Pre-Algebra Examples

$\frac{2}{3 x^{2} y} + \frac{3}{4 x^{3}}$

Step 1

To write $\frac{2}{3 x^{2} y}$ as a fraction with a common denominator, multiply by $\frac{4 x}{4 x}$ .

$\frac{2}{3 x^{2} y} \cdot \frac{4 x}{4 x} + \frac{3}{4 x^{3}}$

Step 2

To write $\frac{3}{4 x^{3}}$ as a fraction with a common denominator, multiply by $\frac{3 y}{3 y}$ .

$\frac{2}{3 x^{2} y} \cdot \frac{4 x}{4 x} + \frac{3}{4 x^{3}} \cdot \frac{3 y}{3 y}$

Step 3

Write each expression with a common denominator of $12 y x^{3}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{2}{3 x^{2} y}$ by $\frac{4 x}{4 x}$ .

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

Step 3.2

Multiply $4$ by $3$ .

$\frac{2 (4 x)}{12 x^{2} y x} + \frac{3}{4 x^{3}} \cdot \frac{3 y}{3 y}$

Step 3.3

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

$\frac{2 (4 x)}{12 (x^{1} x^{2}) y} + \frac{3}{4 x^{3}} \cdot \frac{3 y}{3 y}$

Step 3.4

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

$\frac{2 (4 x)}{12 x^{1 + 2} y} + \frac{3}{4 x^{3}} \cdot \frac{3 y}{3 y}$

Step 3.5

Add $1$ and $2$ .

$\frac{2 (4 x)}{12 x^{3} y} + \frac{3}{4 x^{3}} \cdot \frac{3 y}{3 y}$

Step 3.6

Multiply $\frac{3}{4 x^{3}}$ by $\frac{3 y}{3 y}$ .

$\frac{2 (4 x)}{12 x^{3} y} + \frac{3 (3 y)}{4 x^{3} (3 y)}$

Step 3.7

Multiply $3$ by $4$ .

$\frac{2 (4 x)}{12 x^{3} y} + \frac{3 (3 y)}{12 x^{3} y}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 (4 x) + 3 (3 y)}{12 x^{3} y}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $2$ by $4$ .

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

Step 5.2

Multiply $3$ by $3$ .

$\frac{8 x + 9 y}{12 x^{3} y}$