Algebra Examples

$6 (\frac{1}{2} w - \frac{3}{4})$

Step 1

Combine $\frac{1}{2}$ and $w$ .

$6 (\frac{w}{2} - \frac{3}{4})$

Step 2

To write $\frac{w}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$6 (\frac{w}{2} \cdot \frac{2}{2} - \frac{3}{4})$

Step 3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{w}{2}$ by $\frac{2}{2}$ .

$6 (\frac{w \cdot 2}{2 \cdot 2} - \frac{3}{4})$

Step 3.2

Multiply $2$ by $2$ .

$6 (\frac{w \cdot 2}{4} - \frac{3}{4})$

Step 4

Combine the numerators over the common denominator.

$6 \frac{w \cdot 2 - 3}{4}$

Step 5

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

$6 \frac{2 w - 3}{4}$

Step 6

Simplify terms.

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Step 6.1

Cancel the common factor of $2$ .

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Step 6.1.1

Factor $2$ out of $6$ .

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

Step 6.1.2

Factor $2$ out of $4$ .

$2 \cdot 3 \frac{2 w - 3}{2 \cdot 2}$

Step 6.1.3

Cancel the common factor.

$2 \cdot 3 \frac{2 w - 3}{2 \cdot 2}$

Step 6.1.4

Rewrite the expression.

$3 \frac{2 w - 3}{2}$

Step 6.2

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

$\frac{3 (2 w - 3)}{2}$