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

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

Evaluate

$$\frac{15}{8}=1.875$$

Solution Steps

Convert 1 to fraction \frac{2}{2}.

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

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

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

Add 2 and 1 to get 3.

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

Least common multiple of 2 and 4 is 4. Convert \frac{3}{2} and \frac{1}{4} to fractions with denominator 4.

$$\frac{6}{4}+\frac{1}{4}+\frac{1}{8}$$

Since \frac{6}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{6+1}{4}+\frac{1}{8}$$

Add 6 and 1 to get 7.

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

Least common multiple of 4 and 8 is 8. Convert \frac{7}{4} and \frac{1}{8} to fractions with denominator 8.

$$\frac{14}{8}+\frac{1}{8}$$

Since \frac{14}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

$$\frac{14+1}{8}$$

Add 14 and 1 to get 15.

$$\frac{15}{8}$$

Factor

$$\frac{3 \cdot 5}{2 ^ {3}} = 1\frac{7}{8} = 1.875$$