Solve 11/3-35/6+51/9

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

Evaluate

$$\frac{47}{18}\approx 2.611111111$$

Solution Steps

Multiply 1 and 3 to get 3.

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

Add 3 and 1 to get 4.

$$\frac{4}{3}-\frac{3\times 6+5}{6}+\frac{5\times 9+1}{9}$$

Multiply 3 and 6 to get 18.

$$\frac{4}{3}-\frac{18+5}{6}+\frac{5\times 9+1}{9}$$

Add 18 and 5 to get 23.

$$\frac{4}{3}-\frac{23}{6}+\frac{5\times 9+1}{9}$$

Least common multiple of 3 and 6 is 6. Convert \frac{4}{3} and \frac{23}{6} to fractions with denominator 6.

$$\frac{8}{6}-\frac{23}{6}+\frac{5\times 9+1}{9}$$

Since \frac{8}{6} and \frac{23}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-23}{6}+\frac{5\times 9+1}{9}$$

Subtract 23 from 8 to get -15.

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

Reduce the fraction \frac{-15}{6} to lowest terms by extracting and canceling out 3.

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

Multiply 5 and 9 to get 45.

$$-\frac{5}{2}+\frac{45+1}{9}$$

Add 45 and 1 to get 46.

$$-\frac{5}{2}+\frac{46}{9}$$

Least common multiple of 2 and 9 is 18. Convert -\frac{5}{2} and \frac{46}{9} to fractions with denominator 18.

$$-\frac{45}{18}+\frac{92}{18}$$

Since -\frac{45}{18} and \frac{92}{18} have the same denominator, add them by adding their numerators.

$$\frac{-45+92}{18}$$

Add -45 and 92 to get 47.

$$\frac{47}{18}$$

Factor

$$\frac{47}{2 \cdot 3 ^ {2}} = 2\frac{11}{18} = 2.611111111111111$$