Pre-Algebra Examples

$(5 u^{2} y^{4} - 27 u y^{3}) \div (- 3 u^{2} y^{4})$

Step 1

Rewrite the division as a fraction.

$\frac{5 u^{2} y^{4} - 27 u y^{3}}{- 3 u^{2} y^{4}}$

Step 2

Factor $u y^{3}$ out of $5 u^{2} y^{4} - 27 u y^{3}$ .

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Step 2.1

Factor $u y^{3}$ out of $5 u^{2} y^{4}$ .

$\frac{u y^{3} (5 u y) - 27 u y^{3}}{- 3 u^{2} y^{4}}$

Step 2.2

Factor $u y^{3}$ out of $- 27 u y^{3}$ .

$\frac{u y^{3} (5 u y) + u y^{3} (- 27)}{- 3 u^{2} y^{4}}$

Step 2.3

Factor $u y^{3}$ out of $u y^{3} (5 u y) + u y^{3} (- 27)$ .

$\frac{u y^{3} (5 u y - 27)}{- 3 u^{2} y^{4}}$

Step 3

Cancel the common factor of $u$ and $u^{2}$ .

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Step 3.1

Factor $u$ out of $u y^{3} (5 u y - 27)$ .

$\frac{u (y^{3} (5 u y - 27))}{- 3 u^{2} y^{4}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $u$ out of $- 3 u^{2} y^{4}$ .

$\frac{u (y^{3} (5 u y - 27))}{u (- 3 u y^{4})}$

Step 3.2.2

Cancel the common factor.

$\frac{u (y^{3} (5 u y - 27))}{u (- 3 u y^{4})}$

Step 3.2.3

Rewrite the expression.

$\frac{y^{3} (5 u y - 27)}{- 3 u y^{4}}$

Step 4

Cancel the common factors.

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Step 4.1

Factor $y^{3}$ out of $- 3 u y^{4}$ .

$\frac{y^{3} (5 u y - 27)}{y^{3} (- 3 u y)}$

Step 4.2

Cancel the common factor.

$\frac{y^{3} (5 u y - 27)}{y^{3} (- 3 u y)}$

Step 4.3

Rewrite the expression.

$\frac{5 u y - 27}{- 3 u y}$

Step 5

Move the negative in front of the fraction.

$- \frac{5 u y - 27}{3 u y}$

Step 6

Split the fraction $\frac{5 u y - 27}{3 u y}$ into two fractions.

$- (\frac{5 u y}{3 u y} + \frac{- 27}{3 u y})$

Step 7

Cancel the common factor of $u$ .

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Step 7.1

Cancel the common factor.

$- (\frac{5 u y}{3 u y} + \frac{- 27}{3 u y})$

Step 7.2

Rewrite the expression.

$- (\frac{5 y}{3 y} + \frac{- 27}{3 u y})$

Step 8

Cancel the common factor of $y$ .

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Step 8.1

Cancel the common factor.

$- (\frac{5 y}{3 y} + \frac{- 27}{3 u y})$

Step 8.2

Rewrite the expression.

$- (\frac{5}{3} + \frac{- 27}{3 u y})$

Step 9

Cancel the common factor of $- 27$ and $3$ .

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Step 9.1

Factor $3$ out of $- 27$ .

$- (\frac{5}{3} + \frac{3 \cdot - 9}{3 u y})$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $3$ out of $3 u y$ .

$- (\frac{5}{3} + \frac{3 \cdot - 9}{3 (u y)})$

Step 9.2.2

Cancel the common factor.

$- (\frac{5}{3} + \frac{3 \cdot - 9}{3 (u y)})$

Step 9.2.3

Rewrite the expression.

$- (\frac{5}{3} + \frac{- 9}{u y})$

Step 10

Move the negative in front of the fraction.

$- (\frac{5}{3} - \frac{9}{u y})$