Basic Math Examples

$- \frac{3}{4} \cdot (z - 16) - \frac{1}{8} z$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Apply the distributive property.

$- \frac{3}{4} z - \frac{3}{4} \cdot - 16 - \frac{1}{8} z$

Step 1.2

Combine $z$ and $\frac{3}{4}$ .

$- \frac{z \cdot 3}{4} - \frac{3}{4} \cdot - 16 - \frac{1}{8} z$

Step 1.3

Cancel the common factor of $4$ .

Tap for more steps...

Step 1.3.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$- \frac{z \cdot 3}{4} + \frac{- 3}{4} \cdot - 16 - \frac{1}{8} z$

Step 1.3.2

Factor $4$ out of $- 16$ .

$- \frac{z \cdot 3}{4} + \frac{- 3}{4} \cdot (4 (- 4)) - \frac{1}{8} z$

Step 1.3.3

Cancel the common factor.

$- \frac{z \cdot 3}{4} + \frac{- 3}{4} \cdot (4 \cdot - 4) - \frac{1}{8} z$

Step 1.3.4

Rewrite the expression.

$- \frac{z \cdot 3}{4} - 3 \cdot - 4 - \frac{1}{8} z$

Step 1.4

Multiply $- 3$ by $- 4$ .

$- \frac{z \cdot 3}{4} + 12 - \frac{1}{8} z$

Step 1.5

Move $3$ to the left of $z$ .

$- \frac{3 z}{4} + 12 - \frac{1}{8} z$

Step 1.6

Combine $z$ and $\frac{1}{8}$ .

$- \frac{3 z}{4} + 12 - \frac{z}{8}$

Step 2

To write $- \frac{3 z}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{3 z}{4} \cdot \frac{2}{2} - \frac{z}{8} + 12$

Step 3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.1

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

$- \frac{3 z \cdot 2}{4 \cdot 2} - \frac{z}{8} + 12$

Step 3.2

Multiply $4$ by $2$ .

$- \frac{3 z \cdot 2}{8} - \frac{z}{8} + 12$

Step 4

Combine the numerators over the common denominator.

$\frac{- 3 z \cdot 2 - z}{8} + 12$

Step 5

Simplify each term.

Tap for more steps...

Step 5.1

Simplify the numerator.

Tap for more steps...

Step 5.1.1

Factor $z$ out of $- 3 z \cdot 2 - z$ .

Tap for more steps...

Step 5.1.1.1

Factor $z$ out of $- 3 z \cdot 2$ .

$\frac{z (- 3 \cdot 2) - z}{8} + 12$

Step 5.1.1.2

Factor $z$ out of $- z$ .

$\frac{z (- 3 \cdot 2) + z \cdot - 1}{8} + 12$

Step 5.1.1.3

Factor $z$ out of $z (- 3 \cdot 2) + z \cdot - 1$ .

$\frac{z (- 3 \cdot 2 - 1)}{8} + 12$

Step 5.1.2

Multiply $- 3$ by $2$ .

$\frac{z (- 6 - 1)}{8} + 12$

Step 5.1.3

Subtract $1$ from $- 6$ .

$\frac{z \cdot - 7}{8} + 12$

Step 5.2

Move $- 7$ to the left of $z$ .

$\frac{- 7 \cdot z}{8} + 12$

Step 5.3

Move the negative in front of the fraction.

$- \frac{7 z}{8} + 12$