Algebra Examples

$\frac{3 a}{4} + \frac{2 a}{3} - \frac{a}{12}$

Step 1

Find the common denominator.

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Step 1.1

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

$\frac{3 a}{4} \cdot \frac{3}{3} + \frac{2 a}{3} - \frac{a}{12}$

Step 1.2

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

$\frac{3 a \cdot 3}{4 \cdot 3} + \frac{2 a}{3} - \frac{a}{12}$

Step 1.3

Multiply $\frac{2 a}{3}$ by $\frac{4}{4}$ .

$\frac{3 a \cdot 3}{4 \cdot 3} + \frac{2 a}{3} \cdot \frac{4}{4} - \frac{a}{12}$

Step 1.4

Multiply $\frac{2 a}{3}$ by $\frac{4}{4}$ .

$\frac{3 a \cdot 3}{4 \cdot 3} + \frac{2 a \cdot 4}{3 \cdot 4} - \frac{a}{12}$

Step 1.5

Reorder the factors of $4 \cdot 3$ .

$\frac{3 a \cdot 3}{3 \cdot 4} + \frac{2 a \cdot 4}{3 \cdot 4} - \frac{a}{12}$

Step 1.6

Multiply $3$ by $4$ .

$\frac{3 a \cdot 3}{12} + \frac{2 a \cdot 4}{3 \cdot 4} - \frac{a}{12}$

Step 1.7

Multiply $3$ by $4$ .

$\frac{3 a \cdot 3}{12} + \frac{2 a \cdot 4}{12} - \frac{a}{12}$

Step 2

Combine the numerators over the common denominator.

$\frac{3 a \cdot 3 + 2 a \cdot 4 - a}{12}$

Step 3

Simplify each term.

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Step 3.1

Multiply $3$ by $3$ .

$\frac{9 a + 2 a \cdot 4 - a}{12}$

Step 3.2

Multiply $4$ by $2$ .

$\frac{9 a + 8 a - a}{12}$

Step 4

Simplify terms.

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Step 4.1

Add $9 a$ and $8 a$ .

$\frac{17 a - a}{12}$

Step 4.2

Subtract $a$ from $17 a$ .

$\frac{16 a}{12}$

Step 4.3

Cancel the common factor of $16$ and $12$ .

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Step 4.3.1

Factor $4$ out of $16 a$ .

$\frac{4 (4 a)}{12}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $4$ out of $12$ .

$\frac{4 (4 a)}{4 (3)}$

Step 4.3.2.2

Cancel the common factor.

$\frac{4 (4 a)}{4 \cdot 3}$

Step 4.3.2.3

Rewrite the expression.

$\frac{4 a}{3}$