Solve 10/4+11/9-10/7

$$\frac { 10 } { 4 } + \frac { 11 } { 9 } - \frac { 10 } { 7 }$$

Evaluate

$$\frac{289}{126}\approx 2.293650794$$

Solution Steps

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$\frac{5}{2}+\frac{11}{9}-\frac{10}{7}$$

Least common multiple of 2 and 9 is 18. Convert \frac{5}{2} and \frac{11}{9} to fractions with denominator 18.

$$\frac{45}{18}+\frac{22}{18}-\frac{10}{7}$$

Since \frac{45}{18} and \frac{22}{18} have the same denominator, add them by adding their numerators.

$$\frac{45+22}{18}-\frac{10}{7}$$

Add 45 and 22 to get 67.

$$\frac{67}{18}-\frac{10}{7}$$

Least common multiple of 18 and 7 is 126. Convert \frac{67}{18} and \frac{10}{7} to fractions with denominator 126.

$$\frac{469}{126}-\frac{180}{126}$$

Since \frac{469}{126} and \frac{180}{126} have the same denominator, subtract them by subtracting their numerators.

$$\frac{469-180}{126}$$

Subtract 180 from 469 to get 289.

$$\frac{289}{126}$$

Factor

$$\frac{17 ^ {2}}{2 \cdot 3 ^ {2} \cdot 7} = 2\frac{37}{126} = 2.2936507936507935$$