Pre-Algebra Examples

$A = P (1 + n r)$

Step 1

Rewrite the equation as $P (1 + n r) = A$ .

$P (1 + n r) = A$

Step 2

Divide each term in $P (1 + n r) = A$ by $P$ and simplify.

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Step 2.1

Divide each term in $P (1 + n r) = A$ by $P$ .

$\frac{P (1 + n r)}{P} = \frac{A}{P}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $P$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{P (1 + n r)}{P} = \frac{A}{P}$

Step 2.2.1.2

Divide $1 + n r$ by $1$ .

$1 + n r = \frac{A}{P}$

Step 3

Subtract $1$ from both sides of the equation.

$n r = \frac{A}{P} - 1$

Step 4

Divide each term in $n r = \frac{A}{P} - 1$ by $n$ and simplify.

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Step 4.1

Divide each term in $n r = \frac{A}{P} - 1$ by $n$ .

$\frac{n r}{n} = \frac{\frac{A}{P}}{n} + \frac{- 1}{n}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $n$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{n r}{n} = \frac{\frac{A}{P}}{n} + \frac{- 1}{n}$

Step 4.2.1.2

Divide $r$ by $1$ .

$r = \frac{\frac{A}{P}}{n} + \frac{- 1}{n}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Multiply the numerator by the reciprocal of the denominator.

$r = \frac{A}{P} \cdot \frac{1}{n} + \frac{- 1}{n}$

Step 4.3.1.2

Multiply $\frac{A}{P}$ by $\frac{1}{n}$ .

$r = \frac{A}{P n} + \frac{- 1}{n}$

Step 4.3.1.3

Move the negative in front of the fraction.

$r = \frac{A}{P n} - \frac{1}{n}$