Precalculus Examples

$c (500) = \frac{24 (500) + 1600}{500}$

Step 1

Simplify.

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Step 1.1

Multiply $24$ by $500$ .

$c (500) = \frac{12000 + 1600}{500}$

Step 1.2

Reduce the expression $\frac{12000 + 1600}{500}$ by cancelling the common factors.

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Step 1.2.1

Factor $100$ out of $12000$ .

$c (500) = \frac{100 (120) + 1600}{500}$

Step 1.2.2

Factor $100$ out of $1600$ .

$c (500) = \frac{100 \cdot 120 + 100 \cdot 16}{500}$

Step 1.2.3

Factor $100$ out of $100 \cdot 120 + 100 \cdot 16$ .

$c (500) = \frac{100 \cdot (120 + 16)}{500}$

Step 1.2.4

Factor $100$ out of $500$ .

$c (500) = \frac{100 \cdot (120 + 16)}{100 (5)}$

Step 1.2.5

Cancel the common factor.

$c (500) = \frac{100 \cdot (120 + 16)}{100 \cdot 5}$

Step 1.2.6

Rewrite the expression.

$c (500) = \frac{120 + 16}{5}$

Step 1.3

Add $120$ and $16$ .

$c (500) = \frac{136}{5}$

Step 2

Divide each term in $c (500) = \frac{136}{5}$ by $500$ and simplify.

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Step 2.1

Divide each term in $c (500) = \frac{136}{5}$ by $500$ .

$\frac{c (500)}{500} = \frac{\frac{136}{5}}{500}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $500$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{c \cdot 500}{500} = \frac{\frac{136}{5}}{500}$

Step 2.2.1.2

Divide $c$ by $1$ .

$c = \frac{\frac{136}{5}}{500}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$c = \frac{136}{5} \cdot \frac{1}{500}$

Step 2.3.2

Cancel the common factor of $4$ .

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Step 2.3.2.1

Factor $4$ out of $136$ .

$c = \frac{4 (34)}{5} \cdot \frac{1}{500}$

Step 2.3.2.2

Factor $4$ out of $500$ .

$c = \frac{4 \cdot 34}{5} \cdot \frac{1}{4 \cdot 125}$

Step 2.3.2.3

Cancel the common factor.

$c = \frac{4 \cdot 34}{5} \cdot \frac{1}{4 \cdot 125}$

Step 2.3.2.4

Rewrite the expression.

$c = \frac{34}{5} \cdot \frac{1}{125}$

Step 2.3.3

Multiply $\frac{34}{5}$ by $\frac{1}{125}$ .

$c = \frac{34}{5 \cdot 125}$

Step 2.3.4

Multiply $5$ by $125$ .

$c = \frac{34}{625}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$c = \frac{34}{625}$

Decimal Form:

$c = 0.0544$