Solve 21/3+11/6+75/9

$$2 \frac { 1 } { 3 } + 1 \frac { 1 } { 6 } + 7 \frac { 5 } { 9 }$$

Evaluate

$$\frac{199}{18}\approx 11.055555556$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{6+1}{3}+\frac{1\times 6+1}{6}+\frac{7\times 9+5}{9}$$

Add 6 and 1 to get 7.

$$\frac{7}{3}+\frac{1\times 6+1}{6}+\frac{7\times 9+5}{9}$$

Multiply 1 and 6 to get 6.

$$\frac{7}{3}+\frac{6+1}{6}+\frac{7\times 9+5}{9}$$

Add 6 and 1 to get 7.

$$\frac{7}{3}+\frac{7}{6}+\frac{7\times 9+5}{9}$$

Least common multiple of 3 and 6 is 6. Convert \frac{7}{3} and \frac{7}{6} to fractions with denominator 6.

$$\frac{14}{6}+\frac{7}{6}+\frac{7\times 9+5}{9}$$

Since \frac{14}{6} and \frac{7}{6} have the same denominator, add them by adding their numerators.

$$\frac{14+7}{6}+\frac{7\times 9+5}{9}$$

Add 14 and 7 to get 21.

$$\frac{21}{6}+\frac{7\times 9+5}{9}$$

Reduce the fraction \frac{21}{6} to lowest terms by extracting and canceling out 3.

$$\frac{7}{2}+\frac{7\times 9+5}{9}$$

Multiply 7 and 9 to get 63.

$$\frac{7}{2}+\frac{63+5}{9}$$

Add 63 and 5 to get 68.

$$\frac{7}{2}+\frac{68}{9}$$

Least common multiple of 2 and 9 is 18. Convert \frac{7}{2} and \frac{68}{9} to fractions with denominator 18.

$$\frac{63}{18}+\frac{136}{18}$$

Since \frac{63}{18} and \frac{136}{18} have the same denominator, add them by adding their numerators.

$$\frac{63+136}{18}$$

Add 63 and 136 to get 199.

$$\frac{199}{18}$$

Factor

$$\frac{199}{2 \cdot 3 ^ {2}} = 11\frac{1}{18} = 11.055555555555555$$