Algebra Examples

$\frac{c}{2} - 3 + \frac{6}{d}$ when $c = 14$ and $d = 3$

Step 1

Replace the variable $c$ with $14$ in the expression.

$\frac{14}{2} - 3 + \frac{6}{d}$

Step 2

Replace the variable $d$ with $3$ in the expression.

$\frac{14}{2} - 3 + \frac{6}{3}$

Step 3

Find the common denominator.

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Step 3.1

Multiply $\frac{14}{2}$ by $\frac{3}{3}$ .

$\frac{14}{2} \cdot \frac{3}{3} - 3 + \frac{6}{3}$

Step 3.2

Multiply $\frac{14}{2}$ by $\frac{3}{3}$ .

$\frac{14 \cdot 3}{2 \cdot 3} - 3 + \frac{6}{3}$

Step 3.3

Write $- 3$ as a fraction with denominator $1$ .

$\frac{14 \cdot 3}{2 \cdot 3} + \frac{- 3}{1} + \frac{6}{3}$

Step 3.4

Multiply $\frac{- 3}{1}$ by $\frac{6}{6}$ .

$\frac{14 \cdot 3}{2 \cdot 3} + \frac{- 3}{1} \cdot \frac{6}{6} + \frac{6}{3}$

Step 3.5

Multiply $\frac{- 3}{1}$ by $\frac{6}{6}$ .

$\frac{14 \cdot 3}{2 \cdot 3} + \frac{- 3 \cdot 6}{6} + \frac{6}{3}$

Step 3.6

Multiply $\frac{6}{3}$ by $\frac{2}{2}$ .

$\frac{14 \cdot 3}{2 \cdot 3} + \frac{- 3 \cdot 6}{6} + \frac{6}{3} \cdot \frac{2}{2}$

Step 3.7

Multiply $\frac{6}{3}$ by $\frac{2}{2}$ .

$\frac{14 \cdot 3}{2 \cdot 3} + \frac{- 3 \cdot 6}{6} + \frac{6 \cdot 2}{3 \cdot 2}$

Step 3.8

Multiply $2$ by $3$ .

$\frac{14 \cdot 3}{6} + \frac{- 3 \cdot 6}{6} + \frac{6 \cdot 2}{3 \cdot 2}$

Step 3.9

Reorder the factors of $3 \cdot 2$ .

$\frac{14 \cdot 3}{6} + \frac{- 3 \cdot 6}{6} + \frac{6 \cdot 2}{2 \cdot 3}$

Step 3.10

Multiply $2$ by $3$ .

$\frac{14 \cdot 3}{6} + \frac{- 3 \cdot 6}{6} + \frac{6 \cdot 2}{6}$

Step 4

Combine the numerators over the common denominator.

$\frac{14 \cdot 3 - 3 \cdot 6 + 6 \cdot 2}{6}$

Step 5

Simplify each term.

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Step 5.1

Multiply $14$ by $3$ .

$\frac{42 - 3 \cdot 6 + 6 \cdot 2}{6}$

Step 5.2

Multiply $- 3$ by $6$ .

$\frac{42 - 18 + 6 \cdot 2}{6}$

Step 5.3

Multiply $6$ by $2$ .

$\frac{42 - 18 + 12}{6}$

Step 6

Simplify the expression.

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Step 6.1

Subtract $18$ from $42$ .

$\frac{24 + 12}{6}$

Step 6.2

Add $24$ and $12$ .

$\frac{36}{6}$

Step 6.3

Divide $36$ by $6$ .

$6$