Solve 1/2-1/4+1/8-1/16+frac{1}{32}-frac{1}{64}

$$\frac{ 1 }{ 2 } - \frac{ 1 }{ 4 } + \frac{ 1 }{ 8 } - \frac{ 1 }{ 16 } + \frac{ 1 }{ 32 } - \frac{ 1 }{ 64 }$$

Evaluate

$$\frac{21}{64}=0.328125$$

Solution Steps

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{1}{4} to fractions with denominator 4.

$$\frac{2}{4}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}$$

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

$$\frac{2-1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}$$

Subtract 1 from 2 to get 1.

$$\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}$$

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

$$\frac{2}{8}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}$$

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

$$\frac{2+1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}$$

Add 2 and 1 to get 3.

$$\frac{3}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}$$

Least common multiple of 8 and 16 is 16. Convert \frac{3}{8} and \frac{1}{16} to fractions with denominator 16.

$$\frac{6}{16}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}$$

Since \frac{6}{16} and \frac{1}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-1}{16}+\frac{1}{32}-\frac{1}{64}$$

Subtract 1 from 6 to get 5.

$$\frac{5}{16}+\frac{1}{32}-\frac{1}{64}$$

Least common multiple of 16 and 32 is 32. Convert \frac{5}{16} and \frac{1}{32} to fractions with denominator 32.

$$\frac{10}{32}+\frac{1}{32}-\frac{1}{64}$$

Since \frac{10}{32} and \frac{1}{32} have the same denominator, add them by adding their numerators.

$$\frac{10+1}{32}-\frac{1}{64}$$

Add 10 and 1 to get 11.

$$\frac{11}{32}-\frac{1}{64}$$

Least common multiple of 32 and 64 is 64. Convert \frac{11}{32} and \frac{1}{64} to fractions with denominator 64.

$$\frac{22}{64}-\frac{1}{64}$$

Since \frac{22}{64} and \frac{1}{64} have the same denominator, subtract them by subtracting their numerators.

$$\frac{22-1}{64}$$

Subtract 1 from 22 to get 21.

$$\frac{21}{64}$$

Factor

$$\frac{3 \cdot 7}{2 ^ {6}} = 0.328125$$