Pre-Algebra Examples

$f (- 4) = \frac{1}{4} x^{2} - 5$

Step 1

Divide each term in $f (- 4) = \frac{1}{4} x^{2} - 5$ by $- 4$ .

$\frac{f \cdot - 4}{- 4} = \frac{\frac{1}{4} x^{2}}{- 4} + \frac{- 5}{- 4}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $- 4$ .

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Step 2.1.1

Cancel the common factor.

$\frac{f \cdot - 4}{- 4} = \frac{\frac{1}{4} x^{2}}{- 4} + \frac{- 5}{- 4}$

Step 2.1.2

Divide $f$ by $1$ .

$f = \frac{\frac{1}{4} x^{2}}{- 4} + \frac{- 5}{- 4}$

Step 3

Simplify the right side.

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Step 3.1

Simplify each term.

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Step 3.1.1

Combine $\frac{1}{4}$ and $x^{2}$ .

$f = \frac{\frac{x^{2}}{4}}{- 4} + \frac{- 5}{- 4}$

Step 3.1.2

Multiply the numerator by the reciprocal of the denominator.

$f = \frac{x^{2}}{4} \cdot \frac{1}{- 4} + \frac{- 5}{- 4}$

Step 3.1.3

Combine.

$f = \frac{x^{2} \cdot 1}{4 \cdot - 4} + \frac{- 5}{- 4}$

Step 3.1.4

Multiply $x^{2}$ by $1$ .

$f = \frac{x^{2}}{4 \cdot - 4} + \frac{- 5}{- 4}$

Step 3.1.5

Multiply $4$ by $- 4$ .

$f = \frac{x^{2}}{- 16} + \frac{- 5}{- 4}$

Step 3.1.6

Move the negative in front of the fraction.

$f = - \frac{x^{2}}{16} + \frac{- 5}{- 4}$

Step 3.1.7

Dividing two negative values results in a positive value.

$f = - \frac{x^{2}}{16} + \frac{5}{4}$