Solve 7/8+9/16+27/32+13/64+frac{1}{2}+41+12=

$$\frac{ 7 }{ 8 } + \frac{ 9 }{ 16 } + \frac{ 27 }{ 32 } + \frac{ 13 }{ 64 } + \frac{ 1 }{ 2 } +41+12=$$

Evaluate

$$\frac{3583}{64}=55.984375$$

Solution Steps

Least common multiple of 8 and 16 is 16. Convert \frac{7}{8} and \frac{9}{16} to fractions with denominator 16.

$$\frac{14}{16}+\frac{9}{16}+\frac{27}{32}+\frac{13}{64}+\frac{1}{2}+41+12$$

Since \frac{14}{16} and \frac{9}{16} have the same denominator, add them by adding their numerators.

$$\frac{14+9}{16}+\frac{27}{32}+\frac{13}{64}+\frac{1}{2}+41+12$$

Add 14 and 9 to get 23.

$$\frac{23}{16}+\frac{27}{32}+\frac{13}{64}+\frac{1}{2}+41+12$$

Least common multiple of 16 and 32 is 32. Convert \frac{23}{16} and \frac{27}{32} to fractions with denominator 32.

$$\frac{46}{32}+\frac{27}{32}+\frac{13}{64}+\frac{1}{2}+41+12$$

Since \frac{46}{32} and \frac{27}{32} have the same denominator, add them by adding their numerators.

$$\frac{46+27}{32}+\frac{13}{64}+\frac{1}{2}+41+12$$

Add 46 and 27 to get 73.

$$\frac{73}{32}+\frac{13}{64}+\frac{1}{2}+41+12$$

Least common multiple of 32 and 64 is 64. Convert \frac{73}{32} and \frac{13}{64} to fractions with denominator 64.

$$\frac{146}{64}+\frac{13}{64}+\frac{1}{2}+41+12$$

Since \frac{146}{64} and \frac{13}{64} have the same denominator, add them by adding their numerators.

$$\frac{146+13}{64}+\frac{1}{2}+41+12$$

Add 146 and 13 to get 159.

$$\frac{159}{64}+\frac{1}{2}+41+12$$

Least common multiple of 64 and 2 is 64. Convert \frac{159}{64} and \frac{1}{2} to fractions with denominator 64.

$$\frac{159}{64}+\frac{32}{64}+41+12$$

Since \frac{159}{64} and \frac{32}{64} have the same denominator, add them by adding their numerators.

$$\frac{159+32}{64}+41+12$$

Add 159 and 32 to get 191.

$$\frac{191}{64}+41+12$$

Convert 41 to fraction \frac{2624}{64}.

$$\frac{191}{64}+\frac{2624}{64}+12$$

Since \frac{191}{64} and \frac{2624}{64} have the same denominator, add them by adding their numerators.

$$\frac{191+2624}{64}+12$$

Add 191 and 2624 to get 2815.

$$\frac{2815}{64}+12$$

Convert 12 to fraction \frac{768}{64}.

$$\frac{2815}{64}+\frac{768}{64}$$

Since \frac{2815}{64} and \frac{768}{64} have the same denominator, add them by adding their numerators.

$$\frac{2815+768}{64}$$

Add 2815 and 768 to get 3583.

$$\frac{3583}{64}$$

Factor

$$\frac{3583}{2 ^ {6}} = 55\frac{63}{64} = 55.984375$$