Pre-Algebra Examples

$p = \frac{a}{1 + r t}$

Step 1

Rewrite the equation as $\frac{a}{1 + r t} = p$ .

$\frac{a}{1 + r t} = p$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$1 + r t, 1$

Step 2.2

Remove parentheses.

$1 + r t, 1$

Step 2.3

The LCM of one and any expression is the expression.

$1 + r t$

Step 3

Multiply each term in $\frac{a}{1 + r t} = p$ by $1 + r t$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{a}{1 + r t} = p$ by $1 + r t$ .

$\frac{a}{1 + r t} (1 + r t) = p (1 + r t)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $1 + r t$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{a}{1 + r t} (1 + r t) = p (1 + r t)$

Step 3.2.1.2

Rewrite the expression.

$a = p (1 + r t)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$a = p \cdot 1 + p (r t)$

Step 3.3.2

Multiply $p$ by $1$ .

$a = p + p r t$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $p + p r t = a$ .

$p + p r t = a$

Step 4.2

Subtract $p$ from both sides of the equation.

$p r t = a - p$

Step 4.3

Divide each term in $p r t = a - p$ by $p t$ and simplify.

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Step 4.3.1

Divide each term in $p r t = a - p$ by $p t$ .

$\frac{p r t}{p t} = \frac{a}{p t} + \frac{- p}{p t}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $p$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{p r t}{p t} = \frac{a}{p t} + \frac{- p}{p t}$

Step 4.3.2.1.2

Rewrite the expression.

$\frac{r t}{t} = \frac{a}{p t} + \frac{- p}{p t}$

Step 4.3.2.2

Cancel the common factor of $t$ .

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Step 4.3.2.2.1

Cancel the common factor.

$\frac{r t}{t} = \frac{a}{p t} + \frac{- p}{p t}$

Step 4.3.2.2.2

Divide $r$ by $1$ .

$r = \frac{a}{p t} + \frac{- p}{p t}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Simplify each term.

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Step 4.3.3.1.1

Cancel the common factor of $p$ .

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Step 4.3.3.1.1.1

Cancel the common factor.

$r = \frac{a}{p t} + \frac{- p}{p t}$

Step 4.3.3.1.1.2

Rewrite the expression.

$r = \frac{a}{p t} + \frac{- 1}{t}$

Step 4.3.3.1.2

Move the negative in front of the fraction.

$r = \frac{a}{p t} - \frac{1}{t}$