Algebra Examples

Evaluate $\frac{1}{4} c + 3 d$ when $c = 6$ and $d = 7$

Step 1

Replace the variable $c$ with $6$ in the expression.

$\frac{1}{4} \cdot (6) + 3 d$

Step 2

Replace the variable $d$ with $7$ in the expression.

$\frac{1}{4} \cdot (6) + 3 (7)$

Step 3

Simplify each term.

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Step 3.1

Cancel the common factor of $2$ .

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Step 3.1.1

Factor $2$ out of $4$ .

$\frac{1}{2 (2)} \cdot 6 + 3 (7)$

Step 3.1.2

Factor $2$ out of $6$ .

$\frac{1}{2 \cdot 2} \cdot (2 \cdot 3) + 3 (7)$

Step 3.1.3

Cancel the common factor.

$\frac{1}{2 \cdot 2} \cdot (2 \cdot 3) + 3 (7)$

Step 3.1.4

Rewrite the expression.

$\frac{1}{2} \cdot 3 + 3 (7)$

Step 3.2

Combine $\frac{1}{2}$ and $3$ .

$\frac{3}{2} + 3 (7)$

Step 3.3

Multiply $3$ by $7$ .

$\frac{3}{2} + 21$

Step 4

To write $21$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3}{2} + 21 \cdot \frac{2}{2}$

Step 5

Combine $21$ and $\frac{2}{2}$ .

$\frac{3}{2} + \frac{21 \cdot 2}{2}$

Step 6

Combine the numerators over the common denominator.

$\frac{3 + 21 \cdot 2}{2}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $21$ by $2$ .

$\frac{3 + 42}{2}$

Step 7.2

Add $3$ and $42$ .

$\frac{45}{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{45}{2}$

Decimal Form:

$22.5$

Mixed Number Form:

$22 \frac{1}{2}$