Solve 4-1/3(4-1/3(4-1/3)

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

Evaluate

$$\frac{83}{27}\approx 3.074074074$$

Solution Steps

Convert 4 to fraction \frac{12}{3}.

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

Since \frac{12}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 12 to get 11.

$$4-\frac{1}{3}\left(4-\frac{1}{3}\times \frac{11}{3}\right)$$

Multiply \frac{1}{3} times \frac{11}{3} by multiplying numerator times numerator and denominator times denominator.

$$4-\frac{1}{3}\left(4-\frac{1\times 11}{3\times 3}\right)$$

Do the multiplications in the fraction \frac{1\times 11}{3\times 3}.

$$4-\frac{1}{3}\left(4-\frac{11}{9}\right)$$

Convert 4 to fraction \frac{36}{9}.

$$4-\frac{1}{3}\left(\frac{36}{9}-\frac{11}{9}\right)$$

Since \frac{36}{9} and \frac{11}{9} have the same denominator, subtract them by subtracting their numerators.

$$4-\frac{1}{3}\times \frac{36-11}{9}$$

Subtract 11 from 36 to get 25.

$$4-\frac{1}{3}\times \frac{25}{9}$$

Multiply \frac{1}{3} times \frac{25}{9} by multiplying numerator times numerator and denominator times denominator.

$$4-\frac{1\times 25}{3\times 9}$$

Do the multiplications in the fraction \frac{1\times 25}{3\times 9}.

$$4-\frac{25}{27}$$

Convert 4 to fraction \frac{108}{27}.

$$\frac{108}{27}-\frac{25}{27}$$

Since \frac{108}{27} and \frac{25}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{108-25}{27}$$

Subtract 25 from 108 to get 83.

$$\frac{83}{27}$$

Factor

$$\frac{83}{3 ^ {3}} = 3\frac{2}{27} = 3.074074074074074$$