Solve {l}{2/3+5/6+7/9}{34/9*6}

$$\left. \begin{array} { l } { \frac { 2 } { 3 } + \frac { 5 } { 6 } + \frac { 7 } { 9 } } \\ { 3 \frac { 4 } { 9 } \times 6 } \end{array} \right.$$

Sort

$$\frac{41}{18},\ \frac{62}{3}$$

Solution Steps

Least common multiple of 3 and 6 is 6. Convert \frac{2}{3} and \frac{5}{6} to fractions with denominator 6.

$$sort(\frac{4}{6}+\frac{5}{6}+\frac{7}{9},\frac{3\times 9+4}{9}\times 6)$$

Since \frac{4}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$sort(\frac{4+5}{6}+\frac{7}{9},\frac{3\times 9+4}{9}\times 6)$$

Add 4 and 5 to get 9.

$$sort(\frac{9}{6}+\frac{7}{9},\frac{3\times 9+4}{9}\times 6)$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

$$sort(\frac{3}{2}+\frac{7}{9},\frac{3\times 9+4}{9}\times 6)$$

Least common multiple of 2 and 9 is 18. Convert \frac{3}{2} and \frac{7}{9} to fractions with denominator 18.

$$sort(\frac{27}{18}+\frac{14}{18},\frac{3\times 9+4}{9}\times 6)$$

Since \frac{27}{18} and \frac{14}{18} have the same denominator, add them by adding their numerators.

$$sort(\frac{27+14}{18},\frac{3\times 9+4}{9}\times 6)$$

Add 27 and 14 to get 41.

$$sort(\frac{41}{18},\frac{3\times 9+4}{9}\times 6)$$

Multiply 3 and 9 to get 27.

$$sort(\frac{41}{18},\frac{27+4}{9}\times 6)$$

Add 27 and 4 to get 31.

$$sort(\frac{41}{18},\frac{31}{9}\times 6)$$

Express \frac{31}{9}\times 6 as a single fraction.

$$sort(\frac{41}{18},\frac{31\times 6}{9})$$

Multiply 31 and 6 to get 186.

$$sort(\frac{41}{18},\frac{186}{9})$$

Reduce the fraction \frac{186}{9} to lowest terms by extracting and canceling out 3.

$$sort(\frac{41}{18},\frac{62}{3})$$

Least common denominator of the numbers in the list \frac{41}{18},\frac{62}{3} is 18. Convert numbers in the list to fractions with denominator 18.

$$\frac{41}{18},\frac{372}{18}$$

Evaluate

$$\frac{41}{18},\ \frac{62}{3}$$