Solve {l}{29(7/30)}{(3/4)(2/3)(5/7)}{9(frac{7}{5})(frac{3}{2})}{5-2(frac{5}{3})}{0-3(frac{2}{15})}

$$\left. \begin{array} { l } { 29 ( \frac { 7 } { 30 } ) } \\ { ( \frac { 3 } { 4 } ) ( \frac { 2 } { 3 } ) ( \frac { 5 } { 7 } ) } \\ { 9 ( \frac { 7 } { 5 } ) ( \frac { 3 } { 2 } ) } \\ { 5 - 2 ( \frac { 5 } { 3 } ) } \\ { 0 - 3 ( \frac { 2 } { 15 } ) } \end{array} \right.$$

Sort

$$-\frac{2}{5},\frac{5}{14},\frac{5}{3},\frac{203}{30},\frac{189}{10}$$

Solution Steps

Express 29\times \frac{7}{30} as a single fraction.

$$sort(\frac{29\times 7}{30},\frac{3}{4}\times \frac{2}{3}\times \frac{5}{7},9\times \frac{7}{5}\times \frac{3}{2},5-2\times \frac{5}{3},0-3\times \frac{2}{15})$$

Multiply 29 and 7 to get 203.

$$sort(\frac{203}{30},\frac{3}{4}\times \frac{2}{3}\times \frac{5}{7},9\times \frac{7}{5}\times \frac{3}{2},5-2\times \frac{5}{3},0-3\times \frac{2}{15})$$

Multiply \frac{3}{4} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{203}{30},\frac{3\times 2}{4\times 3}\times \frac{5}{7},9\times \frac{7}{5}\times \frac{3}{2},5-2\times \frac{5}{3},0-3\times \frac{2}{15})$$

Cancel out 3 in both numerator and denominator.

$$sort(\frac{203}{30},\frac{2}{4}\times \frac{5}{7},9\times \frac{7}{5}\times \frac{3}{2},5-2\times \frac{5}{3},0-3\times \frac{2}{15})$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$sort(\frac{203}{30},\frac{1}{2}\times \frac{5}{7},9\times \frac{7}{5}\times \frac{3}{2},5-2\times \frac{5}{3},0-3\times \frac{2}{15})$$

Multiply \frac{1}{2} times \frac{5}{7} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{203}{30},\frac{1\times 5}{2\times 7},9\times \frac{7}{5}\times \frac{3}{2},5-2\times \frac{5}{3},0-3\times \frac{2}{15})$$

Do the multiplications in the fraction \frac{1\times 5}{2\times 7}.

$$sort(\frac{203}{30},\frac{5}{14},9\times \frac{7}{5}\times \frac{3}{2},5-2\times \frac{5}{3},0-3\times \frac{2}{15})$$

Express 9\times \frac{7}{5} as a single fraction.

$$sort(\frac{203}{30},\frac{5}{14},\frac{9\times 7}{5}\times \frac{3}{2},5-2\times \frac{5}{3},0-3\times \frac{2}{15})$$

Multiply 9 and 7 to get 63.

$$sort(\frac{203}{30},\frac{5}{14},\frac{63}{5}\times \frac{3}{2},5-2\times \frac{5}{3},0-3\times \frac{2}{15})$$

Multiply \frac{63}{5} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{203}{30},\frac{5}{14},\frac{63\times 3}{5\times 2},5-2\times \frac{5}{3},0-3\times \frac{2}{15})$$

Do the multiplications in the fraction \frac{63\times 3}{5\times 2}.

$$sort(\frac{203}{30},\frac{5}{14},\frac{189}{10},5-2\times \frac{5}{3},0-3\times \frac{2}{15})$$

Express 2\times \frac{5}{3} as a single fraction.

$$sort(\frac{203}{30},\frac{5}{14},\frac{189}{10},5-\frac{2\times 5}{3},0-3\times \frac{2}{15})$$

Multiply 2 and 5 to get 10.

$$sort(\frac{203}{30},\frac{5}{14},\frac{189}{10},5-\frac{10}{3},0-3\times \frac{2}{15})$$

Convert 5 to fraction \frac{15}{3}.

$$sort(\frac{203}{30},\frac{5}{14},\frac{189}{10},\frac{15}{3}-\frac{10}{3},0-3\times \frac{2}{15})$$

Since \frac{15}{3} and \frac{10}{3} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{203}{30},\frac{5}{14},\frac{189}{10},\frac{15-10}{3},0-3\times \frac{2}{15})$$

Subtract 10 from 15 to get 5.

$$sort(\frac{203}{30},\frac{5}{14},\frac{189}{10},\frac{5}{3},0-3\times \frac{2}{15})$$

Express 3\times \frac{2}{15} as a single fraction.

$$sort(\frac{203}{30},\frac{5}{14},\frac{189}{10},\frac{5}{3},0-\frac{3\times 2}{15})$$

Multiply 3 and 2 to get 6.

$$sort(\frac{203}{30},\frac{5}{14},\frac{189}{10},\frac{5}{3},0-\frac{6}{15})$$

Reduce the fraction \frac{6}{15} to lowest terms by extracting and canceling out 3.

$$sort(\frac{203}{30},\frac{5}{14},\frac{189}{10},\frac{5}{3},0-\frac{2}{5})$$

Subtract \frac{2}{5} from 0 to get -\frac{2}{5}.

$$sort(\frac{203}{30},\frac{5}{14},\frac{189}{10},\frac{5}{3},-\frac{2}{5})$$

Least common denominator of the numbers in the list \frac{203}{30},\frac{5}{14},\frac{189}{10},\frac{5}{3},-\frac{2}{5} is 210. Convert numbers in the list to fractions with denominator 210.

$$\frac{1421}{210},\frac{75}{210},\frac{3969}{210},\frac{350}{210},-\frac{84}{210}$$

To sort the list, start from a single element \frac{1421}{210}.

$$\frac{1421}{210}$$

Insert \frac{75}{210} to the appropriate location in the new list.

$$\frac{75}{210},\frac{1421}{210}$$

Insert \frac{3969}{210} to the appropriate location in the new list.

$$\frac{75}{210},\frac{1421}{210},\frac{3969}{210}$$

Insert \frac{350}{210} to the appropriate location in the new list.

$$\frac{75}{210},\frac{350}{210},\frac{1421}{210},\frac{3969}{210}$$

Insert -\frac{84}{210} to the appropriate location in the new list.

$$-\frac{84}{210},\frac{75}{210},\frac{350}{210},\frac{1421}{210},\frac{3969}{210}$$

Replace the obtained fractions with the initial values.

$$-\frac{2}{5},\frac{5}{14},\frac{5}{3},\frac{203}{30},\frac{189}{10}$$

Evaluate

$$\frac{203}{30},\ \frac{5}{14},\ \frac{189}{10},\ \frac{5}{3},\ -\frac{2}{5}$$