Pre-Algebra Examples

$\frac{3}{12 y} + \frac{9}{24}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $3$ and $12$ .

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Step 1.1.1

Factor $3$ out of $3$ .

$\frac{3 (1)}{12 y} + \frac{9}{24}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $3$ out of $12 y$ .

$\frac{3 (1)}{3 (4 y)} + \frac{9}{24}$

Step 1.1.2.2

Cancel the common factor.

$\frac{3 \cdot 1}{3 (4 y)} + \frac{9}{24}$

Step 1.1.2.3

Rewrite the expression.

$\frac{1}{4 y} + \frac{9}{24}$

Step 1.2

Cancel the common factor of $9$ and $24$ .

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Step 1.2.1

Factor $3$ out of $9$ .

$\frac{1}{4 y} + \frac{3 (3)}{24}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $3$ out of $24$ .

$\frac{1}{4 y} + \frac{3 \cdot 3}{3 \cdot 8}$

Step 1.2.2.2

Cancel the common factor.

$\frac{1}{4 y} + \frac{3 \cdot 3}{3 \cdot 8}$

Step 1.2.2.3

Rewrite the expression.

$\frac{1}{4 y} + \frac{3}{8}$

Step 2

To write $\frac{1}{4 y}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{4 y} \cdot \frac{2}{2} + \frac{3}{8}$

Step 3

To write $\frac{3}{8}$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

$\frac{1}{4 y} \cdot \frac{2}{2} + \frac{3}{8} \cdot \frac{y}{y}$

Step 4

Write each expression with a common denominator of $8 y$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{1}{4 y}$ by $\frac{2}{2}$ .

$\frac{2}{4 y \cdot 2} + \frac{3}{8} \cdot \frac{y}{y}$

Step 4.2

Multiply $2$ by $4$ .

$\frac{2}{8 y} + \frac{3}{8} \cdot \frac{y}{y}$

Step 4.3

Multiply $\frac{3}{8}$ by $\frac{y}{y}$ .

$\frac{2}{8 y} + \frac{3 y}{8 y}$

Step 5

Combine the numerators over the common denominator.

$\frac{2 + 3 y}{8 y}$