Solve {l}{10+5/6}{51/3+31/5}{33/8+3frac{1}{5}}

$$\left. \begin{array} { l } { 10 + \frac { 5 } { 6 } } \\ { 5 \frac { 1 } { 3 } + 3 \frac { 1 } { 5 } } \\ { 3 \frac { 3 } { 8 } + 3 \frac { 1 } { 5 } } \end{array} \right.$$

Sort

$$\frac{263}{40},\frac{128}{15},\frac{65}{6}$$

Solution Steps

Convert 10 to fraction \frac{60}{6}.

$$sort(\frac{60}{6}+\frac{5}{6},\frac{5\times 3+1}{3}+\frac{3\times 5+1}{5},\frac{3\times 8+3}{8}+\frac{3\times 5+1}{5})$$

Since \frac{60}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$sort(\frac{60+5}{6},\frac{5\times 3+1}{3}+\frac{3\times 5+1}{5},\frac{3\times 8+3}{8}+\frac{3\times 5+1}{5})$$

Add 60 and 5 to get 65.

$$sort(\frac{65}{6},\frac{5\times 3+1}{3}+\frac{3\times 5+1}{5},\frac{3\times 8+3}{8}+\frac{3\times 5+1}{5})$$

Multiply 5 and 3 to get 15.

$$sort(\frac{65}{6},\frac{15+1}{3}+\frac{3\times 5+1}{5},\frac{3\times 8+3}{8}+\frac{3\times 5+1}{5})$$

Add 15 and 1 to get 16.

$$sort(\frac{65}{6},\frac{16}{3}+\frac{3\times 5+1}{5},\frac{3\times 8+3}{8}+\frac{3\times 5+1}{5})$$

Multiply 3 and 5 to get 15.

$$sort(\frac{65}{6},\frac{16}{3}+\frac{15+1}{5},\frac{3\times 8+3}{8}+\frac{3\times 5+1}{5})$$

Add 15 and 1 to get 16.

$$sort(\frac{65}{6},\frac{16}{3}+\frac{16}{5},\frac{3\times 8+3}{8}+\frac{3\times 5+1}{5})$$

Least common multiple of 3 and 5 is 15. Convert \frac{16}{3} and \frac{16}{5} to fractions with denominator 15.

$$sort(\frac{65}{6},\frac{80}{15}+\frac{48}{15},\frac{3\times 8+3}{8}+\frac{3\times 5+1}{5})$$

Since \frac{80}{15} and \frac{48}{15} have the same denominator, add them by adding their numerators.

$$sort(\frac{65}{6},\frac{80+48}{15},\frac{3\times 8+3}{8}+\frac{3\times 5+1}{5})$$

Add 80 and 48 to get 128.

$$sort(\frac{65}{6},\frac{128}{15},\frac{3\times 8+3}{8}+\frac{3\times 5+1}{5})$$

Multiply 3 and 8 to get 24.

$$sort(\frac{65}{6},\frac{128}{15},\frac{24+3}{8}+\frac{3\times 5+1}{5})$$

Add 24 and 3 to get 27.

$$sort(\frac{65}{6},\frac{128}{15},\frac{27}{8}+\frac{3\times 5+1}{5})$$

Multiply 3 and 5 to get 15.

$$sort(\frac{65}{6},\frac{128}{15},\frac{27}{8}+\frac{15+1}{5})$$

Add 15 and 1 to get 16.

$$sort(\frac{65}{6},\frac{128}{15},\frac{27}{8}+\frac{16}{5})$$

Least common multiple of 8 and 5 is 40. Convert \frac{27}{8} and \frac{16}{5} to fractions with denominator 40.

$$sort(\frac{65}{6},\frac{128}{15},\frac{135}{40}+\frac{128}{40})$$

Since \frac{135}{40} and \frac{128}{40} have the same denominator, add them by adding their numerators.

$$sort(\frac{65}{6},\frac{128}{15},\frac{135+128}{40})$$

Add 135 and 128 to get 263.

$$sort(\frac{65}{6},\frac{128}{15},\frac{263}{40})$$

Least common denominator of the numbers in the list \frac{65}{6},\frac{128}{15},\frac{263}{40} is 120. Convert numbers in the list to fractions with denominator 120.

$$\frac{1300}{120},\frac{1024}{120},\frac{789}{120}$$

To sort the list, start from a single element \frac{1300}{120}.

$$\frac{1300}{120}$$

Insert \frac{1024}{120} to the appropriate location in the new list.

$$\frac{1024}{120},\frac{1300}{120}$$

Insert \frac{789}{120} to the appropriate location in the new list.

$$\frac{789}{120},\frac{1024}{120},\frac{1300}{120}$$

Replace the obtained fractions with the initial values.

$$\frac{263}{40},\frac{128}{15},\frac{65}{6}$$

Evaluate

$$\frac{65}{6},\ \frac{128}{15},\ \frac{263}{40}$$