Algebra Examples

$6 + \frac{4}{a} + \frac{b}{3}$ when $a = 4$ and $b = 3$

Step 1

Replace the variable $a$ with $4$ in the expression.

$6 + \frac{4}{4} + \frac{b}{3}$

Step 2

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

$6 + \frac{4}{4} + \frac{3}{3}$

Step 3

Find the common denominator.

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Step 3.1

Write $6$ as a fraction with denominator $1$ .

$\frac{6}{1} + \frac{4}{4} + \frac{3}{3}$

Step 3.2

Multiply $\frac{6}{1}$ by $\frac{12}{12}$ .

$\frac{6}{1} \cdot \frac{12}{12} + \frac{4}{4} + \frac{3}{3}$

Step 3.3

Multiply $\frac{6}{1}$ by $\frac{12}{12}$ .

$\frac{6 \cdot 12}{12} + \frac{4}{4} + \frac{3}{3}$

Step 3.4

Multiply $\frac{4}{4}$ by $\frac{3}{3}$ .

$\frac{6 \cdot 12}{12} + \frac{4}{4} \cdot \frac{3}{3} + \frac{3}{3}$

Step 3.5

Multiply $\frac{4}{4}$ by $\frac{3}{3}$ .

$\frac{6 \cdot 12}{12} + \frac{4 \cdot 3}{4 \cdot 3} + \frac{3}{3}$

Step 3.6

Multiply $\frac{3}{3}$ by $\frac{4}{4}$ .

$\frac{6 \cdot 12}{12} + \frac{4 \cdot 3}{4 \cdot 3} + \frac{3}{3} \cdot \frac{4}{4}$

Step 3.7

Multiply $\frac{3}{3}$ by $\frac{4}{4}$ .

$\frac{6 \cdot 12}{12} + \frac{4 \cdot 3}{4 \cdot 3} + \frac{3 \cdot 4}{3 \cdot 4}$

Step 3.8

Reorder the factors of $4 \cdot 3$ .

$\frac{6 \cdot 12}{12} + \frac{4 \cdot 3}{3 \cdot 4} + \frac{3 \cdot 4}{3 \cdot 4}$

Step 3.9

Multiply $3$ by $4$ .

$\frac{6 \cdot 12}{12} + \frac{4 \cdot 3}{12} + \frac{3 \cdot 4}{3 \cdot 4}$

Step 3.10

Multiply $3$ by $4$ .

$\frac{6 \cdot 12}{12} + \frac{4 \cdot 3}{12} + \frac{3 \cdot 4}{12}$

Step 4

Combine the numerators over the common denominator.

$\frac{6 \cdot 12 + 4 \cdot 3 + 3 \cdot 4}{12}$

Step 5

Simplify each term.

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Step 5.1

Multiply $6$ by $12$ .

$\frac{72 + 4 \cdot 3 + 3 \cdot 4}{12}$

Step 5.2

Multiply $4$ by $3$ .

$\frac{72 + 12 + 3 \cdot 4}{12}$

Step 5.3

Multiply $3$ by $4$ .

$\frac{72 + 12 + 12}{12}$

Step 6

Simplify the expression.

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Step 6.1

Add $72$ and $12$ .

$\frac{84 + 12}{12}$

Step 6.2

Add $84$ and $12$ .

$\frac{96}{12}$

Step 6.3

Divide $96$ by $12$ .

$8$