Precalculus Examples

$\frac{2 π}{b} = 4$

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$b, 1$

Step 1.2

The LCM of one and any expression is the expression.

$b$

Step 2

Multiply each term in

$\frac{2 π}{b} = 4$ by

$b$ to eliminate the fractions.

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Step 2.1

Multiply each term in

$\frac{2 π}{b} = 4$ by

$b$ .

$\frac{2 π}{b} b = 4 b$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of

$b$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 π}{b} b = 4 b$

Step 2.2.1.2

Rewrite the expression.

$2 π = 4 b$

Step 3

Solve the equation.

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Step 3.1

Rewrite the equation as

$4 b = 2 π$ .

$4 b = 2 π$

Step 3.2

Divide each term in

$4 b = 2 π$ by

$4$ and simplify.

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Step 3.2.1

Divide each term in

$4 b = 2 π$ by

$4$ .

$\frac{4 b}{4} = \frac{2 π}{4}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of

$4$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{4 b}{4} = \frac{2 π}{4}$

Step 3.2.2.1.2

Divide

$b$ by

$1$ .

$b = \frac{2 π}{4}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Cancel the common factor of

$2$ and

$4$ .

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Step 3.2.3.1.1

Factor

$2$ out of

$2 π$ .

$b = \frac{2 (π)}{4}$

Step 3.2.3.1.2

Cancel the common factors.

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Step 3.2.3.1.2.1

Factor

$2$ out of

$4$ .

$b = \frac{2 π}{2 \cdot 2}$

Step 3.2.3.1.2.2

Cancel the common factor.

$b = \frac{2 π}{2 \cdot 2}$

Step 3.2.3.1.2.3

Rewrite the expression.

$b = \frac{π}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$b = \frac{π}{2}$

Decimal Form:

$b = 1.57079632 \dots$