Solve {l}{5/7-1/3}{23/5-7/8}{4frac{1}{2}*1frac{3}{4}}{2frac{1}{3}divfrac{5}{7}}

$$\left. \begin{array} { l } { \frac { 5 } { 7 } - \frac { 1 } { 3 } } \\ { 2 \frac { 3 } { 5 } - \frac { 7 } { 8 } } \\ { 4 \frac { 1 } { 2 } \times 1 \frac { 3 } { 4 } } \\ { 2 \frac { 1 } { 3 } \div \frac { 5 } { 7 } } \end{array} \right.$$

Sort

$$\frac{8}{21},\frac{69}{40},\frac{49}{15},\frac{63}{8}$$

Solution Steps

Least common multiple of 7 and 3 is 21. Convert \frac{5}{7} and \frac{1}{3} to fractions with denominator 21.

$$sort(\frac{15}{21}-\frac{7}{21},\frac{2\times 5+3}{5}-\frac{7}{8},\frac{4\times 2+1}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Since \frac{15}{21} and \frac{7}{21} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{15-7}{21},\frac{2\times 5+3}{5}-\frac{7}{8},\frac{4\times 2+1}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Subtract 7 from 15 to get 8.

$$sort(\frac{8}{21},\frac{2\times 5+3}{5}-\frac{7}{8},\frac{4\times 2+1}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Multiply 2 and 5 to get 10.

$$sort(\frac{8}{21},\frac{10+3}{5}-\frac{7}{8},\frac{4\times 2+1}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Add 10 and 3 to get 13.

$$sort(\frac{8}{21},\frac{13}{5}-\frac{7}{8},\frac{4\times 2+1}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Least common multiple of 5 and 8 is 40. Convert \frac{13}{5} and \frac{7}{8} to fractions with denominator 40.

$$sort(\frac{8}{21},\frac{104}{40}-\frac{35}{40},\frac{4\times 2+1}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Since \frac{104}{40} and \frac{35}{40} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{8}{21},\frac{104-35}{40},\frac{4\times 2+1}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Subtract 35 from 104 to get 69.

$$sort(\frac{8}{21},\frac{69}{40},\frac{4\times 2+1}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Multiply 4 and 2 to get 8.

$$sort(\frac{8}{21},\frac{69}{40},\frac{8+1}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Add 8 and 1 to get 9.

$$sort(\frac{8}{21},\frac{69}{40},\frac{9}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Multiply 1 and 4 to get 4.

$$sort(\frac{8}{21},\frac{69}{40},\frac{9}{2}\times \frac{4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Add 4 and 3 to get 7.

$$sort(\frac{8}{21},\frac{69}{40},\frac{9}{2}\times \frac{7}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Multiply \frac{9}{2} times \frac{7}{4} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{8}{21},\frac{69}{40},\frac{9\times 7}{2\times 4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Do the multiplications in the fraction \frac{9\times 7}{2\times 4}.

$$sort(\frac{8}{21},\frac{69}{40},\frac{63}{8},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Divide \frac{2\times 3+1}{3} by \frac{5}{7} by multiplying \frac{2\times 3+1}{3} by the reciprocal of \frac{5}{7}.

$$sort(\frac{8}{21},\frac{69}{40},\frac{63}{8},\frac{\left(2\times 3+1\right)\times 7}{3\times 5})$$

Multiply 2 and 3 to get 6.

$$sort(\frac{8}{21},\frac{69}{40},\frac{63}{8},\frac{\left(6+1\right)\times 7}{3\times 5})$$

Add 6 and 1 to get 7.

$$sort(\frac{8}{21},\frac{69}{40},\frac{63}{8},\frac{7\times 7}{3\times 5})$$

Multiply 7 and 7 to get 49.

$$sort(\frac{8}{21},\frac{69}{40},\frac{63}{8},\frac{49}{3\times 5})$$

Multiply 3 and 5 to get 15.

$$sort(\frac{8}{21},\frac{69}{40},\frac{63}{8},\frac{49}{15})$$

Least common denominator of the numbers in the list \frac{8}{21},\frac{69}{40},\frac{63}{8},\frac{49}{15} is 840. Convert numbers in the list to fractions with denominator 840.

$$\frac{320}{840},\frac{1449}{840},\frac{6615}{840},\frac{2744}{840}$$

To sort the list, start from a single element \frac{320}{840}.

$$\frac{320}{840}$$

Insert \frac{1449}{840} to the appropriate location in the new list.

$$\frac{320}{840},\frac{1449}{840}$$

Insert \frac{6615}{840} to the appropriate location in the new list.

$$\frac{320}{840},\frac{1449}{840},\frac{6615}{840}$$

Insert \frac{2744}{840} to the appropriate location in the new list.

$$\frac{320}{840},\frac{1449}{840},\frac{2744}{840},\frac{6615}{840}$$

Replace the obtained fractions with the initial values.

$$\frac{8}{21},\frac{69}{40},\frac{49}{15},\frac{63}{8}$$

Evaluate

$$\frac{8}{21},\ \frac{69}{40},\ \frac{63}{8},\ \frac{49}{15}$$