Pre-Algebra Examples

$- \frac{1}{2} \cdot (7 z + 4) + \frac{1}{5} \cdot (5 z - 15)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- \frac{1}{2} (7 z) - \frac{1}{2} \cdot 4 + \frac{1}{5} \cdot (5 z - 15)$

Step 1.2

Multiply $- \frac{1}{2} (7 z)$ .

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Step 1.2.1

Multiply $7$ by $- 1$ .

$- 7 (\frac{1}{2}) z - \frac{1}{2} \cdot 4 + \frac{1}{5} \cdot (5 z - 15)$

Step 1.2.2

Combine $- 7$ and $\frac{1}{2}$ .

$\frac{- 7}{2} z - \frac{1}{2} \cdot 4 + \frac{1}{5} \cdot (5 z - 15)$

Step 1.2.3

Combine $\frac{- 7}{2}$ and $z$ .

$\frac{- 7 z}{2} - \frac{1}{2} \cdot 4 + \frac{1}{5} \cdot (5 z - 15)$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{- 7 z}{2} + \frac{- 1}{2} \cdot 4 + \frac{1}{5} \cdot (5 z - 15)$

Step 1.3.2

Factor $2$ out of $4$ .

$\frac{- 7 z}{2} + \frac{- 1}{2} \cdot (2 (2)) + \frac{1}{5} \cdot (5 z - 15)$

Step 1.3.3

Cancel the common factor.

$\frac{- 7 z}{2} + \frac{- 1}{2} \cdot (2 \cdot 2) + \frac{1}{5} \cdot (5 z - 15)$

Step 1.3.4

Rewrite the expression.

$\frac{- 7 z}{2} - 1 \cdot 2 + \frac{1}{5} \cdot (5 z - 15)$

Step 1.4

Multiply $- 1$ by $2$ .

$\frac{- 7 z}{2} - 2 + \frac{1}{5} \cdot (5 z - 15)$

Step 1.5

Move the negative in front of the fraction.

$- \frac{7 z}{2} - 2 + \frac{1}{5} \cdot (5 z - 15)$

Step 1.6

Apply the distributive property.

$- \frac{7 z}{2} - 2 + \frac{1}{5} (5 z) + \frac{1}{5} \cdot - 15$

Step 1.7

Cancel the common factor of $5$ .

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Step 1.7.1

Factor $5$ out of $5 z$ .

$- \frac{7 z}{2} - 2 + \frac{1}{5} (5 (z)) + \frac{1}{5} \cdot - 15$

Step 1.7.2

Cancel the common factor.

$- \frac{7 z}{2} - 2 + \frac{1}{5} (5 z) + \frac{1}{5} \cdot - 15$

Step 1.7.3

Rewrite the expression.

$- \frac{7 z}{2} - 2 + z + \frac{1}{5} \cdot - 15$

Step 1.8

Cancel the common factor of $5$ .

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Step 1.8.1

Factor $5$ out of $- 15$ .

$- \frac{7 z}{2} - 2 + z + \frac{1}{5} \cdot (5 (- 3))$

Step 1.8.2

Cancel the common factor.

$- \frac{7 z}{2} - 2 + z + \frac{1}{5} \cdot (5 \cdot - 3)$

Step 1.8.3

Rewrite the expression.

$- \frac{7 z}{2} - 2 + z - 3$

Step 2

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

$- \frac{7 z}{2} + z \cdot \frac{2}{2} - 2 - 3$

Step 3

Combine $z$ and $\frac{2}{2}$ .

$- \frac{7 z}{2} + \frac{z \cdot 2}{2} - 2 - 3$

Step 4

Combine the numerators over the common denominator.

$\frac{- 7 z + z \cdot 2}{2} - 2 - 3$

Step 5

Add $- 7 z$ and $z \cdot 2$ .

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Step 5.1

Reorder $z$ and $2$ .

$\frac{- 7 z + 2 \cdot z}{2} - 2 - 3$

Step 5.2

Add $- 7 z$ and $2 \cdot z$ .

$\frac{- 5 z}{2} - 2 - 3$

Step 6

Move the negative in front of the fraction.

$- \frac{5 z}{2} - 2 - 3$

Step 7

Subtract $3$ from $- 2$ .

$- \frac{5 z}{2} - 5$