Pre-Algebra Examples

$\frac{5}{8 x y} + \frac{1}{12 x^{2}}$

Step 1

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

$\frac{5}{8 x y} \cdot \frac{3 x}{3 x} + \frac{1}{12 x^{2}}$

Step 2

To write $\frac{1}{12 x^{2}}$ as a fraction with a common denominator, multiply by $\frac{2 y}{2 y}$ .

$\frac{5}{8 x y} \cdot \frac{3 x}{3 x} + \frac{1}{12 x^{2}} \cdot \frac{2 y}{2 y}$

Step 3

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

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Step 3.1

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

$\frac{5 (3 x)}{8 x y (3 x)} + \frac{1}{12 x^{2}} \cdot \frac{2 y}{2 y}$

Step 3.2

Multiply $3$ by $8$ .

$\frac{5 (3 x)}{24 x y x} + \frac{1}{12 x^{2}} \cdot \frac{2 y}{2 y}$

Step 3.3

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

$\frac{5 (3 x)}{24 (x^{1} x) y} + \frac{1}{12 x^{2}} \cdot \frac{2 y}{2 y}$

Step 3.4

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

$\frac{5 (3 x)}{24 (x^{1} x^{1}) y} + \frac{1}{12 x^{2}} \cdot \frac{2 y}{2 y}$

Step 3.5

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

$\frac{5 (3 x)}{24 x^{1 + 1} y} + \frac{1}{12 x^{2}} \cdot \frac{2 y}{2 y}$

Step 3.6

Add $1$ and $1$ .

$\frac{5 (3 x)}{24 x^{2} y} + \frac{1}{12 x^{2}} \cdot \frac{2 y}{2 y}$

Step 3.7

Multiply $\frac{1}{12 x^{2}}$ by $\frac{2 y}{2 y}$ .

$\frac{5 (3 x)}{24 x^{2} y} + \frac{2 y}{12 x^{2} (2 y)}$

Step 3.8

Multiply $2$ by $12$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Multiply $5$ by $3$ .

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