Solve 1-1/3(1-1/2(1-1/6))

$$1- \frac{ 1 }{ 3 } (1- \frac{ 1 }{ 2 } (1- \frac{ 1 }{ 6 } ))$$

Evaluate

$$\frac{29}{36}\approx 0.805555556$$

Solution Steps

Convert 1 to fraction \frac{6}{6}.

$$1-\frac{1}{3}\left(1-\frac{1}{2}\left(\frac{6}{6}-\frac{1}{6}\right)\right)$$

Since \frac{6}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$1-\frac{1}{3}\left(1-\frac{1}{2}\times \frac{6-1}{6}\right)$$

Subtract 1 from 6 to get 5.

$$1-\frac{1}{3}\left(1-\frac{1}{2}\times \frac{5}{6}\right)$$

Multiply \frac{1}{2} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$1-\frac{1}{3}\left(1-\frac{1\times 5}{2\times 6}\right)$$

Do the multiplications in the fraction \frac{1\times 5}{2\times 6}.

$$1-\frac{1}{3}\left(1-\frac{5}{12}\right)$$

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

$$1-\frac{1}{3}\left(\frac{12}{12}-\frac{5}{12}\right)$$

Since \frac{12}{12} and \frac{5}{12} have the same denominator, subtract them by subtracting their numerators.

$$1-\frac{1}{3}\times \frac{12-5}{12}$$

Subtract 5 from 12 to get 7.

$$1-\frac{1}{3}\times \frac{7}{12}$$

Multiply \frac{1}{3} times \frac{7}{12} by multiplying numerator times numerator and denominator times denominator.

$$1-\frac{1\times 7}{3\times 12}$$

Do the multiplications in the fraction \frac{1\times 7}{3\times 12}.

$$1-\frac{7}{36}$$

Convert 1 to fraction \frac{36}{36}.

$$\frac{36}{36}-\frac{7}{36}$$

Since \frac{36}{36} and \frac{7}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{36-7}{36}$$

Subtract 7 from 36 to get 29.

$$\frac{29}{36}$$

Factor

$$\frac{29}{2 ^ {2} \cdot 3 ^ {2}} = 0.8055555555555556$$