Algebra Examples

$\frac{1}{a} = \frac{c}{2 b}$

Step 1

Rewrite the equation as $\frac{c}{2 b} = \frac{1}{a}$ .

$\frac{c}{2 b} = \frac{1}{a}$

Step 2

Multiply both sides by $2 b$ .

$\frac{c}{2 b} (2 b) = \frac{1}{a} (2 b)$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{c}{2 b} (2 b)$ .

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Step 3.1.1.1

Rewrite using the commutative property of multiplication.

$2 \frac{c}{2 b} b = \frac{1}{a} (2 b)$

Step 3.1.1.2

Cancel the common factor of $2$ .

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Step 3.1.1.2.1

Factor $2$ out of $2 b$ .

$2 \frac{c}{2 (b)} b = \frac{1}{a} (2 b)$

Step 3.1.1.2.2

Cancel the common factor.

$2 \frac{c}{2 b} b = \frac{1}{a} (2 b)$

Step 3.1.1.2.3

Rewrite the expression.

$\frac{c}{b} b = \frac{1}{a} (2 b)$

Step 3.1.1.3

Cancel the common factor of $b$ .

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Step 3.1.1.3.1

Cancel the common factor.

$\frac{c}{b} b = \frac{1}{a} (2 b)$

Step 3.1.1.3.2

Rewrite the expression.

$c = \frac{1}{a} (2 b)$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{1}{a} (2 b)$ .

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Step 3.2.1.1

Rewrite using the commutative property of multiplication.

$c = 2 \frac{1}{a} b$

Step 3.2.1.2

Combine $2$ and $\frac{1}{a}$ .

$c = \frac{2}{a} b$

Step 3.2.1.3

Combine $\frac{2}{a}$ and $b$ .

$c = \frac{2 b}{a}$