Solve 1+1/2+1/4+1/8+1/16)div(frac{1}{2}*frac{1}{4}*frac{1}{8}*frac{1}{16})

$$1 + \frac { 1 } { 2 } + \frac { 1 } { 4 } + \frac { 1 } { 8 } + \frac { 1 } { 16 } ) \div ( \frac { 1 } { 2 } \times \frac { 1 } { 4 } \times \frac { 1 } { 8 } \times \frac { 1 } { 16 } )$$

Evaluate

$$\frac{31}{16}=1.9375$$

Solution Steps

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

$$\frac{2}{2}+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}$$

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

$$\frac{2+1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}$$

Add 2 and 1 to get 3.

$$\frac{3}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}$$

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

$$\frac{6}{4}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}$$

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

$$\frac{6+1}{4}+\frac{1}{8}+\frac{1}{16}$$

Add 6 and 1 to get 7.

$$\frac{7}{4}+\frac{1}{8}+\frac{1}{16}$$

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

$$\frac{14}{8}+\frac{1}{8}+\frac{1}{16}$$

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

$$\frac{14+1}{8}+\frac{1}{16}$$

Add 14 and 1 to get 15.

$$\frac{15}{8}+\frac{1}{16}$$

Least common multiple of 8 and 16 is 16. Convert \frac{15}{8} and \frac{1}{16} to fractions with denominator 16.

$$\frac{30}{16}+\frac{1}{16}$$

Since \frac{30}{16} and \frac{1}{16} have the same denominator, add them by adding their numerators.

$$\frac{30+1}{16}$$

Add 30 and 1 to get 31.

$$\frac{31}{16}$$

Factor

$$\frac{31}{2 ^ {4}} = 1\frac{15}{16} = 1.9375$$