What is -3\times (-5/9)+(-2) ?

The solution to -3\times (-5/9)+(-2) is -1/3

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-3\times (-5/9)+(-2)

- 3 \cdot (- \frac{5}{9}) + (- 2)

- \frac{1}{3}

Solution steps

- 3 (- \frac{5}{9}) + (- 2)

Follow the PEMDAS order of operations

Multiply and divide (left to right)

- 3 (- \frac{5}{9}) : \frac{5}{3}

- 3 (- \frac{5}{9})

Apply rule

- a \cdot (- b) = a \cdot b

- 3 (- \frac{5}{9}) = 3 \cdot \frac{5}{9}

Convert element to fraction:

3 = \frac{3}{1}

= \frac{3}{1} \cdot \frac{5}{9}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{3 \cdot 5}{1 \cdot 9}

\frac{3 \cdot 5}{1 \cdot 9} = \frac{5}{3}

\frac{3 \cdot 5}{1 \cdot 9}

Multiply the numbers:

1 \cdot 9 = 9

= \frac{3 \cdot 5}{9}

Factor the number:

9 = 3 \cdot 3

= \frac{3 \cdot 5}{3 \cdot 3}

Cancel the common factor:

3

= \frac{5}{3}

= \frac{5}{3}

= \frac{5}{3} + (- 2)

Add and subtract (left to right)

\frac{5}{3} + (- 2) : - \frac{1}{3}

\frac{5}{3} + (- 2)

Apply rule

+ (- a) = - a

+ (- 2) = - 2

= \frac{5}{3} - 2

\frac{5}{3} - 2 = - \frac{1}{3}

\frac{5}{3} - 2

Convert element to fraction:

2 = \frac{2 \cdot 3}{3}

= - \frac{2 \cdot 3}{3} + \frac{5}{3}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- 2 \cdot 3 + 5}{3}

- 2 \cdot 3 + 5 = - 1

- 2 \cdot 3 + 5

Multiply the numbers:

2 \cdot 3 = 6

= - 6 + 5

Add/Subtract the numbers:

- 6 + 5 = - 1

= - 1

= \frac{- 1}{3}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{1}{3}

= - \frac{1}{3}

= - \frac{1}{3}

6 \times 9 + 30 \div (- 3) + 19

8 \div (5 - 3)

6 (1)^{2} + 6 (1)

3^{4} - 1

3^{4} + 5