Solve 18*(2/3+5/6+4/9)

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

Evaluate

$$35$$

Solution Steps

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

$$18\left(\frac{4}{6}+\frac{5}{6}+\frac{4}{9}\right)$$

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

$$18\left(\frac{4+5}{6}+\frac{4}{9}\right)$$

Add 4 and 5 to get 9.

$$18\left(\frac{9}{6}+\frac{4}{9}\right)$$

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

$$18\left(\frac{3}{2}+\frac{4}{9}\right)$$

Least common multiple of 2 and 9 is 18. Convert \frac{3}{2} and \frac{4}{9} to fractions with denominator 18.

$$18\left(\frac{27}{18}+\frac{8}{18}\right)$$

Since \frac{27}{18} and \frac{8}{18} have the same denominator, add them by adding their numerators.

$$18\times \frac{27+8}{18}$$

Add 27 and 8 to get 35.

$$18\times \frac{35}{18}$$

Cancel out 18 and 18.

$$35$$

Factor

$$5\times 7$$