Solve 111/9-32/5-1/6

$$11 \frac { 1 } { 9 } - 3 \frac { 2 } { 5 } - \frac { 1 } { 6 }$$

Evaluate

$$\frac{679}{90}\approx 7.544444444$$

Solution Steps

Multiply 11 and 9 to get 99.

$$\frac{99+1}{9}-\frac{3\times 5+2}{5}-\frac{1}{6}$$

Add 99 and 1 to get 100.

$$\frac{100}{9}-\frac{3\times 5+2}{5}-\frac{1}{6}$$

Multiply 3 and 5 to get 15.

$$\frac{100}{9}-\frac{15+2}{5}-\frac{1}{6}$$

Add 15 and 2 to get 17.

$$\frac{100}{9}-\frac{17}{5}-\frac{1}{6}$$

Least common multiple of 9 and 5 is 45. Convert \frac{100}{9} and \frac{17}{5} to fractions with denominator 45.

$$\frac{500}{45}-\frac{153}{45}-\frac{1}{6}$$

Since \frac{500}{45} and \frac{153}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{500-153}{45}-\frac{1}{6}$$

Subtract 153 from 500 to get 347.

$$\frac{347}{45}-\frac{1}{6}$$

Least common multiple of 45 and 6 is 90. Convert \frac{347}{45} and \frac{1}{6} to fractions with denominator 90.

$$\frac{694}{90}-\frac{15}{90}$$

Since \frac{694}{90} and \frac{15}{90} have the same denominator, subtract them by subtracting their numerators.

$$\frac{694-15}{90}$$

Subtract 15 from 694 to get 679.

$$\frac{679}{90}$$

Factor

$$\frac{7 \cdot 97}{2 \cdot 3 ^ {2} \cdot 5} = 7\frac{49}{90} = 7.544444444444444$$