Solve 1/frac{1{2}}-1/frac{1{2}+1/4/99}

$$\frac { 1 } { \frac { 1 } { 2 } } - \frac { 1 } { \frac { 1 } { 2 } + \frac { \frac { 1 } { 4 } } { 99 } }$$

Evaluate

$$\frac{2}{199}\approx 0.010050251$$

Solution Steps

Divide 1 by \frac{1}{2} by multiplying 1 by the reciprocal of \frac{1}{2}.

$$1\times 2-\frac{1}{\frac{1}{2}+\frac{\frac{1}{4}}{99}}$$

Multiply 1 and 2 to get 2.

$$2-\frac{1}{\frac{1}{2}+\frac{\frac{1}{4}}{99}}$$

Express \frac{\frac{1}{4}}{99} as a single fraction.

$$2-\frac{1}{\frac{1}{2}+\frac{1}{4\times 99}}$$

Multiply 4 and 99 to get 396.

$$2-\frac{1}{\frac{1}{2}+\frac{1}{396}}$$

Least common multiple of 2 and 396 is 396. Convert \frac{1}{2} and \frac{1}{396} to fractions with denominator 396.

$$2-\frac{1}{\frac{198}{396}+\frac{1}{396}}$$

Since \frac{198}{396} and \frac{1}{396} have the same denominator, add them by adding their numerators.

$$2-\frac{1}{\frac{198+1}{396}}$$

Add 198 and 1 to get 199.

$$2-\frac{1}{\frac{199}{396}}$$

Divide 1 by \frac{199}{396} by multiplying 1 by the reciprocal of \frac{199}{396}.

$$2-1\times \frac{396}{199}$$

Multiply 1 and \frac{396}{199} to get \frac{396}{199}.

$$2-\frac{396}{199}$$

Convert 2 to fraction \frac{398}{199}.

$$\frac{398}{199}-\frac{396}{199}$$

Since \frac{398}{199} and \frac{396}{199} have the same denominator, subtract them by subtracting their numerators.

$$\frac{398-396}{199}$$

Subtract 396 from 398 to get 2.

$$\frac{2}{199}$$

Factor

$$\frac{2}{199} = 0.010050251256281407$$