Algebra Examples

$\frac{5}{3 a b} = \frac{x}{12 a^{2} b c^{3}}$

Step 1

Rewrite the equation as $\frac{x}{12 a^{2} b c^{3}} = \frac{5}{3 a b}$ .

$\frac{x}{12 a^{2} b c^{3}} = \frac{5}{3 a b}$

Step 2

Multiply both sides by $12 a^{2} b c^{3}$ .

$\frac{x}{12 a^{2} b c^{3}} (12 a^{2} b c^{3}) = \frac{5}{3 a b} (12 a^{2} b c^{3})$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{x}{12 a^{2} b c^{3}} (12 a^{2} b c^{3})$ .

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Step 3.1.1.1

Rewrite using the commutative property of multiplication.

$12 \frac{x}{12 a^{2} b c^{3}} (a^{2} b c^{3}) = \frac{5}{3 a b} (12 a^{2} b c^{3})$

Step 3.1.1.2

Cancel the common factor of $12$ .

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Step 3.1.1.2.1

Factor $12$ out of $12 a^{2} b c^{3}$ .

$12 \frac{x}{12 (a^{2} b c^{3})} (a^{2} b c^{3}) = \frac{5}{3 a b} (12 a^{2} b c^{3})$

Step 3.1.1.2.2

Cancel the common factor.

$12 \frac{x}{12 (a^{2} b c^{3})} (a^{2} b c^{3}) = \frac{5}{3 a b} (12 a^{2} b c^{3})$

Step 3.1.1.2.3

Rewrite the expression.

$\frac{x}{a^{2} b c^{3}} (a^{2} b c^{3}) = \frac{5}{3 a b} (12 a^{2} b c^{3})$

Step 3.1.1.3

Cancel the common factor of $a^{2} b c^{3}$ .

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Step 3.1.1.3.1

Cancel the common factor.

$\frac{x}{a^{2} b c^{3}} (a^{2} b c^{3}) = \frac{5}{3 a b} (12 a^{2} b c^{3})$

Step 3.1.1.3.2

Rewrite the expression.

$x = \frac{5}{3 a b} (12 a^{2} b c^{3})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{5}{3 a b} (12 a^{2} b c^{3})$ .

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Step 3.2.1.1

Rewrite using the commutative property of multiplication.

$x = 12 \frac{5}{3 a b} (a^{2} b c^{3})$

Step 3.2.1.2

Cancel the common factor of $3$ .

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Step 3.2.1.2.1

Factor $3$ out of $12$ .

$x = 3 (4) \frac{5}{3 a b} (a^{2} b c^{3})$

Step 3.2.1.2.2

Factor $3$ out of $3 a b$ .

$x = 3 (4) \frac{5}{3 (a b)} (a^{2} b c^{3})$

Step 3.2.1.2.3

Cancel the common factor.

$x = 3 \cdot 4 \frac{5}{3 (a b)} (a^{2} b c^{3})$

Step 3.2.1.2.4

Rewrite the expression.

$x = 4 \frac{5}{a b} (a^{2} b c^{3})$

Step 3.2.1.3

Combine $4$ and $\frac{5}{a b}$ .

$x = \frac{4 \cdot 5}{a b} (a^{2} b c^{3})$

Step 3.2.1.4

Multiply $4$ by $5$ .

$x = \frac{20}{a b} (a^{2} b c^{3})$

Step 3.2.1.5

Cancel the common factor of $a b$ .

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Step 3.2.1.5.1

Factor $a b$ out of $a^{2} b c^{3}$ .

$x = \frac{20}{a b} (a b (a c^{3}))$

Step 3.2.1.5.2

Cancel the common factor.

$x = \frac{20}{a b} (a b (a c^{3}))$

Step 3.2.1.5.3

Rewrite the expression.

$x = 20 (a c^{3})$

$x = 20 a c^{3}$