Basic Math Examples

$0.0348 = \frac{\frac{v}{342}}{\frac{v}{342} + \frac{100 - v}{1000}}$

Step 1

Rewrite the equation as $\frac{\frac{v}{342}}{\frac{v}{342} + \frac{100 - v}{1000}} = 0.0348$ .

$\frac{\frac{v}{342}}{\frac{v}{342} + \frac{100 - v}{1000}} = 0.0348$

Step 2

Factor each term.

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Step 2.1

To write $\frac{v}{342}$ as a fraction with a common denominator, multiply by $\frac{500}{500}$ .

$\frac{\frac{v}{342}}{\frac{v}{342} \cdot \frac{500}{500} + \frac{100 - v}{1000}} = 0.0348$

Step 2.2

To write $\frac{100 - v}{1000}$ as a fraction with a common denominator, multiply by $\frac{171}{171}$ .

$\frac{\frac{v}{342}}{\frac{v}{342} \cdot \frac{500}{500} + \frac{100 - v}{1000} \cdot \frac{171}{171}} = 0.0348$

Step 2.3

Write each expression with a common denominator of $171000$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{v}{342}$ by $\frac{500}{500}$ .

$\frac{\frac{v}{342}}{\frac{v \cdot 500}{342 \cdot 500} + \frac{100 - v}{1000} \cdot \frac{171}{171}} = 0.0348$

Step 2.3.2

Multiply $342$ by $500$ .

$\frac{\frac{v}{342}}{\frac{v \cdot 500}{171000} + \frac{100 - v}{1000} \cdot \frac{171}{171}} = 0.0348$

Step 2.3.3

Multiply $\frac{100 - v}{1000}$ by $\frac{171}{171}$ .

$\frac{\frac{v}{342}}{\frac{v \cdot 500}{171000} + \frac{(100 - v) \cdot 171}{1000 \cdot 171}} = 0.0348$

Step 2.3.4

Multiply $1000$ by $171$ .

$\frac{\frac{v}{342}}{\frac{v \cdot 500}{171000} + \frac{(100 - v) \cdot 171}{171000}} = 0.0348$

Step 2.4

Combine the numerators over the common denominator.

$\frac{\frac{v}{342}}{\frac{v \cdot 500 + (100 - v) \cdot 171}{171000}} = 0.0348$

Step 2.5

Rewrite $\frac{v \cdot 500 + (100 - v) \cdot 171}{171000}$ in a factored form.

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Step 2.5.1

Move $500$ to the left of $v$ .

$\frac{\frac{v}{342}}{\frac{500 v + (100 - v) \cdot 171}{171000}} = 0.0348$

Step 2.5.2

Apply the distributive property.

$\frac{\frac{v}{342}}{\frac{500 v + 100 \cdot 171 - v \cdot 171}{171000}} = 0.0348$

Step 2.5.3

Multiply $100$ by $171$ .

$\frac{\frac{v}{342}}{\frac{500 v + 17100 - v \cdot 171}{171000}} = 0.0348$

Step 2.5.4

Multiply $171$ by $- 1$ .

$\frac{\frac{v}{342}}{\frac{500 v + 17100 - 171 v}{171000}} = 0.0348$

Step 2.5.5

Subtract $171 v$ from $500 v$ .

$\frac{\frac{v}{342}}{\frac{329 v + 17100}{171000}} = 0.0348$

Step 2.6

Multiply the numerator by the reciprocal of the denominator.

$\frac{v}{342} \cdot \frac{171000}{329 v + 17100} = 0.0348$

Step 2.7

Cancel the common factor of $342$ .

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Step 2.7.1

Factor $342$ out of $171000$ .

$\frac{v}{342} \cdot \frac{342 (500)}{329 v + 17100} = 0.0348$

Step 2.7.2

Cancel the common factor.

$\frac{v}{342} \cdot \frac{342 \cdot 500}{329 v + 17100} = 0.0348$

Step 2.7.3

Rewrite the expression.

$v \frac{500}{329 v + 17100} = 0.0348$

Step 2.8

Combine $v$ and $\frac{500}{329 v + 17100}$ .

$\frac{v \cdot 500}{329 v + 17100} = 0.0348$

Step 2.9

Move $500$ to the left of $v$ .

$\frac{500 \cdot v}{329 v + 17100} = 0.0348$

Step 2.10

Multiply $500$ by $v$ .

$\frac{500 v}{329 v + 17100} = 0.0348$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

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

$329 v + 17100, 1$

Step 3.2

Remove parentheses.

$329 v + 17100, 1$

Step 3.3

The LCM of one and any expression is the expression.

$329 v + 17100$

Step 4

Multiply each term in $\frac{500 v}{329 v + 17100} = 0.0348$ by $329 v + 17100$ to eliminate the fractions.

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Step 4.1

Multiply each term in $\frac{500 v}{329 v + 17100} = 0.0348$ by $329 v + 17100$ .

$\frac{500 v}{329 v + 17100} (329 v + 17100) = 0.0348 (329 v + 17100)$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $329 v + 17100$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{500 v}{329 v + 17100} (329 v + 17100) = 0.0348 (329 v + 17100)$

Step 4.2.1.2

Rewrite the expression.

$500 v = 0.0348 (329 v + 17100)$

Step 4.3

Simplify the right side.

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Step 4.3.1

Apply the distributive property.

$500 v = 0.0348 (329 v) + 0.0348 \cdot 17100$

Step 4.3.2

Multiply.

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Step 4.3.2.1

Multiply $329$ by $0.0348$ .

$500 v = 11.4492 v + 0.0348 \cdot 17100$

Step 4.3.2.2

Multiply $0.0348$ by $17100$ .

$500 v = 11.4492 v + 595.08$

Step 5

Solve the equation.

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Step 5.1

Move all terms containing $v$ to the left side of the equation.

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Step 5.1.1

Subtract $11.4492 v$ from both sides of the equation.

$500 v - 11.4492 v = 595.08$

Step 5.1.2

Subtract $11.4492 v$ from $500 v$ .

$488.5508 v = 595.08$

Step 5.2

Divide each term in $488.5508 v = 595.08$ by $488.5508$ and simplify.

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Step 5.2.1

Divide each term in $488.5508 v = 595.08$ by $488.5508$ .

$\frac{488.5508 v}{488.5508} = \frac{595.08}{488.5508}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $488.5508$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{488.5508 v}{488.5508} = \frac{595.08}{488.5508}$

Step 5.2.2.1.2

Divide $v$ by $1$ .

$v = \frac{595.08}{488.5508}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $595.08$ by $488.5508$ .

$v = 1.21805142$