Pre-Algebra Examples

$- \frac{4}{5} \cdot (z - 12) - \frac{1}{10} z$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- \frac{4}{5} z - \frac{4}{5} \cdot - 12 - \frac{1}{10} z$

Step 1.2

Combine $z$ and $\frac{4}{5}$ .

$- \frac{z \cdot 4}{5} - \frac{4}{5} \cdot - 12 - \frac{1}{10} z$

Step 1.3

Multiply $- \frac{4}{5} \cdot - 12$ .

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Step 1.3.1

Multiply $- 12$ by $- 1$ .

$- \frac{z \cdot 4}{5} + 12 (\frac{4}{5}) - \frac{1}{10} z$

Step 1.3.2

Combine $12$ and $\frac{4}{5}$ .

$- \frac{z \cdot 4}{5} + \frac{12 \cdot 4}{5} - \frac{1}{10} z$

Step 1.3.3

Multiply $12$ by $4$ .

$- \frac{z \cdot 4}{5} + \frac{48}{5} - \frac{1}{10} z$

Step 1.4

Move $4$ to the left of $z$ .

$- \frac{4 z}{5} + \frac{48}{5} - \frac{1}{10} z$

Step 1.5

Combine $z$ and $\frac{1}{10}$ .

$- \frac{4 z}{5} + \frac{48}{5} - \frac{z}{10}$

Step 2

To write $- \frac{4 z}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{4 z}{5} \cdot \frac{2}{2} - \frac{z}{10} + \frac{48}{5}$

Step 3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{4 z}{5}$ by $\frac{2}{2}$ .

$- \frac{4 z \cdot 2}{5 \cdot 2} - \frac{z}{10} + \frac{48}{5}$

Step 3.2

Multiply $5$ by $2$ .

$- \frac{4 z \cdot 2}{10} - \frac{z}{10} + \frac{48}{5}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 4 z \cdot 2 - z}{10} + \frac{48}{5}$

Step 5

Simplify each term.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Factor $z$ out of $- 4 z \cdot 2 - z$ .

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Step 5.1.1.1

Factor $z$ out of $- 4 z \cdot 2$ .

$\frac{z (- 4 \cdot 2) - z}{10} + \frac{48}{5}$

Step 5.1.1.2

Factor $z$ out of $- z$ .

$\frac{z (- 4 \cdot 2) + z \cdot - 1}{10} + \frac{48}{5}$

Step 5.1.1.3

Factor $z$ out of $z (- 4 \cdot 2) + z \cdot - 1$ .

$\frac{z (- 4 \cdot 2 - 1)}{10} + \frac{48}{5}$

Step 5.1.2

Multiply $- 4$ by $2$ .

$\frac{z (- 8 - 1)}{10} + \frac{48}{5}$

Step 5.1.3

Subtract $1$ from $- 8$ .

$\frac{z \cdot - 9}{10} + \frac{48}{5}$

Step 5.2

Move $- 9$ to the left of $z$ .

$\frac{- 9 \cdot z}{10} + \frac{48}{5}$

Step 5.3

Move the negative in front of the fraction.

$- \frac{9 z}{10} + \frac{48}{5}$