Pre-Algebra Examples

$A = \frac{(a + b) h}{2}$

Step 1

Rewrite the equation as $\frac{(a + b) h}{2} = A$ .

$\frac{(a + b) h}{2} = A$

Step 2

Multiply both sides of the equation by $2$ .

$2 \frac{(a + b) h}{2} = 2 A$

Step 3

Simplify the left side.

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Step 3.1

Simplify $2 \frac{(a + b) h}{2}$ .

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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.

$2 \frac{(a + b) h}{2} = 2 A$

Step 3.1.1.2

Rewrite the expression.

$(a + b) h = 2 A$

Step 3.1.2

Apply the distributive property.

$a h + b h = 2 A$

Step 4

Factor $h$ out of $a h + b h$ .

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Step 4.1

Factor $h$ out of $a h$ .

$h a + b h = 2 A$

Step 4.2

Factor $h$ out of $b h$ .

$h a + h b = 2 A$

Step 4.3

Factor $h$ out of $h a + h b$ .

$h (a + b) = 2 A$

Step 5

Divide each term in $h (a + b) = 2 A$ by $a + b$ and simplify.

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Step 5.1

Divide each term in $h (a + b) = 2 A$ by $a + b$ .

$\frac{h (a + b)}{a + b} = \frac{2 A}{a + b}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $a + b$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{h (a + b)}{a + b} = \frac{2 A}{a + b}$

Step 5.2.1.2

Divide $h$ by $1$ .

$h = \frac{2 A}{a + b}$