Solve 1/frac{1{2}+1/4+1/1+1/100}=

$$\frac { 1 } { \frac { 1 } { 2 } + \frac { 1 } { 4 } + \frac { 1 } { 1 } + \frac { 1 } { 100 } } =$$

Evaluate

$$\frac{25}{44}\approx 0.568181818$$

Solution Steps

Divide 1 by 1 to get 1.

$$\frac{1}{\frac{1}{2}+\frac{1}{4}+1+\frac{1}{100}}$$

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

$$\frac{1}{\frac{2}{4}+\frac{1}{4}+1+\frac{1}{100}}$$

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

$$\frac{1}{\frac{2+1}{4}+1+\frac{1}{100}}$$

Add 2 and 1 to get 3.

$$\frac{1}{\frac{3}{4}+1+\frac{1}{100}}$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{1}{\frac{3}{4}+\frac{4}{4}+\frac{1}{100}}$$

Since \frac{3}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{3+4}{4}+\frac{1}{100}}$$

Add 3 and 4 to get 7.

$$\frac{1}{\frac{7}{4}+\frac{1}{100}}$$

Least common multiple of 4 and 100 is 100. Convert \frac{7}{4} and \frac{1}{100} to fractions with denominator 100.

$$\frac{1}{\frac{175}{100}+\frac{1}{100}}$$

Since \frac{175}{100} and \frac{1}{100} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{175+1}{100}}$$

Add 175 and 1 to get 176.

$$\frac{1}{\frac{176}{100}}$$

Reduce the fraction \frac{176}{100} to lowest terms by extracting and canceling out 4.

$$\frac{1}{\frac{44}{25}}$$

Divide 1 by \frac{44}{25} by multiplying 1 by the reciprocal of \frac{44}{25}.

$$1\times \frac{25}{44}$$

Multiply 1 and \frac{25}{44} to get \frac{25}{44}.

$$\frac{25}{44}$$

Factor

$$\frac{5 ^ {2}}{2 ^ {2} \cdot 11} = 0.5681818181818182$$