Algebra Examples

$\frac{15 a b}{4} \cdot \frac{8}{9 a^{2} b^{2}}$

Step 1

Combine.

$\frac{15 a b \cdot 8}{4 (9 a^{2} b^{2})}$

Step 2

Cancel the common factor of $15$ and $9$ .

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Step 2.1

Factor $3$ out of $15 a b \cdot 8$ .

$\frac{3 (5 a b \cdot 8)}{4 (9 a^{2} b^{2})}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $4 (9 a^{2} b^{2})$ .

$\frac{3 (5 a b \cdot 8)}{3 (4 (3 a^{2} b^{2}))}$

Step 2.2.2

Cancel the common factor.

$\frac{3 (5 a b \cdot 8)}{3 (4 (3 a^{2} b^{2}))}$

Step 2.2.3

Rewrite the expression.

$\frac{5 a b \cdot 8}{4 (3 a^{2} b^{2})}$

$\frac{5 a b \cdot 8}{4 (3 a^{2} b^{2})}$

$\frac{5 a b \cdot 8}{4 (3 a^{2} b^{2})}$

Step 3

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

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Step 3.1

Factor $a$ out of $5 a b \cdot 8$ .

$\frac{a (5 b \cdot 8)}{4 (3 a^{2} b^{2})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $a$ out of $4 (3 a^{2} b^{2})$ .

$\frac{a (5 b \cdot 8)}{a (4 (3 a b^{2}))}$

Step 3.2.2

Cancel the common factor.

$\frac{a (5 b \cdot 8)}{a (4 (3 a b^{2}))}$

Step 3.2.3

Rewrite the expression.

$\frac{5 b \cdot 8}{4 (3 a b^{2})}$

$\frac{5 b \cdot 8}{4 (3 a b^{2})}$

$\frac{5 b \cdot 8}{4 (3 a b^{2})}$

Step 4

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

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Step 4.1

Factor $b$ out of $5 b \cdot 8$ .

$\frac{b (5 \cdot 8)}{4 (3 a b^{2})}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $b$ out of $4 (3 a b^{2})$ .

$\frac{b (5 \cdot 8)}{b (4 (3 a b))}$

Step 4.2.2

Cancel the common factor.

$\frac{b (5 \cdot 8)}{b (4 (3 a b))}$

Step 4.2.3

Rewrite the expression.

$\frac{5 \cdot 8}{4 (3 a b)}$

$\frac{5 \cdot 8}{4 (3 a b)}$

$\frac{5 \cdot 8}{4 (3 a b)}$

Step 5

Cancel the common factor of $8$ and $4$ .

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Step 5.1

Factor $4$ out of $5 \cdot 8$ .

$\frac{4 (5 \cdot 2)}{4 (3 a b)}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Cancel the common factor.

$\frac{4 (5 \cdot 2)}{4 (3 a b)}$

Step 5.2.2

Rewrite the expression.

$\frac{5 \cdot 2}{3 a b}$

$\frac{5 \cdot 2}{3 a b}$

$\frac{5 \cdot 2}{3 a b}$

Step 6

Multiply $5$ by $2$ .

$\frac{10}{3 a b}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$