Algebra Examples

$\frac{- 8 - 16 y}{5} \div \frac{2 y + 1}{15 y}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{- 8 - 16 y}{5} \cdot \frac{15 y}{2 y + 1}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $5$ .

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Step 2.1.1

Factor $5$ out of $15 y$ .

$\frac{- 8 - 16 y}{5} \cdot \frac{5 (3 y)}{2 y + 1}$

Step 2.1.2

Cancel the common factor.

$\frac{- 8 - 16 y}{5} \cdot \frac{5 (3 y)}{2 y + 1}$

Step 2.1.3

Rewrite the expression.

$(- 8 - 16 y) \frac{3 y}{2 y + 1}$

Step 2.2

Multiply $- 8 - 16 y$ by $\frac{3 y}{2 y + 1}$ .

$\frac{(- 8 - 16 y) (3 y)}{2 y + 1}$

Step 3

Simplify the numerator.

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Step 3.1

Factor $8$ out of $- 8 - 16 y$ .

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Step 3.1.1

Factor $8$ out of $- 8$ .

$\frac{(8 (- 1) - 16 y) \cdot 3 y}{2 y + 1}$

Step 3.1.2

Factor $8$ out of $- 16 y$ .

$\frac{(8 (- 1) + 8 (- 2 y)) \cdot 3 y}{2 y + 1}$

Step 3.1.3

Factor $8$ out of $8 (- 1) + 8 (- 2 y)$ .

$\frac{8 (- 1 - 2 y) \cdot 3 y}{2 y + 1}$

Step 3.2

Multiply $3$ by $8$ .

$\frac{24 (- 1 - 2 y) y}{2 y + 1}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

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

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Step 4.1.1

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

$\frac{24 (- 1 (1) - 2 y) y}{2 y + 1}$

Step 4.1.2

Factor $- 1$ out of $- 2 y$ .

$\frac{24 (- 1 (1) - (2 y)) y}{2 y + 1}$

Step 4.1.3

Factor $- 1$ out of $- 1 (1) - (2 y)$ .

$\frac{24 (- 1 (1 + 2 y)) y}{2 y + 1}$

Step 4.1.4

Reorder terms.

$\frac{24 (- 1 (2 y + 1)) y}{2 y + 1}$

Step 4.1.5

Cancel the common factor.

$\frac{24 (- 1 (2 y + 1)) y}{2 y + 1}$

Step 4.1.6

Divide $24 \cdot (- 1) y$ by $1$ .

$24 \cdot (- 1) y$

Step 4.2

Multiply $24$ by $- 1$ .

$- 24 y$