Solve 73/4+(-54/11)-(-31/4)+67/11

$$7 \frac { 3 } { 4 } + ( - 5 \frac { 4 } { 11 } ) - ( - 3 \frac { 1 } { 4 } ) + 6 \frac { 7 } { 11 }$$

Evaluate

$$\frac{135}{11}\approx 12.272727273$$

Solution Steps

Multiply 7 and 4 to get 28.

$$\frac{28+3}{4}-\frac{5\times 11+4}{11}-\left(-\frac{3\times 4+1}{4}\right)+\frac{6\times 11+7}{11}$$

Add 28 and 3 to get 31.

$$\frac{31}{4}-\frac{5\times 11+4}{11}-\left(-\frac{3\times 4+1}{4}\right)+\frac{6\times 11+7}{11}$$

Multiply 5 and 11 to get 55.

$$\frac{31}{4}-\frac{55+4}{11}-\left(-\frac{3\times 4+1}{4}\right)+\frac{6\times 11+7}{11}$$

Add 55 and 4 to get 59.

$$\frac{31}{4}-\frac{59}{11}-\left(-\frac{3\times 4+1}{4}\right)+\frac{6\times 11+7}{11}$$

Least common multiple of 4 and 11 is 44. Convert \frac{31}{4} and \frac{59}{11} to fractions with denominator 44.

$$\frac{341}{44}-\frac{236}{44}-\left(-\frac{3\times 4+1}{4}\right)+\frac{6\times 11+7}{11}$$

Since \frac{341}{44} and \frac{236}{44} have the same denominator, subtract them by subtracting their numerators.

$$\frac{341-236}{44}-\left(-\frac{3\times 4+1}{4}\right)+\frac{6\times 11+7}{11}$$

Subtract 236 from 341 to get 105.

$$\frac{105}{44}-\left(-\frac{3\times 4+1}{4}\right)+\frac{6\times 11+7}{11}$$

Multiply 3 and 4 to get 12.

$$\frac{105}{44}-\left(-\frac{12+1}{4}\right)+\frac{6\times 11+7}{11}$$

Add 12 and 1 to get 13.

$$\frac{105}{44}-\left(-\frac{13}{4}\right)+\frac{6\times 11+7}{11}$$

The opposite of -\frac{13}{4} is \frac{13}{4}.

$$\frac{105}{44}+\frac{13}{4}+\frac{6\times 11+7}{11}$$

Least common multiple of 44 and 4 is 44. Convert \frac{105}{44} and \frac{13}{4} to fractions with denominator 44.

$$\frac{105}{44}+\frac{143}{44}+\frac{6\times 11+7}{11}$$

Since \frac{105}{44} and \frac{143}{44} have the same denominator, add them by adding their numerators.

$$\frac{105+143}{44}+\frac{6\times 11+7}{11}$$

Add 105 and 143 to get 248.

$$\frac{248}{44}+\frac{6\times 11+7}{11}$$

Reduce the fraction \frac{248}{44} to lowest terms by extracting and canceling out 4.

$$\frac{62}{11}+\frac{6\times 11+7}{11}$$

Multiply 6 and 11 to get 66.

$$\frac{62}{11}+\frac{66+7}{11}$$

Add 66 and 7 to get 73.

$$\frac{62}{11}+\frac{73}{11}$$

Since \frac{62}{11} and \frac{73}{11} have the same denominator, add them by adding their numerators.

$$\frac{62+73}{11}$$

Add 62 and 73 to get 135.

$$\frac{135}{11}$$

Factor

$$\frac{3 ^ {3} \cdot 5}{11} = 12\frac{3}{11} = 12.272727272727273$$