Solve 2/3+31/6+42/9+25/18

$$\frac { 2 } { 3 } + 3 \frac { 1 } { 6 } + 4 \frac { 2 } { 9 } + 2 \frac { 5 } { 18 }$$

Evaluate

$$\frac{31}{3}\approx 10.333333333$$

Solution Steps

Multiply 3 and 6 to get 18.

$$\frac{2}{3}+\frac{18+1}{6}+\frac{4\times 9+2}{9}+\frac{2\times 18+5}{18}$$

Add 18 and 1 to get 19.

$$\frac{2}{3}+\frac{19}{6}+\frac{4\times 9+2}{9}+\frac{2\times 18+5}{18}$$

Least common multiple of 3 and 6 is 6. Convert \frac{2}{3} and \frac{19}{6} to fractions with denominator 6.

$$\frac{4}{6}+\frac{19}{6}+\frac{4\times 9+2}{9}+\frac{2\times 18+5}{18}$$

Since \frac{4}{6} and \frac{19}{6} have the same denominator, add them by adding their numerators.

$$\frac{4+19}{6}+\frac{4\times 9+2}{9}+\frac{2\times 18+5}{18}$$

Add 4 and 19 to get 23.

$$\frac{23}{6}+\frac{4\times 9+2}{9}+\frac{2\times 18+5}{18}$$

Multiply 4 and 9 to get 36.

$$\frac{23}{6}+\frac{36+2}{9}+\frac{2\times 18+5}{18}$$

Add 36 and 2 to get 38.

$$\frac{23}{6}+\frac{38}{9}+\frac{2\times 18+5}{18}$$

Least common multiple of 6 and 9 is 18. Convert \frac{23}{6} and \frac{38}{9} to fractions with denominator 18.

$$\frac{69}{18}+\frac{76}{18}+\frac{2\times 18+5}{18}$$

Since \frac{69}{18} and \frac{76}{18} have the same denominator, add them by adding their numerators.

$$\frac{69+76}{18}+\frac{2\times 18+5}{18}$$

Add 69 and 76 to get 145.

$$\frac{145}{18}+\frac{2\times 18+5}{18}$$

Multiply 2 and 18 to get 36.

$$\frac{145}{18}+\frac{36+5}{18}$$

Add 36 and 5 to get 41.

$$\frac{145}{18}+\frac{41}{18}$$

Since \frac{145}{18} and \frac{41}{18} have the same denominator, add them by adding their numerators.

$$\frac{145+41}{18}$$

Add 145 and 41 to get 186.

$$\frac{186}{18}$$

Reduce the fraction \frac{186}{18} to lowest terms by extracting and canceling out 6.

$$\frac{31}{3}$$

Factor

$$\frac{31}{3} = 10\frac{1}{3} = 10.333333333333334$$