Pre-Algebra Examples

$\frac{x + 5}{4} + \frac{x - 2}{8}$

Step 1

To write $\frac{x + 5}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x + 5}{4} \cdot \frac{2}{2} + \frac{x - 2}{8}$

Step 2

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

Multiply $\frac{x + 5}{4}$ by $\frac{2}{2}$ .

$\frac{(x + 5) \cdot 2}{4 \cdot 2} + \frac{x - 2}{8}$

Step 2.2

Multiply $4$ by $2$ .

$\frac{(x + 5) \cdot 2}{8} + \frac{x - 2}{8}$

Step 3

Combine the numerators over the common denominator.

$\frac{(x + 5) \cdot 2 + x - 2}{8}$

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

$\frac{x \cdot 2 + 5 \cdot 2 + x - 2}{8}$

Step 4.2

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

$\frac{2 \cdot x + 5 \cdot 2 + x - 2}{8}$

Step 4.3

Multiply $5$ by $2$ .

$\frac{2 \cdot x + 10 + x - 2}{8}$

Step 4.4

Add $2 x$ and $x$ .

$\frac{3 x + 10 - 2}{8}$

Step 4.5

Subtract $2$ from $10$ .

$\frac{3 x + 8}{8}$