Solve 9/13-(9/13-2/11)+9/11

$$\frac{ 9 }{ 13 } -( \frac{ 9 }{ 13 } - \frac{ 2 }{ 11 } )+ \frac{ 9 }{ 11 }$$

Evaluate

$$1$$

Solution Steps

Least common multiple of 13 and 11 is 143. Convert \frac{9}{13} and \frac{2}{11} to fractions with denominator 143.

$$\frac{9}{13}-\left(\frac{99}{143}-\frac{26}{143}\right)+\frac{9}{11}$$

Since \frac{99}{143} and \frac{26}{143} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{13}-\frac{99-26}{143}+\frac{9}{11}$$

Subtract 26 from 99 to get 73.

$$\frac{9}{13}-\frac{73}{143}+\frac{9}{11}$$

Least common multiple of 13 and 143 is 143. Convert \frac{9}{13} and \frac{73}{143} to fractions with denominator 143.

$$\frac{99}{143}-\frac{73}{143}+\frac{9}{11}$$

Since \frac{99}{143} and \frac{73}{143} have the same denominator, subtract them by subtracting their numerators.

$$\frac{99-73}{143}+\frac{9}{11}$$

Subtract 73 from 99 to get 26.

$$\frac{26}{143}+\frac{9}{11}$$

Reduce the fraction \frac{26}{143} to lowest terms by extracting and canceling out 13.

$$\frac{2}{11}+\frac{9}{11}$$

Since \frac{2}{11} and \frac{9}{11} have the same denominator, add them by adding their numerators.

$$\frac{2+9}{11}$$

Add 2 and 9 to get 11.

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

Divide 11 by 11 to get 1.

$$1$$

Factor

$$1$$