Solve (39/13+5/11-4/13+6/11

$$( 3 \frac { 9 } { 13 } + \frac { 5 } { 11 } - \frac { 4 } { 13 } + \frac { 6 } { 11 }$$

Evaluate

$$\frac{57}{13}\approx 4.384615385$$

Solution Steps

Multiply 3 and 13 to get 39.

$$\frac{39+9}{13}+\frac{5}{11}-\frac{4}{13}+\frac{6}{11}$$

Add 39 and 9 to get 48.

$$\frac{48}{13}+\frac{5}{11}-\frac{4}{13}+\frac{6}{11}$$

Least common multiple of 13 and 11 is 143. Convert \frac{48}{13} and \frac{5}{11} to fractions with denominator 143.

$$\frac{528}{143}+\frac{65}{143}-\frac{4}{13}+\frac{6}{11}$$

Since \frac{528}{143} and \frac{65}{143} have the same denominator, add them by adding their numerators.

$$\frac{528+65}{143}-\frac{4}{13}+\frac{6}{11}$$

Add 528 and 65 to get 593.

$$\frac{593}{143}-\frac{4}{13}+\frac{6}{11}$$

Least common multiple of 143 and 13 is 143. Convert \frac{593}{143} and \frac{4}{13} to fractions with denominator 143.

$$\frac{593}{143}-\frac{44}{143}+\frac{6}{11}$$

Since \frac{593}{143} and \frac{44}{143} have the same denominator, subtract them by subtracting their numerators.

$$\frac{593-44}{143}+\frac{6}{11}$$

Subtract 44 from 593 to get 549.

$$\frac{549}{143}+\frac{6}{11}$$

Least common multiple of 143 and 11 is 143. Convert \frac{549}{143} and \frac{6}{11} to fractions with denominator 143.

$$\frac{549}{143}+\frac{78}{143}$$

Since \frac{549}{143} and \frac{78}{143} have the same denominator, add them by adding their numerators.

$$\frac{549+78}{143}$$

Add 549 and 78 to get 627.

$$\frac{627}{143}$$

Reduce the fraction \frac{627}{143} to lowest terms by extracting and canceling out 11.

$$\frac{57}{13}$$

Factor

$$\frac{3 \cdot 19}{13} = 4\frac{5}{13} = 4.384615384615385$$