Pre-Algebra Examples

$\frac{4 x}{12 y^{2}} + \frac{5 x}{8 y}$

Step 1

Cancel the common factor of $4$ and $12$ .

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Step 1.1

Factor $4$ out of $4 x$ .

$\frac{4 (x)}{12 y^{2}} + \frac{5 x}{8 y}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $4$ out of $12 y^{2}$ .

$\frac{4 (x)}{4 (3 y^{2})} + \frac{5 x}{8 y}$

Step 1.2.2

Cancel the common factor.

$\frac{4 x}{4 (3 y^{2})} + \frac{5 x}{8 y}$

Step 1.2.3

Rewrite the expression.

$\frac{x}{3 y^{2}} + \frac{5 x}{8 y}$

Step 2

To write $\frac{x}{3 y^{2}}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{x}{3 y^{2}} \cdot \frac{8}{8} + \frac{5 x}{8 y}$

Step 3

To write $\frac{5 x}{8 y}$ as a fraction with a common denominator, multiply by $\frac{3 y}{3 y}$ .

$\frac{x}{3 y^{2}} \cdot \frac{8}{8} + \frac{5 x}{8 y} \cdot \frac{3 y}{3 y}$

Step 4

Write each expression with a common denominator of $24 y^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{x}{3 y^{2}}$ by $\frac{8}{8}$ .

$\frac{x \cdot 8}{3 y^{2} \cdot 8} + \frac{5 x}{8 y} \cdot \frac{3 y}{3 y}$

Step 4.2

Multiply $8$ by $3$ .

$\frac{x \cdot 8}{24 y^{2}} + \frac{5 x}{8 y} \cdot \frac{3 y}{3 y}$

Step 4.3

Multiply $\frac{5 x}{8 y}$ by $\frac{3 y}{3 y}$ .

$\frac{x \cdot 8}{24 y^{2}} + \frac{5 x (3 y)}{8 y (3 y)}$

Step 4.4

Multiply $3$ by $8$ .

$\frac{x \cdot 8}{24 y^{2}} + \frac{5 x (3 y)}{24 y \cdot y}$

Step 4.5

Raise $y$ to the power of $1$ .

$\frac{x \cdot 8}{24 y^{2}} + \frac{5 x (3 y)}{24 (y^{1} y)}$

Step 4.6

Raise $y$ to the power of $1$ .

$\frac{x \cdot 8}{24 y^{2}} + \frac{5 x (3 y)}{24 (y^{1} y^{1})}$

Step 4.7

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x \cdot 8}{24 y^{2}} + \frac{5 x (3 y)}{24 y^{1 + 1}}$

Step 4.8

Add $1$ and $1$ .

$\frac{x \cdot 8}{24 y^{2}} + \frac{5 x (3 y)}{24 y^{2}}$

Step 5

Combine the numerators over the common denominator.

$\frac{x \cdot 8 + 5 x (3 y)}{24 y^{2}}$

Step 6

Simplify the numerator.

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Step 6.1

Factor $x$ out of $x \cdot 8 + 5 x \cdot 3 y$ .

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Step 6.1.1

Factor $x$ out of $x \cdot 8$ .

$\frac{x (8) + 5 x \cdot 3 y}{24 y^{2}}$

Step 6.1.2

Factor $x$ out of $5 x \cdot 3 y$ .

$\frac{x (8) + x (5 \cdot 3 y)}{24 y^{2}}$

Step 6.1.3

Factor $x$ out of $x (8) + x (5 \cdot 3 y)$ .

$\frac{x (8 + 5 \cdot 3 y)}{24 y^{2}}$

Step 6.2

Multiply $5$ by $3$ .

$\frac{x (8 + 15 y)}{24 y^{2}}$