Solve {l}{overline{R_{1}}+overline{R_{2}}+1/R_{3}+1/R_{2}}{1/5*67+1/15+frac{1}{17}+frac{1}{10000}}

$$\left. \begin{array} { l } { \overline { R _ { 1 } } + \overline { R _ { 2 } } + \frac { 1 } { R _ { 3 } } + \frac { 1 } { R _ { 2 } } } \\ { \frac { 1 } { 5 \cdot 67 } + \frac { 1 } { 15 } + \frac { 1 } { 17 } + \frac { 1 } { 10000 } } \end{array} \right.$$

Sort

$$0,\ \frac{4393417}{34170000}$$

Solution Steps

Multiply 5 and 67 to get 335.

$$sort(0,\frac{1}{335}+\frac{1}{15}+\frac{1}{17}+\frac{1}{10000})$$

Least common multiple of 335 and 15 is 1005. Convert \frac{1}{335} and \frac{1}{15} to fractions with denominator 1005.

$$sort(0,\frac{3}{1005}+\frac{67}{1005}+\frac{1}{17}+\frac{1}{10000})$$

Since \frac{3}{1005} and \frac{67}{1005} have the same denominator, add them by adding their numerators.

$$sort(0,\frac{3+67}{1005}+\frac{1}{17}+\frac{1}{10000})$$

Add 3 and 67 to get 70.

$$sort(0,\frac{70}{1005}+\frac{1}{17}+\frac{1}{10000})$$

Reduce the fraction \frac{70}{1005} to lowest terms by extracting and canceling out 5.

$$sort(0,\frac{14}{201}+\frac{1}{17}+\frac{1}{10000})$$

Least common multiple of 201 and 17 is 3417. Convert \frac{14}{201} and \frac{1}{17} to fractions with denominator 3417.

$$sort(0,\frac{238}{3417}+\frac{201}{3417}+\frac{1}{10000})$$

Since \frac{238}{3417} and \frac{201}{3417} have the same denominator, add them by adding their numerators.

$$sort(0,\frac{238+201}{3417}+\frac{1}{10000})$$

Add 238 and 201 to get 439.

$$sort(0,\frac{439}{3417}+\frac{1}{10000})$$

Least common multiple of 3417 and 10000 is 34170000. Convert \frac{439}{3417} and \frac{1}{10000} to fractions with denominator 34170000.

$$sort(0,\frac{4390000}{34170000}+\frac{3417}{34170000})$$

Since \frac{4390000}{34170000} and \frac{3417}{34170000} have the same denominator, add them by adding their numerators.

$$sort(0,\frac{4390000+3417}{34170000})$$

Add 4390000 and 3417 to get 4393417.

$$sort(0,\frac{4393417}{34170000})$$

Convert decimal numbers in the list 0,\frac{4393417}{34170000} to fractions.

$$0,\frac{4393417}{34170000}$$

Evaluate

$$0,\ \frac{4393417}{34170000}$$