Solve 2*2/3+5/6-1/12quad3,5/6

$$2 \cdot \frac { 2 } { 3 } + \frac { 5 } { 6 } - \frac { 1 } { 12 } \quad 3 , \frac { 5 } { 6 }$$

Sort

$$\frac{5}{6},\frac{23}{12}$$

Solution Steps

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

$$sort(\frac{2\times 2}{3}+\frac{5}{6}-\frac{1}{12}\times 3,\frac{5}{6})$$

Multiply 2 and 2 to get 4.

$$sort(\frac{4}{3}+\frac{5}{6}-\frac{1}{12}\times 3,\frac{5}{6})$$

Least common multiple of 3 and 6 is 6. Convert \frac{4}{3} and \frac{5}{6} to fractions with denominator 6.

$$sort(\frac{8}{6}+\frac{5}{6}-\frac{1}{12}\times 3,\frac{5}{6})$$

Since \frac{8}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$sort(\frac{8+5}{6}-\frac{1}{12}\times 3,\frac{5}{6})$$

Add 8 and 5 to get 13.

$$sort(\frac{13}{6}-\frac{1}{12}\times 3,\frac{5}{6})$$

Multiply \frac{1}{12} and 3 to get \frac{3}{12}.

$$sort(\frac{13}{6}-\frac{3}{12},\frac{5}{6})$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$sort(\frac{13}{6}-\frac{1}{4},\frac{5}{6})$$

Least common multiple of 6 and 4 is 12. Convert \frac{13}{6} and \frac{1}{4} to fractions with denominator 12.

$$sort(\frac{26}{12}-\frac{3}{12},\frac{5}{6})$$

Since \frac{26}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{26-3}{12},\frac{5}{6})$$

Subtract 3 from 26 to get 23.

$$sort(\frac{23}{12},\frac{5}{6})$$

Least common denominator of the numbers in the list \frac{23}{12},\frac{5}{6} is 12. Convert numbers in the list to fractions with denominator 12.

$$\frac{23}{12},\frac{10}{12}$$

To sort the list, start from a single element \frac{23}{12}.

$$\frac{23}{12}$$

Insert \frac{10}{12} to the appropriate location in the new list.

$$\frac{10}{12},\frac{23}{12}$$

Replace the obtained fractions with the initial values.

$$\frac{5}{6},\frac{23}{12}$$

Evaluate

$$\frac{23}{12},\frac{5}{6}$$