Solve {l}{29(7/30)}{3(3/4)(2/3)(5/7)}{9(-frac{1}{5})(frac{3}{2})}{5-2(frac{5}{3})}{0-3(frac{2}{15})}

$$\left. \begin{array} { l } { 29 ( \frac { 7 } { 30 } ) } \\ { 3 ( \frac { 3 } { 4 } ) ( \frac { 2 } { 3 } ) ( \frac { 5 } { 7 } ) } \\ { 9 ( - \frac { 1 } { 5 } ) ( \frac { 3 } { 2 } ) } \\ { 5 - 2 ( \frac { 5 } { 3 } ) } \\ { 0 - 3 ( \frac { 2 } { 15 } ) } \end{array} \right.$$

Sort

$$-\frac{27}{10},-\frac{2}{5},\frac{15}{14},\frac{5}{3},\frac{203}{30}$$

Solution Steps

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

$$sort(\frac{29\times 7}{30},3\times \frac{3}{4}\times \frac{2}{3}\times \frac{5}{7},9\left(-\frac{1}{5}\right)\times \frac{3}{2},5-2\times \frac{5}{3},0-3\times \frac{2}{15})$$

Multiply 29 and 7 to get 203.

$$sort(\frac{203}{30},3\times \frac{3}{4}\times \frac{2}{3}\times \frac{5}{7},9\left(-\frac{1}{5}\right)\times \frac{3}{2},5-2\times \frac{5}{3},0-3\times \frac{2}{15})$$

Express 3\times \frac{3}{4} as a single fraction.

$$sort(\frac{203}{30},\frac{3\times 3}{4}\times \frac{2}{3}\times \frac{5}{7},9\left(-\frac{1}{5}\right)\times \frac{3}{2},5-2\times \frac{5}{3},0-3\times \frac{2}{15})$$

Multiply 3 and 3 to get 9.

$$sort(\frac{203}{30},\frac{9}{4}\times \frac{2}{3}\times \frac{5}{7},9\left(-\frac{1}{5}\right)\times \frac{3}{2},5-2\times \frac{5}{3},0-3\times \frac{2}{15})$$

Multiply \frac{9}{4} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{203}{30},\frac{9\times 2}{4\times 3}\times \frac{5}{7},9\left(-\frac{1}{5}\right)\times \frac{3}{2},5-2\times \frac{5}{3},0-3\times \frac{2}{15})$$

Do the multiplications in the fraction \frac{9\times 2}{4\times 3}.

$$sort(\frac{203}{30},\frac{18}{12}\times \frac{5}{7},9\left(-\frac{1}{5}\right)\times \frac{3}{2},5-2\times \frac{5}{3},0-3\times \frac{2}{15})$$

Reduce the fraction \frac{18}{12} to lowest terms by extracting and canceling out 6.

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

Multiply \frac{3}{2} times \frac{5}{7} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{3\times 5}{2\times 7}.

$$sort(\frac{203}{30},\frac{15}{14},9\left(-\frac{1}{5}\right)\times \frac{3}{2},5-2\times \frac{5}{3},0-3\times \frac{2}{15})$$

Express 9\left(-\frac{1}{5}\right) as a single fraction.

$$sort(\frac{203}{30},\frac{15}{14},\frac{9\left(-1\right)}{5}\times \frac{3}{2},5-2\times \frac{5}{3},0-3\times \frac{2}{15})$$

Multiply 9 and -1 to get -9.

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

Fraction \frac{-9}{5} can be rewritten as -\frac{9}{5} by extracting the negative sign.

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

Multiply -\frac{9}{5} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-9\times 3}{5\times 2}.

$$sort(\frac{203}{30},\frac{15}{14},\frac{-27}{10},5-2\times \frac{5}{3},0-3\times \frac{2}{15})$$

Fraction \frac{-27}{10} can be rewritten as -\frac{27}{10} by extracting the negative sign.

$$sort(\frac{203}{30},\frac{15}{14},-\frac{27}{10},5-2\times \frac{5}{3},0-3\times \frac{2}{15})$$

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

$$sort(\frac{203}{30},\frac{15}{14},-\frac{27}{10},5-\frac{2\times 5}{3},0-3\times \frac{2}{15})$$

Multiply 2 and 5 to get 10.

$$sort(\frac{203}{30},\frac{15}{14},-\frac{27}{10},5-\frac{10}{3},0-3\times \frac{2}{15})$$

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

$$sort(\frac{203}{30},\frac{15}{14},-\frac{27}{10},\frac{15}{3}-\frac{10}{3},0-3\times \frac{2}{15})$$

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

$$sort(\frac{203}{30},\frac{15}{14},-\frac{27}{10},\frac{15-10}{3},0-3\times \frac{2}{15})$$

Subtract 10 from 15 to get 5.

$$sort(\frac{203}{30},\frac{15}{14},-\frac{27}{10},\frac{5}{3},0-3\times \frac{2}{15})$$

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

$$sort(\frac{203}{30},\frac{15}{14},-\frac{27}{10},\frac{5}{3},0-\frac{3\times 2}{15})$$

Multiply 3 and 2 to get 6.

$$sort(\frac{203}{30},\frac{15}{14},-\frac{27}{10},\frac{5}{3},0-\frac{6}{15})$$

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

$$sort(\frac{203}{30},\frac{15}{14},-\frac{27}{10},\frac{5}{3},0-\frac{2}{5})$$

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

$$sort(\frac{203}{30},\frac{15}{14},-\frac{27}{10},\frac{5}{3},-\frac{2}{5})$$

Least common denominator of the numbers in the list \frac{203}{30},\frac{15}{14},-\frac{27}{10},\frac{5}{3},-\frac{2}{5} is 210. Convert numbers in the list to fractions with denominator 210.

$$\frac{1421}{210},\frac{225}{210},-\frac{567}{210},\frac{350}{210},-\frac{84}{210}$$

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

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

Insert \frac{225}{210} to the appropriate location in the new list.

$$\frac{225}{210},\frac{1421}{210}$$

Insert -\frac{567}{210} to the appropriate location in the new list.

$$-\frac{567}{210},\frac{225}{210},\frac{1421}{210}$$

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

$$-\frac{567}{210},\frac{225}{210},\frac{350}{210},\frac{1421}{210}$$

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

$$-\frac{567}{210},-\frac{84}{210},\frac{225}{210},\frac{350}{210},\frac{1421}{210}$$

Replace the obtained fractions with the initial values.

$$-\frac{27}{10},-\frac{2}{5},\frac{15}{14},\frac{5}{3},\frac{203}{30}$$

Evaluate

$$\frac{203}{30},\ \frac{15}{14},\ -\frac{27}{10},\ \frac{5}{3},\ -\frac{2}{5}$$