Finite Math Examples

$2.2165 = \frac{2.99792 \cdot 10^{8}}{v}$

Step 1

Rewrite the equation as $\frac{2.99792 \cdot 10^{8}}{v} = 2.2165$ .

$\frac{2.99792 \cdot 10^{8}}{v} = 2.2165$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

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

$v, 1$

Step 2.2

The LCM of one and any expression is the expression.

$v$

Step 3

Multiply each term in $\frac{2.99792 \cdot 10^{8}}{v} = 2.2165$ by $v$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{2.99792 \cdot 10^{8}}{v} = 2.2165$ by $v$ .

$\frac{2.99792 \cdot 10^{8}}{v} v = 2.2165 v$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $v$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2.99792 \cdot 10^{8}}{v} v = 2.2165 v$

Step 3.2.1.2

Rewrite the expression.

$2.99792 \cdot 10^{8} = 2.2165 v$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $2.2165 v = 2.99792 \cdot 10^{8}$ .

$2.2165 v = 2.99792 \cdot 10^{8}$

Step 4.2

Divide each term in $2.2165 v = 2.99792 \cdot 10^{8}$ by $2.2165$ and simplify.

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Step 4.2.1

Divide each term in $2.2165 v = 2.99792 \cdot 10^{8}$ by $2.2165$ .

$\frac{2.2165 v}{2.2165} = \frac{2.99792 \cdot 10^{8}}{2.2165}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $2.2165$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{2.2165 v}{2.2165} = \frac{2.99792 \cdot 10^{8}}{2.2165}$

Step 4.2.2.1.2

Divide $v$ by $1$ .

$v = \frac{2.99792 \cdot 10^{8}}{2.2165}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide using scientific notation.

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Step 4.2.3.1.1

Group coefficients together and exponents together to divide numbers in scientific notation.

$v = (\frac{2.99792}{2.2165}) (\frac{10^{8}}{1})$

Step 4.2.3.1.2

Divide $2.99792$ by $2.2165$ .

$v = 1.3525468 \frac{10^{8}}{1}$

Step 4.2.3.1.3

Divide $10^{8}$ by $1$ .

$v = 1.3525468 \cdot 10^{8}$

Step 5

The result can be shown in multiple forms.

Scientific Notation:

$v = 1.3525468 \cdot 10^{8}$

Expanded Form:

$v = 135254680.803068$