Pre-Algebra Examples

$\frac{\frac{26 x y^{2}}{3} - \frac{39 y^{3}}{2}}{- \frac{13 y^{2}}{6}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(\frac{26 x y^{2}}{3} - \frac{39 y^{3}}{2}) (- \frac{6}{13 y^{2}})$

Step 2

Apply the distributive property.

$\frac{26 x y^{2}}{3} (- \frac{6}{13 y^{2}}) - \frac{39 y^{3}}{2} (- \frac{6}{13 y^{2}})$

Step 3

Rewrite using the commutative property of multiplication.

$- \frac{26 x y^{2}}{3} \cdot \frac{6}{13 y^{2}} - \frac{39 y^{3}}{2} (- \frac{6}{13 y^{2}})$

Step 4

Cancel the common factor of $13 y^{2}$ .

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Step 4.1

Move the leading negative in $- \frac{39 y^{3}}{2}$ into the numerator.

$- \frac{26 x y^{2}}{3} \cdot \frac{6}{13 y^{2}} + \frac{- 39 y^{3}}{2} (- \frac{6}{13 y^{2}})$

Step 4.2

Move the leading negative in $- \frac{6}{13 y^{2}}$ into the numerator.

$- \frac{26 x y^{2}}{3} \cdot \frac{6}{13 y^{2}} + \frac{- 39 y^{3}}{2} \cdot \frac{- 6}{13 y^{2}}$

Step 4.3

Factor $13 y^{2}$ out of $- 39 y^{3}$ .

$- \frac{26 x y^{2}}{3} \cdot \frac{6}{13 y^{2}} + \frac{13 y^{2} (- 3 y)}{2} \cdot \frac{- 6}{13 y^{2}}$

Step 4.4

Cancel the common factor.

$- \frac{26 x y^{2}}{3} \cdot \frac{6}{13 y^{2}} + \frac{13 y^{2} (- 3 y)}{2} \cdot \frac{- 6}{13 y^{2}}$

Step 4.5

Rewrite the expression.

$- \frac{26 x y^{2}}{3} \cdot \frac{6}{13 y^{2}} + \frac{- 3 y}{2} \cdot - 6$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Factor $2$ out of $- 6$ .

$- \frac{26 x y^{2}}{3} \cdot \frac{6}{13 y^{2}} + \frac{- 3 y}{2} \cdot (2 (- 3))$

Step 5.2

Cancel the common factor.

$- \frac{26 x y^{2}}{3} \cdot \frac{6}{13 y^{2}} + \frac{- 3 y}{2} \cdot (2 \cdot - 3)$

Step 5.3

Rewrite the expression.

$- \frac{26 x y^{2}}{3} \cdot \frac{6}{13 y^{2}} - 3 y \cdot - 3$

Step 6

Multiply $- 3$ by $- 3$ .

$- \frac{26 x y^{2}}{3} \cdot \frac{6}{13 y^{2}} + 9 y$

Step 7

Simplify each term.

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Step 7.1

Cancel the common factor of $13 y^{2}$ .

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Step 7.1.1

Move the leading negative in $- \frac{26 x y^{2}}{3}$ into the numerator.

$\frac{- 26 x y^{2}}{3} \cdot \frac{6}{13 y^{2}} + 9 y$

Step 7.1.2

Factor $13 y^{2}$ out of $- 26 x y^{2}$ .

$\frac{13 y^{2} (- 2 x)}{3} \cdot \frac{6}{13 y^{2}} + 9 y$

Step 7.1.3

Cancel the common factor.

$\frac{13 y^{2} (- 2 x)}{3} \cdot \frac{6}{13 y^{2}} + 9 y$

Step 7.1.4

Rewrite the expression.

$\frac{- 2 x}{3} \cdot 6 + 9 y$

Step 7.2

Cancel the common factor of $3$ .

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Step 7.2.1

Factor $3$ out of $6$ .

$\frac{- 2 x}{3} \cdot (3 (2)) + 9 y$

Step 7.2.2

Cancel the common factor.

$\frac{- 2 x}{3} \cdot (3 \cdot 2) + 9 y$

Step 7.2.3

Rewrite the expression.

$- 2 x \cdot 2 + 9 y$

Step 7.3

Multiply $2$ by $- 2$ .

$- 4 x + 9 y$