Solve 17/111-26/111+120/11

$$\frac { 17 } { 111 } - \frac { 26 } { 111 } + \frac { 120 } { 11 }$$

Evaluate

$$\frac{4407}{407}\approx 10.828009828$$

Solution Steps

Since \frac{17}{111} and \frac{26}{111} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17-26}{111}+\frac{120}{11}$$

Subtract 26 from 17 to get -9.

$$\frac{-9}{111}+\frac{120}{11}$$

Reduce the fraction \frac{-9}{111} to lowest terms by extracting and canceling out 3.

$$-\frac{3}{37}+\frac{120}{11}$$

Least common multiple of 37 and 11 is 407. Convert -\frac{3}{37} and \frac{120}{11} to fractions with denominator 407.

$$-\frac{33}{407}+\frac{4440}{407}$$

Since -\frac{33}{407} and \frac{4440}{407} have the same denominator, add them by adding their numerators.

$$\frac{-33+4440}{407}$$

Add -33 and 4440 to get 4407.

$$\frac{4407}{407}$$

Factor

$$\frac{3 \cdot 13 \cdot 113}{11 \cdot 37} = 10\frac{337}{407} = 10.828009828009828$$