\times 11+3}{11}$$

Multiply 1 and 11 to get 11.

$$\frac{43}{11}+\frac{11+3}{11}$$

Add 11 and 3 to get 14.

$$\frac{43}{11}+\frac{14}{11}$$

Since \frac{43}{11} and \frac{14}{11} have the same denominator, add them by adding their numerators.

$$\frac{43+14}{11}$$

Add 43 and 14 to get 57.

$$\frac{57}{11}$$

Factor

$$\frac{3 \cdot 19}{11} = 5\frac{2}{11} = 5.181818181818182$$