Pre-Algebra Examples

$\frac{1}{2} \cdot (6 x - 2) - \frac{1}{5} \cdot (30 x - 6 y)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$\frac{1}{2} (6 x) + \frac{1}{2} \cdot - 2 - \frac{1}{5} \cdot (30 x - 6 y)$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Factor $2$ out of $6 x$ .

$\frac{1}{2} (2 (3 x)) + \frac{1}{2} \cdot - 2 - \frac{1}{5} \cdot (30 x - 6 y)$

Step 1.2.2

Cancel the common factor.

$\frac{1}{2} (2 (3 x)) + \frac{1}{2} \cdot - 2 - \frac{1}{5} \cdot (30 x - 6 y)$

Step 1.2.3

Rewrite the expression.

$3 x + \frac{1}{2} \cdot - 2 - \frac{1}{5} \cdot (30 x - 6 y)$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Factor $2$ out of $- 2$ .

$3 x + \frac{1}{2} \cdot (2 (- 1)) - \frac{1}{5} \cdot (30 x - 6 y)$

Step 1.3.2

Cancel the common factor.

$3 x + \frac{1}{2} \cdot (2 \cdot - 1) - \frac{1}{5} \cdot (30 x - 6 y)$

Step 1.3.3

Rewrite the expression.

$3 x - 1 - \frac{1}{5} \cdot (30 x - 6 y)$

Step 1.4

Apply the distributive property.

$3 x - 1 - \frac{1}{5} (30 x) - \frac{1}{5} (- 6 y)$

Step 1.5

Cancel the common factor of $5$ .

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Step 1.5.1

Move the leading negative in $- \frac{1}{5}$ into the numerator.

$3 x - 1 + \frac{- 1}{5} (30 x) - \frac{1}{5} (- 6 y)$

Step 1.5.2

Factor $5$ out of $30 x$ .

$3 x - 1 + \frac{- 1}{5} (5 (6 x)) - \frac{1}{5} (- 6 y)$

Step 1.5.3

Cancel the common factor.

$3 x - 1 + \frac{- 1}{5} (5 (6 x)) - \frac{1}{5} (- 6 y)$

Step 1.5.4

Rewrite the expression.

$3 x - 1 - 1 (6 x) - \frac{1}{5} (- 6 y)$

Step 1.6

Multiply $6$ by $- 1$ .

$3 x - 1 - 6 x - \frac{1}{5} (- 6 y)$

Step 1.7

Multiply $- \frac{1}{5} (- 6 y)$ .

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Step 1.7.1

Multiply $- 6$ by $- 1$ .

$3 x - 1 - 6 x + 6 (\frac{1}{5}) y$

Step 1.7.2

Combine $6$ and $\frac{1}{5}$ .

$3 x - 1 - 6 x + \frac{6}{5} y$

Step 1.7.3

Combine $\frac{6}{5}$ and $y$ .

$3 x - 1 - 6 x + \frac{6 y}{5}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $6 x$ from $3 x$ .

$- 3 x - 1 + \frac{6 y}{5}$

Step 2.2

Move $- 1$ .

$- 3 x + \frac{6 y}{5} - 1$