Algebra Examples

$a = \frac{1}{2} a p$

Step 1

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

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Step 1.1

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

$a = \frac{a}{2} p$

Step 1.2

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

$a = \frac{a p}{2}$

Step 2

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

$a - \frac{a p}{2} = 0$

Step 3

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

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Step 3.1

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

$a \cdot 1 - \frac{a p}{2} = 0$

Step 3.2

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

$a \cdot 1 + a (- \frac{p}{2}) = 0$

Step 3.3

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

$a (1 - \frac{p}{2}) = 0$

Step 4

Divide each term in $a (1 - \frac{p}{2}) = 0$ by $1 - \frac{p}{2}$ and simplify.

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Step 4.1

Divide each term in $a (1 - \frac{p}{2}) = 0$ by $1 - \frac{p}{2}$ .

$\frac{a (1 - \frac{p}{2})}{1 - \frac{p}{2}} = \frac{0}{1 - \frac{p}{2}}$

Step 4.2

Simplify the left side.

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Step 4.2.1

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

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Step 4.2.1.1

Cancel the common factor.

$\frac{a (1 - \frac{p}{2})}{1 - \frac{p}{2}} = \frac{0}{1 - \frac{p}{2}}$

Step 4.2.1.2

Divide $a$ by $1$ .

$a = \frac{0}{1 - \frac{p}{2}}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify the denominator.

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Step 4.3.1.1

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

$a = \frac{0}{\frac{2}{2} - \frac{p}{2}}$

Step 4.3.1.2

Combine the numerators over the common denominator.

$a = \frac{0}{\frac{2 - p}{2}}$

Step 4.3.2

Multiply the numerator by the reciprocal of the denominator.

$a = 0 \frac{2}{2 - p}$

Step 4.3.3

Multiply $0$ by $\frac{2}{2 - p}$ .

$a = 0$

Step 5

To rewrite as a function of $p$ , write the equation so that $a$ is by itself on one side of the equal sign and an expression involving only $p$ is on the other side.

$f (p) = 0$