Finite Math Examples

$r = \frac{n}{4} \cdot (a + l)$

Step 1

Rewrite the equation as $\frac{n}{4} \cdot (a + l) = r$ .

$\frac{n}{4} \cdot (a + l) = r$

Step 2

Multiply each term in $\frac{n}{4} \cdot (a + l) = r$ by $\frac{4}{n}$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{n}{4} \cdot (a + l) = r$ by $\frac{4}{n}$ .

$\frac{n}{4} \cdot (a + l) \frac{4}{n} = r \frac{4}{n}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify terms.

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Step 2.2.1.1

Apply the distributive property.

$(\frac{n}{4} a + \frac{n}{4} l) \frac{4}{n} = r \frac{4}{n}$

Step 2.2.1.2

Combine $\frac{n}{4}$ and $a$ .

$(\frac{n a}{4} + \frac{n}{4} l) \frac{4}{n} = r \frac{4}{n}$

Step 2.2.1.3

Combine $\frac{n}{4}$ and $l$ .

$(\frac{n a}{4} + \frac{n l}{4}) \frac{4}{n} = r \frac{4}{n}$

Step 2.2.1.4

Multiply $\frac{n a}{4} + \frac{n l}{4}$ by $\frac{4}{n}$ .

$\frac{(\frac{n a}{4} + \frac{n l}{4}) \cdot 4}{n} = r \frac{4}{n}$

Step 2.2.2

Simplify the numerator.

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Step 2.2.2.1

Combine the numerators over the common denominator.

$\frac{\frac{n a + n l}{4} \cdot 4}{n} = r \frac{4}{n}$

Step 2.2.2.2

Factor $n$ out of $n a + n l$ .

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Step 2.2.2.2.1

Factor $n$ out of $n a$ .

$\frac{\frac{n (a) + n l}{4} \cdot 4}{n} = r \frac{4}{n}$

Step 2.2.2.2.2

Factor $n$ out of $n l$ .

$\frac{\frac{n (a) + n (l)}{4} \cdot 4}{n} = r \frac{4}{n}$

Step 2.2.2.2.3

Factor $n$ out of $n (a) + n (l)$ .

$\frac{\frac{n (a + l)}{4} \cdot 4}{n} = r \frac{4}{n}$

Step 2.2.3

Combine $\frac{n (a + l)}{4}$ and $4$ .

$\frac{\frac{n (a + l) \cdot 4}{4}}{n} = r \frac{4}{n}$

Step 2.2.4

Reduce the expression by cancelling the common factors.

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Step 2.2.4.1

Reduce the expression $\frac{n (a + l) \cdot 4}{4}$ by cancelling the common factors.

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Step 2.2.4.1.1

Cancel the common factor.

$\frac{\frac{n (a + l) \cdot 4}{4}}{n} = r \frac{4}{n}$

Step 2.2.4.1.2

Rewrite the expression.

$\frac{\frac{n (a + l)}{1}}{n} = r \frac{4}{n}$

Step 2.2.4.2

Divide $n (a + l)$ by $1$ .

$\frac{n (a + l)}{n} = r \frac{4}{n}$

Step 2.2.5

Cancel the common factor of $n$ .

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Step 2.2.5.1

Cancel the common factor.

$\frac{n (a + l)}{n} = r \frac{4}{n}$

Step 2.2.5.2

Divide $a + l$ by $1$ .

$a + l = r \frac{4}{n}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Combine $r$ and $\frac{4}{n}$ .

$a + l = \frac{r \cdot 4}{n}$

Step 2.3.2

Move $4$ to the left of $r$ .

$a + l = \frac{4 r}{n}$

Step 3

Subtract $a$ from both sides of the equation.

$l = \frac{4 r}{n} - a$