Solve for B (2pi)/B=4pi

$\frac{2 π}{B} = 4 π$

Step 1

Find the LCD of the terms in the equation.

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

$B, 1$

The LCM of one and any expression is the expression.

$B$

Step 2

Multiply each term in $\frac{2 π}{B} = 4 π$ by $B$ to eliminate the fractions.

Multiply each term in $\frac{2 π}{B} = 4 π$ by $B$ .

$\frac{2 π}{B} B = 4 π B$

Simplify the left side.

Cancel the common factor of $B$ .

Cancel the common factor.

$\frac{2 π}{B} B = 4 π B$

Rewrite the expression.

$2 π = 4 π B$

Step 3

Solve the equation.

Rewrite the equation as $4 π B = 2 π$ .

$4 π B = 2 π$

Divide each term in $4 π B = 2 π$ by $4 π$ and simplify.

Divide each term in $4 π B = 2 π$ by $4 π$ .

$\frac{4 π B}{4 π} = \frac{2 π}{4 π}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 π B}{4 π} = \frac{2 π}{4 π}$

Rewrite the expression.

$\frac{π B}{π} = \frac{2 π}{4 π}$

Cancel the common factor of $π$ .

Cancel the common factor.

$\frac{π B}{π} = \frac{2 π}{4 π}$

Divide $B$ by $1$ .

$B = \frac{2 π}{4 π}$

Simplify the right side.

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2 π$ .

$B = \frac{2 (π)}{4 π}$

Cancel the common factors.

Factor $2$ out of $4 π$ .

$B = \frac{2 (π)}{2 (2 π)}$

Cancel the common factor.

$B = \frac{2 π}{2 (2 π)}$

Rewrite the expression.

$B = \frac{π}{2 π}$

Cancel the common factor of $π$ .

Cancel the common factor.

$B = \frac{π}{2 π}$

Rewrite the expression.

$B = \frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$B = \frac{1}{2}$

Decimal Form:

$B = 0.5$

Solve for B (2pi)/B=4pi

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