Solve 1/10099/99/frac{99{100}1/100+frac{1}{100}frac{99}{99}}

$$\frac{ \frac{ 1 }{ 100 } \frac{ 99 }{ 99 } }{ \frac{ 99 }{ 100 } \frac{ 1 }{ 100 } + \frac{ 1 }{ 100 } \frac{ 99 }{ 99 } }$$

Evaluate

$$\frac{100}{199}\approx 0.502512563$$

Solution Steps

Divide 99 by 99 to get 1.

$$\frac{\frac{1}{100}\times 1}{\frac{99}{100}\times \frac{1}{100}+\frac{1}{100}\times \frac{99}{99}}$$

Divide 99 by 99 to get 1.

$$\frac{\frac{1}{100}\times 1}{\frac{99}{100}\times \frac{1}{100}+\frac{1}{100}\times 1}$$

Multiply \frac{1}{100} and 1 to get \frac{1}{100}.

$$\frac{\frac{1}{100}}{\frac{99}{100}\times \frac{1}{100}+\frac{1}{100}\times 1}$$

Multiply \frac{99}{100} times \frac{1}{100} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{100}}{\frac{99\times 1}{100\times 100}+\frac{1}{100}\times 1}$$

Do the multiplications in the fraction \frac{99\times 1}{100\times 100}.

$$\frac{\frac{1}{100}}{\frac{99}{10000}+\frac{1}{100}\times 1}$$

Multiply \frac{1}{100} and 1 to get \frac{1}{100}.

$$\frac{\frac{1}{100}}{\frac{99}{10000}+\frac{1}{100}}$$

Least common multiple of 10000 and 100 is 10000. Convert \frac{99}{10000} and \frac{1}{100} to fractions with denominator 10000.

$$\frac{\frac{1}{100}}{\frac{99}{10000}+\frac{100}{10000}}$$

Since \frac{99}{10000} and \frac{100}{10000} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{100}}{\frac{99+100}{10000}}$$

Add 99 and 100 to get 199.

$$\frac{\frac{1}{100}}{\frac{199}{10000}}$$

Divide \frac{1}{100} by \frac{199}{10000} by multiplying \frac{1}{100} by the reciprocal of \frac{199}{10000}.

$$\frac{1}{100}\times \frac{10000}{199}$$

Multiply \frac{1}{100} times \frac{10000}{199} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 10000}{100\times 199}$$

Do the multiplications in the fraction \frac{1\times 10000}{100\times 199}.

$$\frac{10000}{19900}$$

Reduce the fraction \frac{10000}{19900} to lowest terms by extracting and canceling out 100.

$$\frac{100}{199}$$

Factor

$$\frac{2 ^ {2} \cdot 5 ^ {2}}{199} = 0.5025125628140703$$