Solve 55/9-23/8

$$5 \frac { 5 } { 9 } - 2 \frac { 3 } { 8 }$$

Evaluate

$$\frac{229}{72}\approx 3.180555556$$

Solution Steps

Multiply 5 and 9 to get 45.

$$\frac{45+5}{9}-\frac{2\times 8+3}{8}$$

Add 45 and 5 to get 50.

$$\frac{50}{9}-\frac{2\times 8+3}{8}$$

Multiply 2 and 8 to get 16.

$$\frac{50}{9}-\frac{16+3}{8}$$

Add 16 and 3 to get 19.

$$\frac{50}{9}-\frac{19}{8}$$

Least common multiple of 9 and 8 is 72. Convert \frac{50}{9} and \frac{19}{8} to fractions with denominator 72.

$$\frac{400}{72}-\frac{171}{72}$$

Since \frac{400}{72} and \frac{171}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{400-171}{72}$$

Subtract 171 from 400 to get 229.

$$\frac{229}{72}$$

Factor

$$\frac{229}{2 ^ {3} \cdot 3 ^ {2}} = 3\frac{13}{72} = 3.1805555555555554$$