Pre-Algebra Examples

$\frac{5}{7} \cdot (x + y) - \frac{2}{7} \cdot (x - 1)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$\frac{5}{7} x + \frac{5}{7} y - \frac{2}{7} \cdot (x - 1)$

Step 1.2

Combine $\frac{5}{7}$ and $x$ .

$\frac{5 x}{7} + \frac{5}{7} y - \frac{2}{7} \cdot (x - 1)$

Step 1.3

Combine $\frac{5}{7}$ and $y$ .

$\frac{5 x}{7} + \frac{5 y}{7} - \frac{2}{7} \cdot (x - 1)$

Step 1.4

Apply the distributive property.

$\frac{5 x}{7} + \frac{5 y}{7} - \frac{2}{7} x - \frac{2}{7} \cdot - 1$

Step 1.5

Combine $x$ and $\frac{2}{7}$ .

$\frac{5 x}{7} + \frac{5 y}{7} - \frac{x \cdot 2}{7} - \frac{2}{7} \cdot - 1$

Step 1.6

Multiply $- \frac{2}{7} \cdot - 1$ .

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Step 1.6.1

Multiply $- 1$ by $- 1$ .

$\frac{5 x}{7} + \frac{5 y}{7} - \frac{x \cdot 2}{7} + 1 (\frac{2}{7})$

Step 1.6.2

Multiply $\frac{2}{7}$ by $1$ .

$\frac{5 x}{7} + \frac{5 y}{7} - \frac{x \cdot 2}{7} + \frac{2}{7}$

Step 1.7

Move $2$ to the left of $x$ .

$\frac{5 x}{7} + \frac{5 y}{7} - \frac{2 x}{7} + \frac{2}{7}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{5 x + 5 y - 2 x + 2}{7}$

Step 2.2

Subtract $2 x$ from $5 x$ .

$\frac{3 x + 5 y + 2}{7}$