Solve 3(2+1/2)(2+1/8)(2+1/128)

$$3 ( 2 + \frac { 1 } { 2 } ) ( 2 + \frac { 1 } { 8 } ) ( 2 + \frac { 1 } { 128 } )$$

Evaluate

$$\frac{65535}{2048}\approx 31.999511719$$

Solution Steps

Convert 2 to fraction \frac{4}{2}.

$$3\left(\frac{4}{2}+\frac{1}{2}\right)\left(2+\frac{1}{8}\right)\left(2+\frac{1}{128}\right)$$

Since \frac{4}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$3\times \frac{4+1}{2}\left(2+\frac{1}{8}\right)\left(2+\frac{1}{128}\right)$$

Add 4 and 1 to get 5.

$$3\times \frac{5}{2}\left(2+\frac{1}{8}\right)\left(2+\frac{1}{128}\right)$$

Express 3\times \frac{5}{2} as a single fraction.

$$\frac{3\times 5}{2}\left(2+\frac{1}{8}\right)\left(2+\frac{1}{128}\right)$$

Multiply 3 and 5 to get 15.

$$\frac{15}{2}\left(2+\frac{1}{8}\right)\left(2+\frac{1}{128}\right)$$

Convert 2 to fraction \frac{16}{8}.

$$\frac{15}{2}\left(\frac{16}{8}+\frac{1}{8}\right)\left(2+\frac{1}{128}\right)$$

Since \frac{16}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

$$\frac{15}{2}\times \frac{16+1}{8}\left(2+\frac{1}{128}\right)$$

Add 16 and 1 to get 17.

$$\frac{15}{2}\times \frac{17}{8}\left(2+\frac{1}{128}\right)$$

Multiply \frac{15}{2} times \frac{17}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15\times 17}{2\times 8}\left(2+\frac{1}{128}\right)$$

Do the multiplications in the fraction \frac{15\times 17}{2\times 8}.

$$\frac{255}{16}\left(2+\frac{1}{128}\right)$$

Convert 2 to fraction \frac{256}{128}.

$$\frac{255}{16}\left(\frac{256}{128}+\frac{1}{128}\right)$$

Since \frac{256}{128} and \frac{1}{128} have the same denominator, add them by adding their numerators.

$$\frac{255}{16}\times \frac{256+1}{128}$$

Add 256 and 1 to get 257.

$$\frac{255}{16}\times \frac{257}{128}$$

Multiply \frac{255}{16} times \frac{257}{128} by multiplying numerator times numerator and denominator times denominator.

$$\frac{255\times 257}{16\times 128}$$

Do the multiplications in the fraction \frac{255\times 257}{16\times 128}.

$$\frac{65535}{2048}$$

Factor

$$\frac{3 \cdot 5 \cdot 17 \cdot 257}{2 ^ {11}} = 31\frac{2047}{2048} = 31.99951171875$$