Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Multiply the numerator by the reciprocal of the denominator.

$- \frac{1}{5} \cdot \frac{1}{- \frac{1}{5} + 1} - 1$

Step 1.2

Simplify the denominator.

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Step 1.2.1

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

$- \frac{1}{5} \cdot \frac{1}{- \frac{1}{5} + \frac{5}{5}} - 1$

Step 1.2.2

Combine the numerators over the common denominator.

$- \frac{1}{5} \cdot \frac{1}{\frac{- 1 + 5}{5}} - 1$

Step 1.2.3

Add $- 1$ and $5$ .

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

Step 1.3

Multiply the numerator by the reciprocal of the denominator.

$- \frac{1}{5} (1 (\frac{5}{4})) - 1$

Step 1.4

Multiply $\frac{5}{4}$ by $1$ .

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

Step 1.5

Cancel the common factor of $5$ .

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Step 1.5.1

Move the leading negative in $- \frac{1}{5}$ into the numerator.

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

Step 1.5.2

Cancel the common factor.

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

Step 1.5.3

Rewrite the expression.

$- \frac{1}{4} - 1$

Step 2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{1}{4} - 1 \cdot \frac{4}{4}$

Step 3

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

$- \frac{1}{4} + \frac{- 1 \cdot 4}{4}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 1 - 1 \cdot 4}{4}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 1$ by $4$ .

$\frac{- 1 - 4}{4}$

Step 5.2

Subtract $4$ from $- 1$ .

$\frac{- 5}{4}$

Step 6

Move the negative in front of the fraction.

$- \frac{5}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{5}{4}$

Decimal Form:

$- 1.25$

Mixed Number Form:

$- 1 \frac{1}{4}$