Solve 1/16+1/8+1/4+1/2+1+2+4+8

$$\frac{ 1 }{ 16 } + \frac{ 1 }{ 8 } + \frac{ 1 }{ 4 } + \frac{ 1 }{ 2 } +1+2+4+8$$

Evaluate

$$\frac{255}{16}=15.9375$$

Solution Steps

Least common multiple of 16 and 8 is 16. Convert \frac{1}{16} and \frac{1}{8} to fractions with denominator 16.

$$\frac{1}{16}+\frac{2}{16}+\frac{1}{4}+\frac{1}{2}+1+2+4+8$$

Since \frac{1}{16} and \frac{2}{16} have the same denominator, add them by adding their numerators.

$$\frac{1+2}{16}+\frac{1}{4}+\frac{1}{2}+1+2+4+8$$

Add 1 and 2 to get 3.

$$\frac{3}{16}+\frac{1}{4}+\frac{1}{2}+1+2+4+8$$

Least common multiple of 16 and 4 is 16. Convert \frac{3}{16} and \frac{1}{4} to fractions with denominator 16.

$$\frac{3}{16}+\frac{4}{16}+\frac{1}{2}+1+2+4+8$$

Since \frac{3}{16} and \frac{4}{16} have the same denominator, add them by adding their numerators.

$$\frac{3+4}{16}+\frac{1}{2}+1+2+4+8$$

Add 3 and 4 to get 7.

$$\frac{7}{16}+\frac{1}{2}+1+2+4+8$$

Least common multiple of 16 and 2 is 16. Convert \frac{7}{16} and \frac{1}{2} to fractions with denominator 16.

$$\frac{7}{16}+\frac{8}{16}+1+2+4+8$$

Since \frac{7}{16} and \frac{8}{16} have the same denominator, add them by adding their numerators.

$$\frac{7+8}{16}+1+2+4+8$$

Add 7 and 8 to get 15.

$$\frac{15}{16}+1+2+4+8$$

Convert 1 to fraction \frac{16}{16}.

$$\frac{15}{16}+\frac{16}{16}+2+4+8$$

Since \frac{15}{16} and \frac{16}{16} have the same denominator, add them by adding their numerators.

$$\frac{15+16}{16}+2+4+8$$

Add 15 and 16 to get 31.

$$\frac{31}{16}+2+4+8$$

Convert 2 to fraction \frac{32}{16}.

$$\frac{31}{16}+\frac{32}{16}+4+8$$

Since \frac{31}{16} and \frac{32}{16} have the same denominator, add them by adding their numerators.

$$\frac{31+32}{16}+4+8$$

Add 31 and 32 to get 63.

$$\frac{63}{16}+4+8$$

Convert 4 to fraction \frac{64}{16}.

$$\frac{63}{16}+\frac{64}{16}+8$$

Since \frac{63}{16} and \frac{64}{16} have the same denominator, add them by adding their numerators.

$$\frac{63+64}{16}+8$$

Add 63 and 64 to get 127.

$$\frac{127}{16}+8$$

Convert 8 to fraction \frac{128}{16}.

$$\frac{127}{16}+\frac{128}{16}$$

Since \frac{127}{16} and \frac{128}{16} have the same denominator, add them by adding their numerators.

$$\frac{127+128}{16}$$

Add 127 and 128 to get 255.

$$\frac{255}{16}$$

Factor

$$\frac{3 \cdot 5 \cdot 17}{2 ^ {4}} = 15\frac{15}{16} = 15.9375$$