Algebra Examples

$(1 - \frac{1}{2}) \cdot (1 - \frac{1}{3}) \cdot (1 - \frac{1}{4}) \cdot (1 - \frac{1}{5})$

Step 1

Simplify the expression.

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Step 1.1

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

$(\frac{2}{2} - \frac{1}{2}) \cdot (1 - \frac{1}{3}) \cdot (1 - \frac{1}{4}) \cdot (1 - \frac{1}{5})$

Step 1.2

Combine the numerators over the common denominator.

$\frac{2 - 1}{2} \cdot (1 - \frac{1}{3}) \cdot (1 - \frac{1}{4}) \cdot (1 - \frac{1}{5})$

Step 1.3

Subtract $1$ from $2$ .

$\frac{1}{2} \cdot (1 - \frac{1}{3}) \cdot (1 - \frac{1}{4}) \cdot (1 - \frac{1}{5})$

Step 1.4

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

$\frac{1}{2} \cdot (\frac{3}{3} - \frac{1}{3}) \cdot (1 - \frac{1}{4}) \cdot (1 - \frac{1}{5})$

Step 1.5

Combine the numerators over the common denominator.

$\frac{1}{2} \cdot \frac{3 - 1}{3} \cdot (1 - \frac{1}{4}) \cdot (1 - \frac{1}{5})$

Step 1.6

Subtract $1$ from $3$ .

$\frac{1}{2} \cdot \frac{2}{3} \cdot (1 - \frac{1}{4}) \cdot (1 - \frac{1}{5})$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Cancel the common factor.

$\frac{1}{2} \cdot \frac{2}{3} \cdot (1 - \frac{1}{4}) \cdot (1 - \frac{1}{5})$

Step 2.2

Rewrite the expression.

$\frac{1}{3} \cdot (1 - \frac{1}{4}) \cdot (1 - \frac{1}{5})$

Step 3

Simplify the expression.

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Step 3.1

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

$\frac{1}{3} \cdot (\frac{4}{4} - \frac{1}{4}) \cdot (1 - \frac{1}{5})$

Step 3.2

Combine the numerators over the common denominator.

$\frac{1}{3} \cdot \frac{4 - 1}{4} \cdot (1 - \frac{1}{5})$

Step 3.3

Subtract $1$ from $4$ .

$\frac{1}{3} \cdot \frac{3}{4} \cdot (1 - \frac{1}{5})$

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Cancel the common factor.

$\frac{1}{3} \cdot \frac{3}{4} \cdot (1 - \frac{1}{5})$

Step 4.2

Rewrite the expression.

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

Step 5

Simplify the expression.

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Step 5.1

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

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

Step 5.2

Combine the numerators over the common denominator.

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

Step 5.3

Subtract $1$ from $5$ .

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

Step 6

Cancel the common factor of $4$ .

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

$\frac{1}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{5}$

Decimal Form:

$0.2$