Algebra Examples

$f (\frac{1}{2}) = - \frac{2}{3} x + 5$

Step 1

Replace the variable $x$ with $\frac{1}{2}$ in the expression.

$f (\frac{1}{2}) = - \frac{2}{3} \cdot \frac{1}{2} + 5$

Step 2

Simplify the result.

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Step 2.1

Simplify each term.

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Step 2.1.1

Cancel the common factor of $2$ .

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Step 2.1.1.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$f (\frac{1}{2}) = \frac{- 2}{3} \cdot \frac{1}{2} + 5$

Step 2.1.1.2

Factor $2$ out of $- 2$ .

$f (\frac{1}{2}) = \frac{2 (- 1)}{3} \cdot \frac{1}{2} + 5$

Step 2.1.1.3

Cancel the common factor.

$f (\frac{1}{2}) = \frac{2 \cdot - 1}{3} \cdot \frac{1}{2} + 5$

Step 2.1.1.4

Rewrite the expression.

$f (\frac{1}{2}) = \frac{- 1}{3} + 5$

Step 2.1.2

Move the negative in front of the fraction.

$f (\frac{1}{2}) = - \frac{1}{3} + 5$

Step 2.2

To write $5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$f (\frac{1}{2}) = - \frac{1}{3} + 5 \cdot \frac{3}{3}$

Step 2.3

Combine $5$ and $\frac{3}{3}$ .

$f (\frac{1}{2}) = - \frac{1}{3} + \frac{5 \cdot 3}{3}$

Step 2.4

Combine the numerators over the common denominator.

$f (\frac{1}{2}) = \frac{- 1 + 5 \cdot 3}{3}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $5$ by $3$ .

$f (\frac{1}{2}) = \frac{- 1 + 15}{3}$

Step 2.5.2

Add $- 1$ and $15$ .

$f (\frac{1}{2}) = \frac{14}{3}$

Step 2.6

The final answer is $\frac{14}{3}$ .

$\frac{14}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{14}{3}$

Decimal Form:

$4.\overline{6}$

Mixed Number Form:

$4 \frac{2}{3}$

Step 4