Basic Math Examples

$\frac{a}{6} + \frac{3}{2} + \frac{a}{3}$

Step 1

Find the common denominator.

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Step 1.1

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

$\frac{a}{6} + \frac{3}{2} \cdot \frac{3}{3} + \frac{a}{3}$

Step 1.2

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

$\frac{a}{6} + \frac{3 \cdot 3}{2 \cdot 3} + \frac{a}{3}$

Step 1.3

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

$\frac{a}{6} + \frac{3 \cdot 3}{2 \cdot 3} + \frac{a}{3} \cdot \frac{2}{2}$

Step 1.4

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

$\frac{a}{6} + \frac{3 \cdot 3}{2 \cdot 3} + \frac{a \cdot 2}{3 \cdot 2}$

Step 1.5

Multiply $2$ by $3$ .

$\frac{a}{6} + \frac{3 \cdot 3}{6} + \frac{a \cdot 2}{3 \cdot 2}$

Step 1.6

Reorder the factors of $3 \cdot 2$ .

$\frac{a}{6} + \frac{3 \cdot 3}{6} + \frac{a \cdot 2}{2 \cdot 3}$

Step 1.7

Multiply $2$ by $3$ .

$\frac{a}{6} + \frac{3 \cdot 3}{6} + \frac{a \cdot 2}{6}$

Step 2

Combine the numerators over the common denominator.

$\frac{a + 3 \cdot 3 + a \cdot 2}{6}$

Step 3

Simplify each term.

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Step 3.1

Multiply $3$ by $3$ .

$\frac{a + 9 + a \cdot 2}{6}$

Step 3.2

Move $2$ to the left of $a$ .

$\frac{a + 9 + 2 a}{6}$

Step 4

Simplify terms.

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Step 4.1

Add $a$ and $2 a$ .

$\frac{3 a + 9}{6}$

Step 4.2

Cancel the common factor of $3 a + 9$ and $6$ .

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Step 4.2.1

Factor $3$ out of $3 a$ .

$\frac{3 (a) + 9}{6}$

Step 4.2.2

Factor $3$ out of $9$ .

$\frac{3 a + 3 \cdot 3}{6}$

Step 4.2.3

Factor $3$ out of $3 a + 3 \cdot 3$ .

$\frac{3 (a + 3)}{6}$

Step 4.2.4

Cancel the common factors.

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Step 4.2.4.1

Factor $3$ out of $6$ .

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

Step 4.2.4.2

Cancel the common factor.

$\frac{3 (a + 3)}{3 \cdot 2}$

Step 4.2.4.3

Rewrite the expression.

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