Evaluate (1-1/2)(1-1/3)(1-1/4)*(1-1/5)

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

Step 1

Simplify the expression.

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

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

Combine the numerators over the common denominator.

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

Subtract $1$ from $2$ .

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

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

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

Combine the numerators over the common denominator.

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

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 $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Simplify the expression.

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

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

Combine the numerators over the common denominator.

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

Subtract $1$ from $4$ .

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

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

Simplify the expression.

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

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

Combine the numerators over the common denominator.

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

Subtract $1$ from $5$ .

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

Step 6

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{5}$

Decimal Form:

$0.2$

Evaluate (1-1/2)*(1-1/3)*(1-1/4)*(1-1/5)

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Evaluate (1-1/2)(1-1/3)(1-1/4)*(1-1/5)