Algebra Examples

$\frac{5}{8} x + \frac{1}{2} (\frac{1}{4} x + 10)$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{5}{8}$ and $x$ .

$\frac{5 x}{8} + \frac{1}{2} \cdot (\frac{1}{4} x + 10)$

Step 1.2

Combine $\frac{1}{4}$ and $x$ .

$\frac{5 x}{8} + \frac{1}{2} \cdot (\frac{x}{4} + 10)$

Step 1.3

Apply the distributive property.

$\frac{5 x}{8} + \frac{1}{2} \cdot \frac{x}{4} + \frac{1}{2} \cdot 10$

Step 1.4

Multiply $\frac{1}{2} \cdot \frac{x}{4}$ .

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Step 1.4.1

Multiply $\frac{1}{2}$ by $\frac{x}{4}$ .

$\frac{5 x}{8} + \frac{x}{2 \cdot 4} + \frac{1}{2} \cdot 10$

Step 1.4.2

Multiply $2$ by $4$ .

$\frac{5 x}{8} + \frac{x}{8} + \frac{1}{2} \cdot 10$

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

Factor $2$ out of $10$ .

$\frac{5 x}{8} + \frac{x}{8} + \frac{1}{2} \cdot (2 (5))$

Step 1.5.2

Cancel the common factor.

$\frac{5 x}{8} + \frac{x}{8} + \frac{1}{2} \cdot (2 \cdot 5)$

Step 1.5.3

Rewrite the expression.

$\frac{5 x}{8} + \frac{x}{8} + 5$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$5 + \frac{5 x + x}{8}$

Step 2.2

Add $5 x$ and $x$ .

$5 + \frac{6 x}{8}$

Step 2.3

Cancel the common factor of $6$ and $8$ .

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Step 2.3.1

Factor $2$ out of $6 x$ .

$5 + \frac{2 (3 x)}{8}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $2$ out of $8$ .

$5 + \frac{2 (3 x)}{2 (4)}$

Step 2.3.2.2

Cancel the common factor.

$5 + \frac{2 (3 x)}{2 \cdot 4}$

Step 2.3.2.3

Rewrite the expression.

$5 + \frac{3 x}{4}$