Basic Math Examples

$\frac{16 - z^{2} \div 5 z^{4}}{12 - 3 z \div 4 z - 1}$

Step 1

Rewrite the division as a fraction.

$\frac{16 - \frac{z^{2}}{5 z^{4}}}{12 - 3 z \div 4 z - 1}$

Step 2

Cancel the common factor of $z^{2}$ and $z^{4}$ .

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Step 2.1

Multiply by $1$ .

$\frac{16 - \frac{z^{2} \cdot 1}{5 z^{4}}}{12 - 3 z \div 4 z - 1}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $z^{2}$ out of $5 z^{4}$ .

$\frac{16 - \frac{z^{2} \cdot 1}{z^{2} (5 z^{2})}}{12 - 3 z \div 4 z - 1}$

Step 2.2.2

Cancel the common factor.

$\frac{16 - \frac{z^{2} \cdot 1}{z^{2} (5 z^{2})}}{12 - 3 z \div 4 z - 1}$

Step 2.2.3

Rewrite the expression.

$\frac{16 - \frac{1}{5 z^{2}}}{12 - 3 z \div 4 z - 1}$

Step 3

Rewrite the division as a fraction.

$\frac{16 - \frac{1}{5 z^{2}}}{12 - \frac{3 z}{4 z} - 1}$

Step 4

Cancel the common factor of $z$ .

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Step 4.1

Cancel the common factor.

$\frac{16 - \frac{1}{5 z^{2}}}{12 - \frac{3 z}{4 z} - 1}$

Step 4.2

Rewrite the expression.

$\frac{16 - \frac{1}{5 z^{2}}}{12 - \frac{3}{4} - 1}$

Step 5

To write $12$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{16 - \frac{1}{5 z^{2}}}{12 \cdot \frac{4}{4} - \frac{3}{4} - 1}$

Step 6

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

$\frac{16 - \frac{1}{5 z^{2}}}{\frac{12 \cdot 4}{4} - \frac{3}{4} - 1}$

Step 7

Combine the numerators over the common denominator.

$\frac{16 - \frac{1}{5 z^{2}}}{\frac{12 \cdot 4 - 3}{4} - 1}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $12$ by $4$ .

$\frac{16 - \frac{1}{5 z^{2}}}{\frac{48 - 3}{4} - 1}$

Step 8.2

Subtract $3$ from $48$ .

$\frac{16 - \frac{1}{5 z^{2}}}{\frac{45}{4} - 1}$

Step 9

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{16 - \frac{1}{5 z^{2}}}{\frac{45}{4} - 1 \cdot \frac{4}{4}}$

Step 10

Combine $- 1$ and $\frac{4}{4}$ .

$\frac{16 - \frac{1}{5 z^{2}}}{\frac{45}{4} + \frac{- 1 \cdot 4}{4}}$

Step 11

Combine the numerators over the common denominator.

$\frac{16 - \frac{1}{5 z^{2}}}{\frac{45 - 1 \cdot 4}{4}}$

Step 12

Simplify the numerator.

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Step 12.1

Multiply $- 1$ by $4$ .

$\frac{16 - \frac{1}{5 z^{2}}}{\frac{45 - 4}{4}}$

Step 12.2

Subtract $4$ from $45$ .

$\frac{16 - \frac{1}{5 z^{2}}}{\frac{41}{4}}$