Solve {l}{185/8-41/4}{121/4-82/5}

$$\left. \begin{array} { l } { 18 \frac { 5 } { 8 } - 4 \frac { 1 } { 4 } } \\ { 12 \frac { 1 } { 4 } - 8 \frac { 2 } { 5 } } \end{array} \right.$$

Sort

$$\frac{77}{20},\frac{115}{8}$$

Solution Steps

Multiply 18 and 8 to get 144.

$$sort(\frac{144+5}{8}-\frac{4\times 4+1}{4},\frac{12\times 4+1}{4}-\frac{8\times 5+2}{5})$$

Add 144 and 5 to get 149.

$$sort(\frac{149}{8}-\frac{4\times 4+1}{4},\frac{12\times 4+1}{4}-\frac{8\times 5+2}{5})$$

Multiply 4 and 4 to get 16.

$$sort(\frac{149}{8}-\frac{16+1}{4},\frac{12\times 4+1}{4}-\frac{8\times 5+2}{5})$$

Add 16 and 1 to get 17.

$$sort(\frac{149}{8}-\frac{17}{4},\frac{12\times 4+1}{4}-\frac{8\times 5+2}{5})$$

Least common multiple of 8 and 4 is 8. Convert \frac{149}{8} and \frac{17}{4} to fractions with denominator 8.

$$sort(\frac{149}{8}-\frac{34}{8},\frac{12\times 4+1}{4}-\frac{8\times 5+2}{5})$$

Since \frac{149}{8} and \frac{34}{8} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{149-34}{8},\frac{12\times 4+1}{4}-\frac{8\times 5+2}{5})$$

Subtract 34 from 149 to get 115.

$$sort(\frac{115}{8},\frac{12\times 4+1}{4}-\frac{8\times 5+2}{5})$$

Multiply 12 and 4 to get 48.

$$sort(\frac{115}{8},\frac{48+1}{4}-\frac{8\times 5+2}{5})$$

Add 48 and 1 to get 49.

$$sort(\frac{115}{8},\frac{49}{4}-\frac{8\times 5+2}{5})$$

Multiply 8 and 5 to get 40.

$$sort(\frac{115}{8},\frac{49}{4}-\frac{40+2}{5})$$

Add 40 and 2 to get 42.

$$sort(\frac{115}{8},\frac{49}{4}-\frac{42}{5})$$

Least common multiple of 4 and 5 is 20. Convert \frac{49}{4} and \frac{42}{5} to fractions with denominator 20.

$$sort(\frac{115}{8},\frac{245}{20}-\frac{168}{20})$$

Since \frac{245}{20} and \frac{168}{20} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{115}{8},\frac{245-168}{20})$$

Subtract 168 from 245 to get 77.

$$sort(\frac{115}{8},\frac{77}{20})$$

Least common denominator of the numbers in the list \frac{115}{8},\frac{77}{20} is 40. Convert numbers in the list to fractions with denominator 40.

$$\frac{575}{40},\frac{154}{40}$$

To sort the list, start from a single element \frac{575}{40}.

$$\frac{575}{40}$$

Insert \frac{154}{40} to the appropriate location in the new list.

$$\frac{154}{40},\frac{575}{40}$$

Replace the obtained fractions with the initial values.

$$\frac{77}{20},\frac{115}{8}$$

Evaluate

$$\frac{115}{8},\ \frac{77}{20}$$