Solve 18(5a-4b/6-a-2b/9)

$$18 ( \frac { 5 a - 4 b } { 6 } - \frac { a - 2 b } { 9 } )$$

Evaluate

$$13a-8b$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 9 is 18. Multiply \frac{5a-4b}{6} times \frac{3}{3}. Multiply \frac{a-2b}{9} times \frac{2}{2}.

$$18\left(\frac{3\left(5a-4b\right)}{18}-\frac{2\left(a-2b\right)}{18}\right)$$

Since \frac{3\left(5a-4b\right)}{18} and \frac{2\left(a-2b\right)}{18} have the same denominator, subtract them by subtracting their numerators.

$$18\times \frac{3\left(5a-4b\right)-2\left(a-2b\right)}{18}$$

Do the multiplications in 3\left(5a-4b\right)-2\left(a-2b\right).

$$18\times \frac{15a-12b-2a+4b}{18}$$

Combine like terms in 15a-12b-2a+4b.

$$18\times \frac{13a-8b}{18}$$

Cancel out 18 and 18.

$$13a-8b$$

Expand

$$13a-8b$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 9 is 18. Multiply \frac{5a-4b}{6} times \frac{3}{3}. Multiply \frac{a-2b}{9} times \frac{2}{2}.

$$18\left(\frac{3\left(5a-4b\right)}{18}-\frac{2\left(a-2b\right)}{18}\right)$$

Since \frac{3\left(5a-4b\right)}{18} and \frac{2\left(a-2b\right)}{18} have the same denominator, subtract them by subtracting their numerators.

$$18\times \frac{3\left(5a-4b\right)-2\left(a-2b\right)}{18}$$

Do the multiplications in 3\left(5a-4b\right)-2\left(a-2b\right).

$$18\times \frac{15a-12b-2a+4b}{18}$$

Combine like terms in 15a-12b-2a+4b.

$$18\times \frac{13a-8b}{18}$$

Cancel out 18 and 18.

$$13a-8b$$