Basic Math Examples

$\frac{3 y - 18}{6 y^{2} - 36 y} \div \frac{7}{12 y}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{3 y - 18}{6 y^{2} - 36 y} \cdot \frac{12 y}{7}$

Step 2

Factor $3$ out of $3 y - 18$ .

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Step 2.1

Factor $3$ out of $3 y$ .

$\frac{3 (y) - 18}{6 y^{2} - 36 y} \cdot \frac{12 y}{7}$

Step 2.2

Factor $3$ out of $- 18$ .

$\frac{3 y + 3 \cdot - 6}{6 y^{2} - 36 y} \cdot \frac{12 y}{7}$

Step 2.3

Factor $3$ out of $3 y + 3 \cdot - 6$ .

$\frac{3 (y - 6)}{6 y^{2} - 36 y} \cdot \frac{12 y}{7}$

Step 3

Factor $6 y$ out of $6 y^{2} - 36 y$ .

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Step 3.1

Factor $6 y$ out of $6 y^{2}$ .

$\frac{3 (y - 6)}{6 y (y) - 36 y} \cdot \frac{12 y}{7}$

Step 3.2

Factor $6 y$ out of $- 36 y$ .

$\frac{3 (y - 6)}{6 y (y) + 6 y (- 6)} \cdot \frac{12 y}{7}$

Step 3.3

Factor $6 y$ out of $6 y (y) + 6 y (- 6)$ .

$\frac{3 (y - 6)}{6 y (y - 6)} \cdot \frac{12 y}{7}$

Step 4

Cancel the common factor of $6 y$ .

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Step 4.1

Factor $6 y$ out of $12 y$ .

$\frac{3 (y - 6)}{6 y (y - 6)} \cdot \frac{6 y (2)}{7}$

Step 4.2

Cancel the common factor.

$\frac{3 (y - 6)}{6 y (y - 6)} \cdot \frac{6 y \cdot 2}{7}$

Step 4.3

Rewrite the expression.

$\frac{3 (y - 6)}{y - 6} \cdot \frac{2}{7}$

Step 5

Multiply $\frac{3 (y - 6)}{y - 6}$ by $\frac{2}{7}$ .

$\frac{3 (y - 6) \cdot 2}{(y - 6) \cdot 7}$

Step 6

Multiply $2$ by $3$ .

$\frac{6 (y - 6)}{(y - 6) \cdot 7}$

Step 7

Cancel the common factor of $y - 6$ .

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Step 7.1

Cancel the common factor.

$\frac{6 (y - 6)}{(y - 6) \cdot 7}$

Step 7.2

Rewrite the expression.

$\frac{6}{7}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{6}{7}$

Decimal Form:

$0.\overline{857142}$