Basic Math Examples

$\frac{5 y}{10 y + 5} \cdot \frac{6 y}{7}$

Step 1

Factor $5$ out of $10 y + 5$ .

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Step 1.1

Factor $5$ out of $10 y$ .

$\frac{5 y}{5 (2 y) + 5} \cdot \frac{6 y}{7}$

Step 1.2

Factor $5$ out of $5$ .

$\frac{5 y}{5 (2 y) + 5 (1)} \cdot \frac{6 y}{7}$

Step 1.3

Factor $5$ out of $5 (2 y) + 5 (1)$ .

$\frac{5 y}{5 (2 y + 1)} \cdot \frac{6 y}{7}$

Step 2

Cancel the common factor of $5$ .

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Step 2.1

Cancel the common factor.

$\frac{5 y}{5 (2 y + 1)} \cdot \frac{6 y}{7}$

Step 2.2

Rewrite the expression.

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

Step 3

Multiply $\frac{y}{2 y + 1} \cdot \frac{6 y}{7}$ .

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Step 3.1

Multiply $\frac{y}{2 y + 1}$ by $\frac{6 y}{7}$ .

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

Step 3.2

Raise $y$ to the power of $1$ .

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

Step 3.3

Raise $y$ to the power of $1$ .

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

Step 3.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 3.5

Add $1$ and $1$ .

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

Step 4

Move $7$ to the left of $2 y + 1$ .

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