Algebra Examples

$\frac{x - 1}{2} \div \frac{5}{4}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x - 1}{2} \cdot \frac{4}{5}$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Factor $2$ out of $4$ .

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

Step 2.2

Cancel the common factor.

$\frac{x - 1}{2} \cdot \frac{2 \cdot 2}{5}$

Step 2.3

Rewrite the expression.

$(x - 1) \frac{2}{5}$

Step 3

Apply the distributive property.

$x \frac{2}{5} - 1 (\frac{2}{5})$

Step 4

Combine $x$ and $\frac{2}{5}$ .

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

Step 5

Rewrite $- 1 (\frac{2}{5})$ as $- (\frac{2}{5})$ .

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

Step 6

Combine the numerators over the common denominator.

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

Step 7

Reorder factors in $x \cdot 2 - 2$ .

$\frac{2 x - 2}{5}$

Step 8

Factor $2$ out of $2 x - 2$ .

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Step 8.1

Factor $2$ out of $2 x$ .

$\frac{2 (x) - 2}{5}$

Step 8.2

Factor $2$ out of $- 2$ .

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

Step 8.3

Factor $2$ out of $2 (x) + 2 (- 1)$ .

$\frac{2 (x - 1)}{5}$