Solve {c}{2/3div4/5}{1/4+3/5-1/3}

$$\left. \begin{array} { c } { 2 / 3 \div 4 / 5 } \\ { 1 / 4 + 3 / 5 - 1 / 3 } \end{array} \right.$$

Sort

$$\frac{31}{60},\frac{5}{6}$$

Solution Steps

Divide \frac{2}{3} by \frac{4}{5} by multiplying \frac{2}{3} by the reciprocal of \frac{4}{5}.

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

Multiply \frac{2}{3} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{2\times 5}{3\times 4}.

$$sort(\frac{10}{12},\frac{1}{4}+\frac{3}{5}-\frac{1}{3})$$

Reduce the fraction \frac{10}{12} to lowest terms by extracting and canceling out 2.

$$sort(\frac{5}{6},\frac{1}{4}+\frac{3}{5}-\frac{1}{3})$$

Least common multiple of 4 and 5 is 20. Convert \frac{1}{4} and \frac{3}{5} to fractions with denominator 20.

$$sort(\frac{5}{6},\frac{5}{20}+\frac{12}{20}-\frac{1}{3})$$

Since \frac{5}{20} and \frac{12}{20} have the same denominator, add them by adding their numerators.

$$sort(\frac{5}{6},\frac{5+12}{20}-\frac{1}{3})$$

Add 5 and 12 to get 17.

$$sort(\frac{5}{6},\frac{17}{20}-\frac{1}{3})$$

Least common multiple of 20 and 3 is 60. Convert \frac{17}{20} and \frac{1}{3} to fractions with denominator 60.

$$sort(\frac{5}{6},\frac{51}{60}-\frac{20}{60})$$

Since \frac{51}{60} and \frac{20}{60} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{5}{6},\frac{51-20}{60})$$

Subtract 20 from 51 to get 31.

$$sort(\frac{5}{6},\frac{31}{60})$$

Least common denominator of the numbers in the list \frac{5}{6},\frac{31}{60} is 60. Convert numbers in the list to fractions with denominator 60.

$$\frac{50}{60},\frac{31}{60}$$

To sort the list, start from a single element \frac{50}{60}.

$$\frac{50}{60}$$

Insert \frac{31}{60} to the appropriate location in the new list.

$$\frac{31}{60},\frac{50}{60}$$

Replace the obtained fractions with the initial values.

$$\frac{31}{60},\frac{5}{6}$$

Evaluate

$$\frac{5}{6},\ \frac{31}{60}$$