Basic Math Examples

$\frac{7 y}{14 y + 7} \cdot \frac{12 y + 6}{3}$

Step 1

Factor $7$ out of $14 y + 7$ .

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Step 1.1

Factor $7$ out of $14 y$ .

$\frac{7 y}{7 (2 y) + 7} \cdot \frac{12 y + 6}{3}$

Step 1.2

Factor $7$ out of $7$ .

$\frac{7 y}{7 (2 y) + 7 (1)} \cdot \frac{12 y + 6}{3}$

Step 1.3

Factor $7$ out of $7 (2 y) + 7 (1)$ .

$\frac{7 y}{7 (2 y + 1)} \cdot \frac{12 y + 6}{3}$

Step 2

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

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Step 2.1

Factor $6$ out of $12 y$ .

$\frac{7 y}{7 (2 y + 1)} \cdot \frac{6 (2 y) + 6}{3}$

Step 2.2

Factor $6$ out of $6$ .

$\frac{7 y}{7 (2 y + 1)} \cdot \frac{6 (2 y) + 6 (1)}{3}$

Step 2.3

Factor $6$ out of $6 (2 y) + 6 (1)$ .

$\frac{7 y}{7 (2 y + 1)} \cdot \frac{6 (2 y + 1)}{3}$

Step 3

Cancel the common factor of $2 y + 1$ .

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Step 3.1

Factor $2 y + 1$ out of $7 (2 y + 1)$ .

$\frac{7 y}{(2 y + 1) \cdot 7} \cdot \frac{6 (2 y + 1)}{3}$

Step 3.2

Factor $2 y + 1$ out of $6 (2 y + 1)$ .

$\frac{7 y}{(2 y + 1) \cdot 7} \cdot \frac{(2 y + 1) \cdot 6}{3}$

Step 3.3

Cancel the common factor.

$\frac{7 y}{(2 y + 1) \cdot 7} \cdot \frac{(2 y + 1) \cdot 6}{3}$

Step 3.4

Rewrite the expression.

$\frac{7 y}{7} \cdot \frac{6}{3}$

Step 4

Multiply $\frac{7 y}{7}$ by $\frac{6}{3}$ .

$\frac{7 y \cdot 6}{7 \cdot 3}$

Step 5

Multiply.

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Step 5.1

Multiply $6$ by $7$ .

$\frac{42 y}{7 \cdot 3}$

Step 5.2

Multiply $7$ by $3$ .

$\frac{42 y}{21}$

Step 6

Cancel the common factor of $42$ and $21$ .

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Step 6.1

Factor $21$ out of $42 y$ .

$\frac{21 (2 y)}{21}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $21$ out of $21$ .

$\frac{21 (2 y)}{21 (1)}$

Step 6.2.2

Cancel the common factor.

$\frac{21 (2 y)}{21 \cdot 1}$

Step 6.2.3

Rewrite the expression.

$\frac{2 y}{1}$

Step 6.2.4

Divide $2 y$ by $1$ .

$2 y$