Pre-Algebra Examples

$A = \frac{1}{2} \cdot (h (a + b))$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot (h (a + b)) = A$ .

$\frac{1}{2} \cdot (h (a + b)) = A$

Step 2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (h (a + b))) = 2 A$

Step 3

Simplify the left side.

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Step 3.1

Simplify $2 (\frac{1}{2} \cdot (h (a + b)))$ .

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Step 3.1.1

Apply the distributive property.

$2 (\frac{1}{2} \cdot (h a + h b)) = 2 A$

Step 3.1.2

Apply the distributive property.

$2 (\frac{1}{2} (h a) + \frac{1}{2} (h b)) = 2 A$

Step 3.1.3

Multiply $\frac{1}{2} (h a)$ .

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Step 3.1.3.1

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

$2 (\frac{h}{2} a + \frac{1}{2} (h b)) = 2 A$

Step 3.1.3.2

Combine $\frac{h}{2}$ and $a$ .

$2 (\frac{h a}{2} + \frac{1}{2} (h b)) = 2 A$

$2 (\frac{h a}{2} + \frac{1}{2} (h b)) = 2 A$

Step 3.1.4

Multiply $\frac{1}{2} (h b)$ .

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Step 3.1.4.1

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

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

Step 3.1.4.2

Combine $\frac{h}{2}$ and $b$ .

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

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

Step 3.1.5

Apply the distributive property.

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

Step 3.1.6

Cancel the common factor of $2$ .

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Step 3.1.6.1

Cancel the common factor.

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

Step 3.1.6.2

Rewrite the expression.

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

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

Step 3.1.7

Cancel the common factor of $2$ .

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Step 3.1.7.1

Cancel the common factor.

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

Step 3.1.7.2

Rewrite the expression.

$h a + h b = 2 A$

$h a + h b = 2 A$

$h a + h b = 2 A$

$h a + h b = 2 A$

Step 4

Subtract $h b$ from both sides of the equation.

$h a = 2 A - h b$

Step 5

Divide each term in $h a = 2 A - h b$ by $h$ and simplify.

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Step 5.1

Divide each term in $h a = 2 A - h b$ by $h$ .

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

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $h$ .

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Step 5.2.1.1

Cancel the common factor.

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

Step 5.2.1.2

Divide $a$ by $1$ .

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

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

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

Step 5.3

Simplify the right side.

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Step 5.3.1

Simplify each term.

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Step 5.3.1.1

Cancel the common factor of $h$ .

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Step 5.3.1.1.1

Cancel the common factor.

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

Step 5.3.1.1.2

Divide $- 1 b$ by $1$ .

$a = \frac{2 A}{h} - 1 b$

$a = \frac{2 A}{h} - 1 b$

Step 5.3.1.2

Rewrite $- 1 b$ as $- b$ .

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

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

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

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

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