Pre-Algebra Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

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

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

Step 1.4

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

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Step 1.4.1

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

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

Step 1.4.2

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

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

Step 2

Subtract $\frac{a h}{2}$ from both sides of the equation.

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

Step 3

Factor $a$ out of $a - \frac{a h}{2}$ .

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Step 3.1

Factor $a$ out of $a^{1}$ .

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

Step 3.2

Factor $a$ out of $- \frac{a h}{2}$ .

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

Step 3.3

Factor $a$ out of $a \cdot 1 + a (- \frac{h}{2})$ .

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

Step 4

Divide each term in $a (1 - \frac{h}{2}) = \frac{b h}{2}$ by $1 - \frac{h}{2}$ and simplify.

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Step 4.1

Divide each term in $a (1 - \frac{h}{2}) = \frac{b h}{2}$ by $1 - \frac{h}{2}$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $1 - \frac{h}{2}$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $a$ by $1$ .

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 4.3.2

Simplify the denominator.

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Step 4.3.2.1

Write $1$ as a fraction with a common denominator.

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

Step 4.3.2.2

Combine the numerators over the common denominator.

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

Step 4.3.3

Multiply the numerator by the reciprocal of the denominator.

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

Step 4.3.4

Multiply $\frac{2}{2 - h}$ by $1$ .

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

Step 4.3.5

Cancel the common factor of $2$ .

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Step 4.3.5.1

Cancel the common factor.

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

Step 4.3.5.2

Rewrite the expression.

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

Step 4.3.6

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

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

Step 4.3.7

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

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