Pre-Algebra Examples

$\frac{3}{10 x} - \frac{4}{15 y}$

Step 1

To write $\frac{3}{10 x}$ as a fraction with a common denominator, multiply by $\frac{3 y}{3 y}$ .

$\frac{3}{10 x} \cdot \frac{3 y}{3 y} - \frac{4}{15 y}$

Step 2

To write $- \frac{4}{15 y}$ as a fraction with a common denominator, multiply by $\frac{2 x}{2 x}$ .

$\frac{3}{10 x} \cdot \frac{3 y}{3 y} - \frac{4}{15 y} \cdot \frac{2 x}{2 x}$

Step 3

Write each expression with a common denominator of $30 x y$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{3}{10 x}$ by $\frac{3 y}{3 y}$ .

$\frac{3 (3 y)}{10 x (3 y)} - \frac{4}{15 y} \cdot \frac{2 x}{2 x}$

Step 3.2

Multiply $3$ by $10$ .

$\frac{3 (3 y)}{30 x y} - \frac{4}{15 y} \cdot \frac{2 x}{2 x}$

Step 3.3

Multiply $\frac{4}{15 y}$ by $\frac{2 x}{2 x}$ .

$\frac{3 (3 y)}{30 x y} - \frac{4 (2 x)}{15 y (2 x)}$

Step 3.4

Multiply $2$ by $15$ .

$\frac{3 (3 y)}{30 x y} - \frac{4 (2 x)}{30 y x}$

Step 3.5

Reorder the factors of $30 y x$ .

$\frac{3 (3 y)}{30 x y} - \frac{4 (2 x)}{30 x y}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 (3 y) - 4 (2 x)}{30 x y}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $3$ by $3$ .

$\frac{9 y - 4 \cdot 2 x}{30 x y}$

Step 5.2

Multiply $- 4$ by $2$ .

$\frac{9 y - 8 x}{30 x y}$