Algebra Examples

$\frac{\frac{1}{4} + x}{\frac{1}{2}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

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

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

Step 3

Simplify terms.

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Step 3.1

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

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

Step 3.2

Combine the numerators over the common denominator.

$\frac{1 + x \cdot 4}{4} \cdot 2$

Step 4

Move $4$ to the left of $x$ .

$\frac{1 + 4 x}{4} \cdot 2$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Factor $2$ out of $4$ .

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

Step 5.2

Cancel the common factor.

$\frac{1 + 4 x}{2 \cdot 2} \cdot 2$

Step 5.3

Rewrite the expression.

$\frac{1 + 4 x}{2}$