Precalculus Examples

$\frac{6}{1 - \frac{1}{5}}$

Step 1

Simplify the denominator.

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Step 1.1

Write $1$ as a fraction with a common denominator.

$\frac{6}{\frac{5}{5} - \frac{1}{5}}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{6}{\frac{5 - 1}{5}}$

Step 1.3

Subtract $1$ from $5$ .

$\frac{6}{\frac{4}{5}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$6 (\frac{5}{4})$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Factor $2$ out of $6$ .

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

Step 3.2

Factor $2$ out of $4$ .

$2 \cdot 3 \frac{5}{2 \cdot 2}$

Step 3.3

Cancel the common factor.

$2 \cdot 3 \frac{5}{2 \cdot 2}$

Step 3.4

Rewrite the expression.

$3 (\frac{5}{2})$

Step 4

Combine $3$ and $\frac{5}{2}$ .

$\frac{3 \cdot 5}{2}$

Step 5

Multiply $3$ by $5$ .

$\frac{15}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{15}{2}$

Decimal Form:

$7.5$

Mixed Number Form:

$7 \frac{1}{2}$