Basic Math Examples

$(w - \frac{4}{9}) (- \frac{2}{3}) = - \frac{4}{5}$

Step 1

Multiply each term in $(w - \frac{4}{9}) (- \frac{2}{3}) = - \frac{4}{5}$ by $- \frac{3}{2}$ to eliminate the fractions.

Tap for more steps...

Step 1.1

Multiply each term in $(w - \frac{4}{9}) (- \frac{2}{3}) = - \frac{4}{5}$ by $- \frac{3}{2}$ .

$(w - \frac{4}{9}) (- \frac{2}{3}) (- \frac{3}{2}) = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

Apply the distributive property.

$(w (- \frac{2}{3}) - \frac{4}{9} (- \frac{2}{3})) (- \frac{3}{2}) = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.2

Combine $w$ and $\frac{2}{3}$ .

$(- \frac{w \cdot 2}{3} - \frac{4}{9} (- \frac{2}{3})) (- \frac{3}{2}) = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.3

Multiply $- \frac{4}{9} (- \frac{2}{3})$ .

Tap for more steps...

Step 1.2.3.1

Multiply $- 1$ by $- 1$ .

$(- \frac{w \cdot 2}{3} + 1 (\frac{4}{9}) \frac{2}{3}) (- \frac{3}{2}) = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.3.2

Multiply $\frac{4}{9}$ by $1$ .

$(- \frac{w \cdot 2}{3} + \frac{4}{9} \cdot \frac{2}{3}) (- \frac{3}{2}) = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.3.3

Multiply $\frac{4}{9}$ by $\frac{2}{3}$ .

$(- \frac{w \cdot 2}{3} + \frac{4 \cdot 2}{9 \cdot 3}) (- \frac{3}{2}) = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.3.4

Multiply $4$ by $2$ .

$(- \frac{w \cdot 2}{3} + \frac{8}{9 \cdot 3}) (- \frac{3}{2}) = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.3.5

Multiply $9$ by $3$ .

$(- \frac{w \cdot 2}{3} + \frac{8}{27}) (- \frac{3}{2}) = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.4

Move $2$ to the left of $w$ .

$(- \frac{2 w}{3} + \frac{8}{27}) (- \frac{3}{2}) = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.5

Simplify terms.

Tap for more steps...

Step 1.2.5.1

Apply the distributive property.

$- \frac{2 w}{3} (- \frac{3}{2}) + \frac{8}{27} (- \frac{3}{2}) = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.5.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.2.5.2.1

Move the leading negative in $- \frac{2 w}{3}$ into the numerator.

$\frac{- 2 w}{3} (- \frac{3}{2}) + \frac{8}{27} (- \frac{3}{2}) = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.5.2.2

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$\frac{- 2 w}{3} \cdot \frac{- 3}{2} + \frac{8}{27} (- \frac{3}{2}) = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.5.2.3

Factor $2$ out of $- 2 w$ .

$\frac{2 (- w)}{3} \cdot \frac{- 3}{2} + \frac{8}{27} (- \frac{3}{2}) = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.5.2.4

Cancel the common factor.

$\frac{2 (- w)}{3} \cdot \frac{- 3}{2} + \frac{8}{27} (- \frac{3}{2}) = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.5.2.5

Rewrite the expression.

$\frac{- w}{3} \cdot - 3 + \frac{8}{27} (- \frac{3}{2}) = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.5.3

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.2.5.3.1

Factor $3$ out of $- 3$ .

$\frac{- w}{3} \cdot (3 (- 1)) + \frac{8}{27} (- \frac{3}{2}) = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.5.3.2

Cancel the common factor.

$\frac{- w}{3} \cdot (3 \cdot - 1) + \frac{8}{27} (- \frac{3}{2}) = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.5.3.3

Rewrite the expression.

$- w \cdot - 1 + \frac{8}{27} (- \frac{3}{2}) = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.5.4

Multiply.

Tap for more steps...

Step 1.2.5.4.1

Multiply $- 1$ by $- 1$ .

$1 w + \frac{8}{27} (- \frac{3}{2}) = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.5.4.2

Multiply $w$ by $1$ .

$w + \frac{8}{27} (- \frac{3}{2}) = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.5.5

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.2.5.5.1

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$w + \frac{8}{27} \cdot \frac{- 3}{2} = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.5.5.2

Factor $2$ out of $8$ .

$w + \frac{2 (4)}{27} \cdot \frac{- 3}{2} = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.5.5.3

Cancel the common factor.

$w + \frac{2 \cdot 4}{27} \cdot \frac{- 3}{2} = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.5.5.4

Rewrite the expression.

$w + \frac{4}{27} \cdot - 3 = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.5.6

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.2.5.6.1

Factor $3$ out of $27$ .

$w + \frac{4}{3 (9)} \cdot - 3 = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.5.6.2

Factor $3$ out of $- 3$ .

$w + \frac{4}{3 \cdot 9} \cdot (3 \cdot - 1) = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.5.6.3

Cancel the common factor.

$w + \frac{4}{3 \cdot 9} \cdot (3 \cdot - 1) = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.5.6.4

Rewrite the expression.

$w + \frac{4}{9} \cdot - 1 = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.5.7

Combine $\frac{4}{9}$ and $- 1$ .

$w + \frac{4 \cdot - 1}{9} = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.5.8

Simplify the expression.

Tap for more steps...

Step 1.2.5.8.1

Multiply $4$ by $- 1$ .

$w + \frac{- 4}{9} = - \frac{4}{5} (- \frac{3}{2})$

Step 1.2.5.8.2

Move the negative in front of the fraction.

$w - \frac{4}{9} = - \frac{4}{5} (- \frac{3}{2})$

Step 1.3

Simplify the right side.

Tap for more steps...

Step 1.3.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.3.1.1

Move the leading negative in $- \frac{4}{5}$ into the numerator.

$w - \frac{4}{9} = \frac{- 4}{5} (- \frac{3}{2})$

Step 1.3.1.2

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$w - \frac{4}{9} = \frac{- 4}{5} \cdot \frac{- 3}{2}$

Step 1.3.1.3

Factor $2$ out of $- 4$ .

$w - \frac{4}{9} = \frac{2 (- 2)}{5} \cdot \frac{- 3}{2}$

Step 1.3.1.4

Cancel the common factor.

$w - \frac{4}{9} = \frac{2 \cdot - 2}{5} \cdot \frac{- 3}{2}$

Step 1.3.1.5

Rewrite the expression.

$w - \frac{4}{9} = \frac{- 2}{5} \cdot - 3$

Step 1.3.2

Combine $\frac{- 2}{5}$ and $- 3$ .

$w - \frac{4}{9} = \frac{- 2 \cdot - 3}{5}$

Step 1.3.3

Multiply $- 2$ by $- 3$ .

$w - \frac{4}{9} = \frac{6}{5}$

Step 2

Move all terms not containing $w$ to the right side of the equation.

Tap for more steps...

Step 2.1

Add $\frac{4}{9}$ to both sides of the equation.

$w = \frac{6}{5} + \frac{4}{9}$

Step 2.2

To write $\frac{6}{5}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$w = \frac{6}{5} \cdot \frac{9}{9} + \frac{4}{9}$

Step 2.3

To write $\frac{4}{9}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$w = \frac{6}{5} \cdot \frac{9}{9} + \frac{4}{9} \cdot \frac{5}{5}$

Step 2.4

Write each expression with a common denominator of $45$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 2.4.1

Multiply $\frac{6}{5}$ by $\frac{9}{9}$ .

$w = \frac{6 \cdot 9}{5 \cdot 9} + \frac{4}{9} \cdot \frac{5}{5}$

Step 2.4.2

Multiply $5$ by $9$ .

$w = \frac{6 \cdot 9}{45} + \frac{4}{9} \cdot \frac{5}{5}$

Step 2.4.3

Multiply $\frac{4}{9}$ by $\frac{5}{5}$ .

$w = \frac{6 \cdot 9}{45} + \frac{4 \cdot 5}{9 \cdot 5}$

Step 2.4.4

Multiply $9$ by $5$ .

$w = \frac{6 \cdot 9}{45} + \frac{4 \cdot 5}{45}$

Step 2.5

Combine the numerators over the common denominator.

$w = \frac{6 \cdot 9 + 4 \cdot 5}{45}$

Step 2.6

Simplify the numerator.

Tap for more steps...

Step 2.6.1

Multiply $6$ by $9$ .

$w = \frac{54 + 4 \cdot 5}{45}$

Step 2.6.2

Multiply $4$ by $5$ .

$w = \frac{54 + 20}{45}$

Step 2.6.3

Add $54$ and $20$ .

$w = \frac{74}{45}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$w = \frac{74}{45}$

Decimal Form:

$w = 1.6\overline{4}$

Mixed Number Form:

$w = 1 \frac{29}{45}$