Basic Math Examples

$- \frac{5}{8} z - \frac{3}{4} z$

Step 1

Simplify each term.

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Step 1.1

Combine $z$ and $\frac{5}{8}$ .

$- \frac{z \cdot 5}{8} - \frac{3}{4} z$

Step 1.2

Move $5$ to the left of $z$ .

$- \frac{5 \cdot z}{8} - \frac{3}{4} z$

Step 1.3

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

$- \frac{5 z}{8} - \frac{z \cdot 3}{4}$

Step 1.4

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

$- \frac{5 z}{8} - \frac{3 z}{4}$

Step 2

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

$- \frac{5 z}{8} - \frac{3 z}{4} \cdot \frac{2}{2}$

Step 3

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

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Step 3.1

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

$- \frac{5 z}{8} - \frac{3 z \cdot 2}{4 \cdot 2}$

Step 3.2

Multiply $4$ by $2$ .

$- \frac{5 z}{8} - \frac{3 z \cdot 2}{8}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 5 z - 3 z \cdot 2}{8}$

Step 5

Simplify the numerator.

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Step 5.1

Factor $z$ out of $- 5 z - 3 z \cdot 2$ .

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Step 5.1.1

Factor $z$ out of $- 5 z$ .

$\frac{z \cdot - 5 - 3 z \cdot 2}{8}$

Step 5.1.2

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

$\frac{z \cdot - 5 + z (- 3 \cdot 2)}{8}$

Step 5.1.3

Factor $z$ out of $z \cdot - 5 + z (- 3 \cdot 2)$ .

$\frac{z (- 5 - 3 \cdot 2)}{8}$

Step 5.2

Multiply $- 3$ by $2$ .

$\frac{z (- 5 - 6)}{8}$

Step 5.3

Subtract $6$ from $- 5$ .

$\frac{z \cdot - 11}{8}$

Step 6

Simplify the expression.

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Step 6.1

Move $- 11$ to the left of $z$ .

$\frac{- 11 \cdot z}{8}$

Step 6.2

Move the negative in front of the fraction.

$- \frac{11 z}{8}$