Pre-Algebra Examples

$s = \frac{r (a + c)}{2}$

Step 1

Rewrite the equation as $\frac{r (a + c)}{2} = s$ .

$\frac{r (a + c)}{2} = s$

Step 2

Multiply both sides of the equation by $2$ .

$2 \frac{r (a + c)}{2} = 2 s$

Step 3

Simplify the left side.

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Step 3.1

Simplify $2 \frac{r (a + c)}{2}$ .

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Step 3.1.1

Cancel the common factor of $2$ .

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Step 3.1.1.1

Cancel the common factor.

$2 \frac{r (a + c)}{2} = 2 s$

Step 3.1.1.2

Rewrite the expression.

$r (a + c) = 2 s$

Step 3.1.2

Apply the distributive property.

$r a + r c = 2 s$

Step 4

Factor $r$ out of $r a + r c$ .

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Step 4.1

Factor $r$ out of $r a$ .

$r (a) + r c = 2 s$

Step 4.2

Factor $r$ out of $r c$ .

$r (a) + r (c) = 2 s$

Step 4.3

Factor $r$ out of $r (a) + r (c)$ .

$r (a + c) = 2 s$

Step 5

Divide each term in $r (a + c) = 2 s$ by $a + c$ and simplify.

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Step 5.1

Divide each term in $r (a + c) = 2 s$ by $a + c$ .

$\frac{r (a + c)}{a + c} = \frac{2 s}{a + c}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $a + c$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{r (a + c)}{a + c} = \frac{2 s}{a + c}$

Step 5.2.1.2

Divide $r$ by $1$ .

$r = \frac{2 s}{a + c}$