Solve (1-1/2)(1-1/3)(1-1/4)*(1-1/12)

$$( 1 - \frac { 1 } { 2 } ) ( 1 - \frac { 1 } { 3 } ) ( 1 - \frac { 1 } { 4 } ) \cdot ( 1 - \frac { 1 } { 12 } )$$

Evaluate

$$\frac{11}{48}\approx 0.229166667$$

Solution Steps

Convert 1 to fraction \frac{2}{2}.

$$\left(\frac{2}{2}-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{12}\right)$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-1}{2}\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{12}\right)$$

Subtract 1 from 2 to get 1.

$$\frac{1}{2}\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{12}\right)$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{1}{2}\left(\frac{3}{3}-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{12}\right)$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}\times \frac{3-1}{3}\left(1-\frac{1}{4}\right)\left(1-\frac{1}{12}\right)$$

Subtract 1 from 3 to get 2.

$$\frac{1}{2}\times \frac{2}{3}\left(1-\frac{1}{4}\right)\left(1-\frac{1}{12}\right)$$

Multiply \frac{1}{2} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 2}{2\times 3}\left(1-\frac{1}{4}\right)\left(1-\frac{1}{12}\right)$$

Cancel out 2 in both numerator and denominator.

$$\frac{1}{3}\left(1-\frac{1}{4}\right)\left(1-\frac{1}{12}\right)$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{1}{3}\left(\frac{4}{4}-\frac{1}{4}\right)\left(1-\frac{1}{12}\right)$$

Since \frac{4}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{3}\times \frac{4-1}{4}\left(1-\frac{1}{12}\right)$$

Subtract 1 from 4 to get 3.

$$\frac{1}{3}\times \frac{3}{4}\left(1-\frac{1}{12}\right)$$

Multiply \frac{1}{3} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 3}{3\times 4}\left(1-\frac{1}{12}\right)$$

Cancel out 3 in both numerator and denominator.

$$\frac{1}{4}\left(1-\frac{1}{12}\right)$$

Convert 1 to fraction \frac{12}{12}.

$$\frac{1}{4}\left(\frac{12}{12}-\frac{1}{12}\right)$$

Since \frac{12}{12} and \frac{1}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{4}\times \frac{12-1}{12}$$

Subtract 1 from 12 to get 11.

$$\frac{1}{4}\times \frac{11}{12}$$

Multiply \frac{1}{4} times \frac{11}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 11}{4\times 12}$$

Do the multiplications in the fraction \frac{1\times 11}{4\times 12}.

$$\frac{11}{48}$$

Factor

$$\frac{11}{2 ^ {4} \cdot 3} = 0.22916666666666666$$