Basic Math Examples

$\frac{1}{2} \cdot (m v^{2}) = mg h$

Step 1

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (m v^{2})) = 2 (mg h)$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $2 (\frac{1}{2} \cdot (m v^{2}))$ .

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Step 2.1.1.1

Multiply $\frac{1}{2} (m v^{2})$ .

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Step 2.1.1.1.1

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

$2 (\frac{m}{2} v^{2}) = 2 (mg h)$

Step 2.1.1.1.2

Combine $\frac{m}{2}$ and $v^{2}$ .

$2 \frac{m v^{2}}{2} = 2 (mg h)$

$2 \frac{m v^{2}}{2} = 2 (mg h)$

Step 2.1.1.2

Cancel the common factor of $2$ .

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Step 2.1.1.2.1

Cancel the common factor.

$2 \frac{m v^{2}}{2} = 2 (mg h)$

Step 2.1.1.2.2

Rewrite the expression.

$m v^{2} = 2 (mg h)$

$m v^{2} = 2 (mg h)$

$m v^{2} = 2 (mg h)$

$m v^{2} = 2 (mg h)$

Step 2.2

Simplify the right side.

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Step 2.2.1

Remove parentheses.

$m v^{2} = 2 mg h$

$m v^{2} = 2 mg h$

$m v^{2} = 2 mg h$

Step 3

Divide each term in $m v^{2} = 2 mg h$ by $v^{2}$ and simplify.

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Step 3.1

Divide each term in $m v^{2} = 2 mg h$ by $v^{2}$ .

$\frac{m v^{2}}{v^{2}} = \frac{2 mg h}{v^{2}}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $v^{2}$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{m v^{2}}{v^{2}} = \frac{2 mg h}{v^{2}}$

Step 3.2.1.2

Divide $m$ by $1$ .

$m = \frac{2 mg h}{v^{2}}$

$m = \frac{2 mg h}{v^{2}}$

$m = \frac{2 mg h}{v^{2}}$

$m = \frac{2 mg h}{v^{2}}$

Step 4

Rewrite the expression.

$m = \frac{2 h}{v^{2}} mg$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$