Basic Math Examples

$s = \frac{1}{2} \cdot (u + v) \cdot t$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot (u + v) \cdot t = s$ .

$\frac{1}{2} \cdot (u + v) \cdot t = s$

Step 2

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

$\frac{t}{2} \cdot (u + v) = s$

Step 3

Multiply each term in $\frac{t}{2} \cdot (u + v) = s$ by $\frac{2}{t}$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{t}{2} \cdot (u + v) = s$ by $\frac{2}{t}$ .

$\frac{t}{2} \cdot (u + v) \frac{2}{t} = s \frac{2}{t}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify terms.

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Step 3.2.1.1

Apply the distributive property.

$(\frac{t}{2} u + \frac{t}{2} v) \frac{2}{t} = s \frac{2}{t}$

Step 3.2.1.2

Combine $\frac{t}{2}$ and $u$ .

$(\frac{t u}{2} + \frac{t}{2} v) \frac{2}{t} = s \frac{2}{t}$

Step 3.2.1.3

Combine $\frac{t}{2}$ and $v$ .

$(\frac{t u}{2} + \frac{t v}{2}) \frac{2}{t} = s \frac{2}{t}$

Step 3.2.1.4

Multiply $\frac{t u}{2} + \frac{t v}{2}$ by $\frac{2}{t}$ .

$\frac{(\frac{t u}{2} + \frac{t v}{2}) \cdot 2}{t} = s \frac{2}{t}$

Step 3.2.2

Simplify the numerator.

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Step 3.2.2.1

Combine the numerators over the common denominator.

$\frac{\frac{t u + t v}{2} \cdot 2}{t} = s \frac{2}{t}$

Step 3.2.2.2

Factor $t$ out of $t u + t v$ .

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Step 3.2.2.2.1

Factor $t$ out of $t u$ .

$\frac{\frac{t (u) + t v}{2} \cdot 2}{t} = s \frac{2}{t}$

Step 3.2.2.2.2

Factor $t$ out of $t v$ .

$\frac{\frac{t (u) + t (v)}{2} \cdot 2}{t} = s \frac{2}{t}$

Step 3.2.2.2.3

Factor $t$ out of $t (u) + t (v)$ .

$\frac{\frac{t (u + v)}{2} \cdot 2}{t} = s \frac{2}{t}$

Step 3.2.3

Combine $\frac{t (u + v)}{2}$ and $2$ .

$\frac{\frac{t (u + v) \cdot 2}{2}}{t} = s \frac{2}{t}$

Step 3.2.4

Reduce the expression by cancelling the common factors.

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Step 3.2.4.1

Reduce the expression $\frac{t (u + v) \cdot 2}{2}$ by cancelling the common factors.

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Step 3.2.4.1.1

Cancel the common factor.

$\frac{\frac{t (u + v) \cdot 2}{2}}{t} = s \frac{2}{t}$

Step 3.2.4.1.2

Rewrite the expression.

$\frac{\frac{t (u + v)}{1}}{t} = s \frac{2}{t}$

Step 3.2.4.2

Divide $t (u + v)$ by $1$ .

$\frac{t (u + v)}{t} = s \frac{2}{t}$

Step 3.2.5

Cancel the common factor of $t$ .

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Step 3.2.5.1

Cancel the common factor.

$\frac{t (u + v)}{t} = s \frac{2}{t}$

Step 3.2.5.2

Divide $u + v$ by $1$ .

$u + v = s \frac{2}{t}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Combine $s$ and $\frac{2}{t}$ .

$u + v = \frac{s \cdot 2}{t}$

Step 3.3.2

Move $2$ to the left of $s$ .

$u + v = \frac{2 s}{t}$

Step 4

Subtract $u$ from both sides of the equation.

$v = \frac{2 s}{t} - u$