Pre-Algebra Examples

$\frac{3 y + 3}{6 y + 12} \div \frac{18}{5 y + 5}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{3 y + 3}{6 y + 12} \cdot \frac{5 y + 5}{18}$

Step 2

Cancel the common factor of $3 y + 3$ and $6 y + 12$ .

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Step 2.1

Factor $3$ out of $3 y$ .

$\frac{3 (y) + 3}{6 y + 12} \cdot \frac{5 y + 5}{18}$

Step 2.2

Factor $3$ out of $3$ .

$\frac{3 (y) + 3 (1)}{6 y + 12} \cdot \frac{5 y + 5}{18}$

Step 2.3

Factor $3$ out of $3 (y) + 3 (1)$ .

$\frac{3 (y + 1)}{6 y + 12} \cdot \frac{5 y + 5}{18}$

Step 2.4

Cancel the common factors.

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Step 2.4.1

Factor $3$ out of $6 y$ .

$\frac{3 (y + 1)}{3 (2 y) + 12} \cdot \frac{5 y + 5}{18}$

Step 2.4.2

Factor $3$ out of $12$ .

$\frac{3 (y + 1)}{3 (2 y) + 3 (4)} \cdot \frac{5 y + 5}{18}$

Step 2.4.3

Factor $3$ out of $3 (2 y) + 3 (4)$ .

$\frac{3 (y + 1)}{3 (2 y + 4)} \cdot \frac{5 y + 5}{18}$

Step 2.4.4

Cancel the common factor.

$\frac{3 (y + 1)}{3 (2 y + 4)} \cdot \frac{5 y + 5}{18}$

Step 2.4.5

Rewrite the expression.

$\frac{y + 1}{2 y + 4} \cdot \frac{5 y + 5}{18}$

Step 3

Factor $2$ out of $2 y + 4$ .

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Step 3.1

Factor $2$ out of $2 y$ .

$\frac{y + 1}{2 (y) + 4} \cdot \frac{5 y + 5}{18}$

Step 3.2

Factor $2$ out of $4$ .

$\frac{y + 1}{2 y + 2 \cdot 2} \cdot \frac{5 y + 5}{18}$

Step 3.3

Factor $2$ out of $2 y + 2 \cdot 2$ .

$\frac{y + 1}{2 (y + 2)} \cdot \frac{5 y + 5}{18}$

Step 4

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

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Step 4.1

Factor $5$ out of $5 y$ .

$\frac{y + 1}{2 (y + 2)} \cdot \frac{5 (y) + 5}{18}$

Step 4.2

Factor $5$ out of $5$ .

$\frac{y + 1}{2 (y + 2)} \cdot \frac{5 (y) + 5 (1)}{18}$

Step 4.3

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

$\frac{y + 1}{2 (y + 2)} \cdot \frac{5 (y + 1)}{18}$

Step 5

Multiply $\frac{y + 1}{2 (y + 2)} \cdot \frac{5 (y + 1)}{18}$ .

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Step 5.1

Multiply $\frac{y + 1}{2 (y + 2)}$ by $\frac{5 (y + 1)}{18}$ .

$\frac{(y + 1) (5 (y + 1))}{2 (y + 2) \cdot 18}$

Step 5.2

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

$\frac{5 ({(y + 1)}^{1} (y + 1))}{2 (y + 2) \cdot 18}$

Step 5.3

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

$\frac{5 ({(y + 1)}^{1} {(y + 1)}^{1})}{2 (y + 2) \cdot 18}$

Step 5.4

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

$\frac{5 {(y + 1)}^{1 + 1}}{2 (y + 2) \cdot 18}$

Step 5.5

Add $1$ and $1$ .

$\frac{5 {(y + 1)}^{2}}{2 (y + 2) \cdot 18}$

Step 5.6

Multiply $18$ by $2$ .

$\frac{5 {(y + 1)}^{2}}{36 (y + 2)}$