Basic Math Examples

$- \frac{21}{14} - \frac{14}{z}$

Step 1

Cancel the common factor of $21$ and $14$ .

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Step 1.1

Factor $7$ out of $21$ .

$- \frac{7 (3)}{14} - \frac{14}{z}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $7$ out of $14$ .

$- \frac{7 \cdot 3}{7 \cdot 2} - \frac{14}{z}$

Step 1.2.2

Cancel the common factor.

$- \frac{7 \cdot 3}{7 \cdot 2} - \frac{14}{z}$

Step 1.2.3

Rewrite the expression.

$- \frac{3}{2} - \frac{14}{z}$

Step 2

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

$- \frac{3}{2} \cdot \frac{z}{z} - \frac{14}{z}$

Step 3

To write $- \frac{14}{z}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{3}{2} \cdot \frac{z}{z} - \frac{14}{z} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of $2 z$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

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

$- \frac{3 z}{2 z} - \frac{14}{z} \cdot \frac{2}{2}$

Step 4.2

Multiply $\frac{14}{z}$ by $\frac{2}{2}$ .

$- \frac{3 z}{2 z} - \frac{14 \cdot 2}{z \cdot 2}$

Step 4.3

Reorder the factors of $z \cdot 2$ .

$- \frac{3 z}{2 z} - \frac{14 \cdot 2}{2 z}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 3 z - 14 \cdot 2}{2 z}$

Step 6

Multiply $- 14$ by $2$ .

$\frac{- 3 z - 28}{2 z}$

Step 7

Factor $- 1$ out of $- 3 z$ .

$\frac{- (3 z) - 28}{2 z}$

Step 8

Rewrite $- 28$ as $- 1 (28)$ .

$\frac{- (3 z) - 1 (28)}{2 z}$

Step 9

Factor $- 1$ out of $- (3 z) - 1 (28)$ .

$\frac{- (3 z + 28)}{2 z}$

Step 10

Simplify the expression.

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Step 10.1

Rewrite $- (3 z + 28)$ as $- 1 (3 z + 28)$ .

$\frac{- 1 (3 z + 28)}{2 z}$

Step 10.2

Move the negative in front of the fraction.

$- \frac{3 z + 28}{2 z}$