Solve 27*(1/3-4/9-5/27)

$$27 \cdot ( \frac { 1 } { 3 } - \frac { 4 } { 9 } - \frac { 5 } { 27 } )$$

Evaluate

$$-8$$

Solution Steps

Least common multiple of 3 and 9 is 9. Convert \frac{1}{3} and \frac{4}{9} to fractions with denominator 9.

$$27\left(\frac{3}{9}-\frac{4}{9}-\frac{5}{27}\right)$$

Since \frac{3}{9} and \frac{4}{9} have the same denominator, subtract them by subtracting their numerators.

$$27\left(\frac{3-4}{9}-\frac{5}{27}\right)$$

Subtract 4 from 3 to get -1.

$$27\left(-\frac{1}{9}-\frac{5}{27}\right)$$

Least common multiple of 9 and 27 is 27. Convert -\frac{1}{9} and \frac{5}{27} to fractions with denominator 27.

$$27\left(-\frac{3}{27}-\frac{5}{27}\right)$$

Since -\frac{3}{27} and \frac{5}{27} have the same denominator, subtract them by subtracting their numerators.

$$27\times \frac{-3-5}{27}$$

Subtract 5 from -3 to get -8.

$$27\left(-\frac{8}{27}\right)$$

Cancel out 27 and 27.

$$-8$$

Factor

$$-8$$