Solve (-4/13)+(-4/17)+4/13+(-13/17)

$$(- \frac{ 4 }{ 13 } )+(- \frac{ 4 }{ 17 } )+ \frac{ 4 }{ 13 } +(- \frac{ 13 }{ 17 } )$$

Evaluate

$$-1$$

Solution Steps

Least common multiple of 13 and 17 is 221. Convert -\frac{4}{13} and \frac{4}{17} to fractions with denominator 221.

$$-\frac{68}{221}-\frac{52}{221}+\frac{4}{13}-\frac{13}{17}$$

Since -\frac{68}{221} and \frac{52}{221} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-68-52}{221}+\frac{4}{13}-\frac{13}{17}$$

Subtract 52 from -68 to get -120.

$$-\frac{120}{221}+\frac{4}{13}-\frac{13}{17}$$

Least common multiple of 221 and 13 is 221. Convert -\frac{120}{221} and \frac{4}{13} to fractions with denominator 221.

$$-\frac{120}{221}+\frac{68}{221}-\frac{13}{17}$$

Since -\frac{120}{221} and \frac{68}{221} have the same denominator, add them by adding their numerators.

$$\frac{-120+68}{221}-\frac{13}{17}$$

Add -120 and 68 to get -52.

$$\frac{-52}{221}-\frac{13}{17}$$

Reduce the fraction \frac{-52}{221} to lowest terms by extracting and canceling out 13.

$$-\frac{4}{17}-\frac{13}{17}$$

Since -\frac{4}{17} and \frac{13}{17} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-4-13}{17}$$

Subtract 13 from -4 to get -17.

$$\frac{-17}{17}$$

Divide -17 by 17 to get -1.

$$-1$$

Factor

$$-1$$