Solve 2-1/2+1/8-1/32+1/128

$$2 - \frac { 1 } { 2 } + \frac { 1 } { 8 } - \frac { 1 } { 32 } + \frac { 1 } { 128 }$$

Evaluate

$$\frac{205}{128}=1.6015625$$

Solution Steps

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

$$\frac{4}{2}-\frac{1}{2}+\frac{1}{8}-\frac{1}{32}+\frac{1}{128}$$

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

$$\frac{4-1}{2}+\frac{1}{8}-\frac{1}{32}+\frac{1}{128}$$

Subtract 1 from 4 to get 3.

$$\frac{3}{2}+\frac{1}{8}-\frac{1}{32}+\frac{1}{128}$$

Least common multiple of 2 and 8 is 8. Convert \frac{3}{2} and \frac{1}{8} to fractions with denominator 8.

$$\frac{12}{8}+\frac{1}{8}-\frac{1}{32}+\frac{1}{128}$$

Since \frac{12}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

$$\frac{12+1}{8}-\frac{1}{32}+\frac{1}{128}$$

Add 12 and 1 to get 13.

$$\frac{13}{8}-\frac{1}{32}+\frac{1}{128}$$

Least common multiple of 8 and 32 is 32. Convert \frac{13}{8} and \frac{1}{32} to fractions with denominator 32.

$$\frac{52}{32}-\frac{1}{32}+\frac{1}{128}$$

Since \frac{52}{32} and \frac{1}{32} have the same denominator, subtract them by subtracting their numerators.

$$\frac{52-1}{32}+\frac{1}{128}$$

Subtract 1 from 52 to get 51.

$$\frac{51}{32}+\frac{1}{128}$$

Least common multiple of 32 and 128 is 128. Convert \frac{51}{32} and \frac{1}{128} to fractions with denominator 128.

$$\frac{204}{128}+\frac{1}{128}$$

Since \frac{204}{128} and \frac{1}{128} have the same denominator, add them by adding their numerators.

$$\frac{204+1}{128}$$

Add 204 and 1 to get 205.

$$\frac{205}{128}$$

Factor

$$\frac{5 \cdot 41}{2 ^ {7}} = 1\frac{77}{128} = 1.6015625$$