Solve {r}{151/2+72/3}{-91/9}

$$\left. \begin{array} { r } { 15 \frac { 1 } { 2 } + 7 \frac { 2 } { 3 } } \\ { - 9 \frac { 1 } { 9 } } \end{array} \right.$$

Evaluate

$$\frac{253}{18}\approx 14.055555556$$

Solution Steps

Multiply 15 and 2 to get 30.

$$\frac{30+1}{2}+\frac{7\times 3+2}{3}-\frac{9\times 9+1}{9}$$

Add 30 and 1 to get 31.

$$\frac{31}{2}+\frac{7\times 3+2}{3}-\frac{9\times 9+1}{9}$$

Multiply 7 and 3 to get 21.

$$\frac{31}{2}+\frac{21+2}{3}-\frac{9\times 9+1}{9}$$

Add 21 and 2 to get 23.

$$\frac{31}{2}+\frac{23}{3}-\frac{9\times 9+1}{9}$$

Least common multiple of 2 and 3 is 6. Convert \frac{31}{2} and \frac{23}{3} to fractions with denominator 6.

$$\frac{93}{6}+\frac{46}{6}-\frac{9\times 9+1}{9}$$

Since \frac{93}{6} and \frac{46}{6} have the same denominator, add them by adding their numerators.

$$\frac{93+46}{6}-\frac{9\times 9+1}{9}$$

Add 93 and 46 to get 139.

$$\frac{139}{6}-\frac{9\times 9+1}{9}$$

Multiply 9 and 9 to get 81.

$$\frac{139}{6}-\frac{81+1}{9}$$

Add 81 and 1 to get 82.

$$\frac{139}{6}-\frac{82}{9}$$

Least common multiple of 6 and 9 is 18. Convert \frac{139}{6} and \frac{82}{9} to fractions with denominator 18.

$$\frac{417}{18}-\frac{164}{18}$$

Since \frac{417}{18} and \frac{164}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{417-164}{18}$$

Subtract 164 from 417 to get 253.

$$\frac{253}{18}$$

Factor

$$\frac{11 \cdot 23}{2 \cdot 3 ^ {2}} = 14\frac{1}{18} = 14.055555555555555$$