Solve 1/4+1/8+1/8+1/8+frac{1}{16}+frac{1}{32}

$$\frac{ 1 }{ 4 } + \frac{ 1 }{ 8 } + \frac{ 1 }{ 8 } + \frac{ 1 }{ 8 } + \frac{ 1 }{ 16 } + \frac{ 1 }{ 32 }$$

Evaluate

$$\frac{23}{32}=0.71875$$

Solution Steps

Least common multiple of 4 and 8 is 8. Convert \frac{1}{4} and \frac{1}{8} to fractions with denominator 8.

$$\frac{2}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}$$

Since \frac{2}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

$$\frac{2+1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}$$

Add 2 and 1 to get 3.

$$\frac{3}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}$$

Since \frac{3}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

$$\frac{3+1}{8}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}$$

Add 3 and 1 to get 4.

$$\frac{4}{8}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}$$

Since \frac{4}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

$$\frac{4+1}{8}+\frac{1}{16}+\frac{1}{32}$$

Add 4 and 1 to get 5.

$$\frac{5}{8}+\frac{1}{16}+\frac{1}{32}$$

Least common multiple of 8 and 16 is 16. Convert \frac{5}{8} and \frac{1}{16} to fractions with denominator 16.

$$\frac{10}{16}+\frac{1}{16}+\frac{1}{32}$$

Since \frac{10}{16} and \frac{1}{16} have the same denominator, add them by adding their numerators.

$$\frac{10+1}{16}+\frac{1}{32}$$

Add 10 and 1 to get 11.

$$\frac{11}{16}+\frac{1}{32}$$

Least common multiple of 16 and 32 is 32. Convert \frac{11}{16} and \frac{1}{32} to fractions with denominator 32.

$$\frac{22}{32}+\frac{1}{32}$$

Since \frac{22}{32} and \frac{1}{32} have the same denominator, add them by adding their numerators.

$$\frac{22+1}{32}$$

Add 22 and 1 to get 23.

$$\frac{23}{32}$$

Factor

$$\frac{23}{2 ^ {5}} = 0.71875$$