Basic Math Examples

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

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 1.2

Combine $- 1$ and $\frac{5}{5}$ .

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

Step 1.3

Combine the numerators over the common denominator.

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

Step 1.4

Simplify the numerator.

Tap for more steps...

Step 1.4.1

Multiply $- 1$ by $5$ .

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

Step 1.4.2

Subtract $5$ from $1$ .

$\frac{\frac{- 4}{5} (2 - \frac{1}{5})}{\frac{1}{5} + 1}$

Step 1.5

Move the negative in front of the fraction.

$\frac{- \frac{4}{5} (2 - \frac{1}{5})}{\frac{1}{5} + 1}$

Step 1.6

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{- \frac{4}{5} (2 \cdot \frac{5}{5} - \frac{1}{5})}{\frac{1}{5} + 1}$

Step 1.7

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

$\frac{- \frac{4}{5} (\frac{2 \cdot 5}{5} - \frac{1}{5})}{\frac{1}{5} + 1}$

Step 1.8

Combine the numerators over the common denominator.

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

Step 1.9

Simplify the numerator.

Tap for more steps...

Step 1.9.1

Multiply $2$ by $5$ .

$\frac{- \frac{4}{5} \cdot \frac{10 - 1}{5}}{\frac{1}{5} + 1}$

Step 1.9.2

Subtract $1$ from $10$ .

$\frac{- \frac{4}{5} \cdot \frac{9}{5}}{\frac{1}{5} + 1}$

Step 1.10

Combine exponents.

Tap for more steps...

Step 1.10.1

Multiply $\frac{9}{5}$ by $\frac{4}{5}$ .

$\frac{- \frac{9 \cdot 4}{5 \cdot 5}}{\frac{1}{5} + 1}$

Step 1.10.2

Multiply $9$ by $4$ .

$\frac{- \frac{36}{5 \cdot 5}}{\frac{1}{5} + 1}$

Step 1.10.3

Multiply $5$ by $5$ .

$\frac{- \frac{36}{25}}{\frac{1}{5} + 1}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

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

$\frac{- \frac{36}{25}}{\frac{1}{5} + \frac{5}{5}}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{- \frac{36}{25}}{\frac{1 + 5}{5}}$

Step 2.3

Add $1$ and $5$ .

$\frac{- \frac{36}{25}}{\frac{6}{5}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$- \frac{36}{25} \cdot \frac{5}{6}$

Step 4

Cancel the common factor of $6$ .

Tap for more steps...

Step 4.1

Move the leading negative in $- \frac{36}{25}$ into the numerator.

$\frac{- 36}{25} \cdot \frac{5}{6}$

Step 4.2

Factor $6$ out of $- 36$ .

$\frac{6 (- 6)}{25} \cdot \frac{5}{6}$

Step 4.3

Cancel the common factor.

$\frac{6 \cdot - 6}{25} \cdot \frac{5}{6}$

Step 4.4

Rewrite the expression.

$\frac{- 6}{25} \cdot 5$

Step 5

Cancel the common factor of $5$ .

Tap for more steps...

Step 5.1

Factor $5$ out of $25$ .

$\frac{- 6}{5 (5)} \cdot 5$

Step 5.2

Cancel the common factor.

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

Step 5.3

Rewrite the expression.

$\frac{- 6}{5}$

Step 6

Move the negative in front of the fraction.

$- \frac{6}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{6}{5}$

Decimal Form:

$- 1.2$

Mixed Number Form:

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