Solve 5*[6*(-5/27)+2]-2-[3*(-5/27)+3]

$$5 \cdot [ 6 \cdot ( - \frac { 5 } { 27 } ) + 2 ] - 2 - [ 3 \cdot ( - \frac { 5 } { 27 } ) + 3 ]$$

Evaluate

$$0$$

Solution Steps

Express 6\left(-\frac{5}{27}\right) as a single fraction.

$$5\left(\frac{6\left(-5\right)}{27}+2\right)-2-\left(3\left(-\frac{5}{27}\right)+3\right)$$

Multiply 6 and -5 to get -30.

$$5\left(\frac{-30}{27}+2\right)-2-\left(3\left(-\frac{5}{27}\right)+3\right)$$

Reduce the fraction \frac{-30}{27} to lowest terms by extracting and canceling out 3.

$$5\left(-\frac{10}{9}+2\right)-2-\left(3\left(-\frac{5}{27}\right)+3\right)$$

Convert 2 to fraction \frac{18}{9}.

$$5\left(-\frac{10}{9}+\frac{18}{9}\right)-2-\left(3\left(-\frac{5}{27}\right)+3\right)$$

Since -\frac{10}{9} and \frac{18}{9} have the same denominator, add them by adding their numerators.

$$5\times \frac{-10+18}{9}-2-\left(3\left(-\frac{5}{27}\right)+3\right)$$

Add -10 and 18 to get 8.

$$5\times \frac{8}{9}-2-\left(3\left(-\frac{5}{27}\right)+3\right)$$

Express 5\times \frac{8}{9} as a single fraction.

$$\frac{5\times 8}{9}-2-\left(3\left(-\frac{5}{27}\right)+3\right)$$

Multiply 5 and 8 to get 40.

$$\frac{40}{9}-2-\left(3\left(-\frac{5}{27}\right)+3\right)$$

Convert 2 to fraction \frac{18}{9}.

$$\frac{40}{9}-\frac{18}{9}-\left(3\left(-\frac{5}{27}\right)+3\right)$$

Since \frac{40}{9} and \frac{18}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{40-18}{9}-\left(3\left(-\frac{5}{27}\right)+3\right)$$

Subtract 18 from 40 to get 22.

$$\frac{22}{9}-\left(3\left(-\frac{5}{27}\right)+3\right)$$

Express 3\left(-\frac{5}{27}\right) as a single fraction.

$$\frac{22}{9}-\left(\frac{3\left(-5\right)}{27}+3\right)$$

Multiply 3 and -5 to get -15.

$$\frac{22}{9}-\left(\frac{-15}{27}+3\right)$$

Reduce the fraction \frac{-15}{27} to lowest terms by extracting and canceling out 3.

$$\frac{22}{9}-\left(-\frac{5}{9}+3\right)$$

Convert 3 to fraction \frac{27}{9}.

$$\frac{22}{9}-\left(-\frac{5}{9}+\frac{27}{9}\right)$$

Since -\frac{5}{9} and \frac{27}{9} have the same denominator, add them by adding their numerators.

$$\frac{22}{9}-\frac{-5+27}{9}$$

Add -5 and 27 to get 22.

$$\frac{22}{9}-\frac{22}{9}$$

Subtract \frac{22}{9} from \frac{22}{9} to get 0.

$$0$$

Factor

$$0$$