Solve 191/3-(81/9+31/6)

$$19 \frac { 1 } { 3 } - ( 8 \frac { 1 } { 9 } + 3 \frac { 1 } { 6 } )$$

Evaluate

$$\frac{145}{18}\approx 8.055555556$$

Solution Steps

Multiply 19 and 3 to get 57.

$$\frac{57+1}{3}-\left(\frac{8\times 9+1}{9}+\frac{3\times 6+1}{6}\right)$$

Add 57 and 1 to get 58.

$$\frac{58}{3}-\left(\frac{8\times 9+1}{9}+\frac{3\times 6+1}{6}\right)$$

Multiply 8 and 9 to get 72.

$$\frac{58}{3}-\left(\frac{72+1}{9}+\frac{3\times 6+1}{6}\right)$$

Add 72 and 1 to get 73.

$$\frac{58}{3}-\left(\frac{73}{9}+\frac{3\times 6+1}{6}\right)$$

Multiply 3 and 6 to get 18.

$$\frac{58}{3}-\left(\frac{73}{9}+\frac{18+1}{6}\right)$$

Add 18 and 1 to get 19.

$$\frac{58}{3}-\left(\frac{73}{9}+\frac{19}{6}\right)$$

Least common multiple of 9 and 6 is 18. Convert \frac{73}{9} and \frac{19}{6} to fractions with denominator 18.

$$\frac{58}{3}-\left(\frac{146}{18}+\frac{57}{18}\right)$$

Since \frac{146}{18} and \frac{57}{18} have the same denominator, add them by adding their numerators.

$$\frac{58}{3}-\frac{146+57}{18}$$

Add 146 and 57 to get 203.

$$\frac{58}{3}-\frac{203}{18}$$

Least common multiple of 3 and 18 is 18. Convert \frac{58}{3} and \frac{203}{18} to fractions with denominator 18.

$$\frac{348}{18}-\frac{203}{18}$$

Since \frac{348}{18} and \frac{203}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{348-203}{18}$$

Subtract 203 from 348 to get 145.

$$\frac{145}{18}$$

Factor

$$\frac{5 \cdot 29}{2 \cdot 3 ^ {2}} = 8\frac{1}{18} = 8.055555555555555$$