Solve 115/13-(10/17+31/13)

$$11 \frac { 5 } { 13 } - ( \frac { 10 } { 17 } + \frac { 31 } { 13 } )$$

Evaluate

$$\frac{143}{17}\approx 8.411764706$$

Solution Steps

Multiply 11 and 13 to get 143.

$$\frac{143+5}{13}-\left(\frac{10}{17}+\frac{31}{13}\right)$$

Add 143 and 5 to get 148.

$$\frac{148}{13}-\left(\frac{10}{17}+\frac{31}{13}\right)$$

Least common multiple of 17 and 13 is 221. Convert \frac{10}{17} and \frac{31}{13} to fractions with denominator 221.

$$\frac{148}{13}-\left(\frac{130}{221}+\frac{527}{221}\right)$$

Since \frac{130}{221} and \frac{527}{221} have the same denominator, add them by adding their numerators.

$$\frac{148}{13}-\frac{130+527}{221}$$

Add 130 and 527 to get 657.

$$\frac{148}{13}-\frac{657}{221}$$

Least common multiple of 13 and 221 is 221. Convert \frac{148}{13} and \frac{657}{221} to fractions with denominator 221.

$$\frac{2516}{221}-\frac{657}{221}$$

Since \frac{2516}{221} and \frac{657}{221} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2516-657}{221}$$

Subtract 657 from 2516 to get 1859.

$$\frac{1859}{221}$$

Reduce the fraction \frac{1859}{221} to lowest terms by extracting and canceling out 13.

$$\frac{143}{17}$$

Factor

$$\frac{11 \cdot 13}{17} = 8\frac{7}{17} = 8.411764705882353$$