Solve {l}{(1/2)^2+1:1/2+(1-1/2)-(1+1/2)}{12frac{3}{4}-(2frac{1}{3}+6frac{5}{12})}

$$\left. \begin{array} { l } { ( \frac { 1 } { 2 } ) ^ { 2 } + 1 : \frac { 1 } { 2 } + ( 1 - \frac { 1 } { 2 } ) - ( 1 + \frac { 1 } { 2 } ) } \\ { 12 \frac { 3 } { 4 } - ( 2 \frac { 1 } { 3 } + 6 \frac { 5 } { 12 } ) } \end{array} \right.$$

Sort

$$\frac{5}{4},\ 4$$

Solution Steps

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$sort(\frac{1}{4}+\frac{1}{\frac{1}{2}}+1-\frac{1}{2}-\left(1+\frac{1}{2}\right),\frac{12\times 4+3}{4}-\left(\frac{2\times 3+1}{3}+\frac{6\times 12+5}{12}\right))$$

Divide 1 by \frac{1}{2} by multiplying 1 by the reciprocal of \frac{1}{2}.

$$sort(\frac{1}{4}+1\times 2+1-\frac{1}{2}-\left(1+\frac{1}{2}\right),\frac{12\times 4+3}{4}-\left(\frac{2\times 3+1}{3}+\frac{6\times 12+5}{12}\right))$$

Multiply 1 and 2 to get 2.

$$sort(\frac{1}{4}+2+1-\frac{1}{2}-\left(1+\frac{1}{2}\right),\frac{12\times 4+3}{4}-\left(\frac{2\times 3+1}{3}+\frac{6\times 12+5}{12}\right))$$

Convert 2 to fraction \frac{8}{4}.

$$sort(\frac{1}{4}+\frac{8}{4}+1-\frac{1}{2}-\left(1+\frac{1}{2}\right),\frac{12\times 4+3}{4}-\left(\frac{2\times 3+1}{3}+\frac{6\times 12+5}{12}\right))$$

Since \frac{1}{4} and \frac{8}{4} have the same denominator, add them by adding their numerators.

$$sort(\frac{1+8}{4}+1-\frac{1}{2}-\left(1+\frac{1}{2}\right),\frac{12\times 4+3}{4}-\left(\frac{2\times 3+1}{3}+\frac{6\times 12+5}{12}\right))$$

Add 1 and 8 to get 9.

$$sort(\frac{9}{4}+1-\frac{1}{2}-\left(1+\frac{1}{2}\right),\frac{12\times 4+3}{4}-\left(\frac{2\times 3+1}{3}+\frac{6\times 12+5}{12}\right))$$

Convert 1 to fraction \frac{4}{4}.

$$sort(\frac{9}{4}+\frac{4}{4}-\frac{1}{2}-\left(1+\frac{1}{2}\right),\frac{12\times 4+3}{4}-\left(\frac{2\times 3+1}{3}+\frac{6\times 12+5}{12}\right))$$

Since \frac{9}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

$$sort(\frac{9+4}{4}-\frac{1}{2}-\left(1+\frac{1}{2}\right),\frac{12\times 4+3}{4}-\left(\frac{2\times 3+1}{3}+\frac{6\times 12+5}{12}\right))$$

Add 9 and 4 to get 13.

$$sort(\frac{13}{4}-\frac{1}{2}-\left(1+\frac{1}{2}\right),\frac{12\times 4+3}{4}-\left(\frac{2\times 3+1}{3}+\frac{6\times 12+5}{12}\right))$$

Least common multiple of 4 and 2 is 4. Convert \frac{13}{4} and \frac{1}{2} to fractions with denominator 4.

$$sort(\frac{13}{4}-\frac{2}{4}-\left(1+\frac{1}{2}\right),\frac{12\times 4+3}{4}-\left(\frac{2\times 3+1}{3}+\frac{6\times 12+5}{12}\right))$$

Since \frac{13}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{13-2}{4}-\left(1+\frac{1}{2}\right),\frac{12\times 4+3}{4}-\left(\frac{2\times 3+1}{3}+\frac{6\times 12+5}{12}\right))$$

Subtract 2 from 13 to get 11.

$$sort(\frac{11}{4}-\left(1+\frac{1}{2}\right),\frac{12\times 4+3}{4}-\left(\frac{2\times 3+1}{3}+\frac{6\times 12+5}{12}\right))$$

Convert 1 to fraction \frac{2}{2}.

$$sort(\frac{11}{4}-\left(\frac{2}{2}+\frac{1}{2}\right),\frac{12\times 4+3}{4}-\left(\frac{2\times 3+1}{3}+\frac{6\times 12+5}{12}\right))$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$sort(\frac{11}{4}-\frac{2+1}{2},\frac{12\times 4+3}{4}-\left(\frac{2\times 3+1}{3}+\frac{6\times 12+5}{12}\right))$$

Add 2 and 1 to get 3.

$$sort(\frac{11}{4}-\frac{3}{2},\frac{12\times 4+3}{4}-\left(\frac{2\times 3+1}{3}+\frac{6\times 12+5}{12}\right))$$

Least common multiple of 4 and 2 is 4. Convert \frac{11}{4} and \frac{3}{2} to fractions with denominator 4.

$$sort(\frac{11}{4}-\frac{6}{4},\frac{12\times 4+3}{4}-\left(\frac{2\times 3+1}{3}+\frac{6\times 12+5}{12}\right))$$

Since \frac{11}{4} and \frac{6}{4} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{11-6}{4},\frac{12\times 4+3}{4}-\left(\frac{2\times 3+1}{3}+\frac{6\times 12+5}{12}\right))$$

Subtract 6 from 11 to get 5.

$$sort(\frac{5}{4},\frac{12\times 4+3}{4}-\left(\frac{2\times 3+1}{3}+\frac{6\times 12+5}{12}\right))$$

Multiply 12 and 4 to get 48.

$$sort(\frac{5}{4},\frac{48+3}{4}-\left(\frac{2\times 3+1}{3}+\frac{6\times 12+5}{12}\right))$$

Add 48 and 3 to get 51.

$$sort(\frac{5}{4},\frac{51}{4}-\left(\frac{2\times 3+1}{3}+\frac{6\times 12+5}{12}\right))$$

Multiply 2 and 3 to get 6.

$$sort(\frac{5}{4},\frac{51}{4}-\left(\frac{6+1}{3}+\frac{6\times 12+5}{12}\right))$$

Add 6 and 1 to get 7.

$$sort(\frac{5}{4},\frac{51}{4}-\left(\frac{7}{3}+\frac{6\times 12+5}{12}\right))$$

Multiply 6 and 12 to get 72.

$$sort(\frac{5}{4},\frac{51}{4}-\left(\frac{7}{3}+\frac{72+5}{12}\right))$$

Add 72 and 5 to get 77.

$$sort(\frac{5}{4},\frac{51}{4}-\left(\frac{7}{3}+\frac{77}{12}\right))$$

Least common multiple of 3 and 12 is 12. Convert \frac{7}{3} and \frac{77}{12} to fractions with denominator 12.

$$sort(\frac{5}{4},\frac{51}{4}-\left(\frac{28}{12}+\frac{77}{12}\right))$$

Since \frac{28}{12} and \frac{77}{12} have the same denominator, add them by adding their numerators.

$$sort(\frac{5}{4},\frac{51}{4}-\frac{28+77}{12})$$

Add 28 and 77 to get 105.

$$sort(\frac{5}{4},\frac{51}{4}-\frac{105}{12})$$

Reduce the fraction \frac{105}{12} to lowest terms by extracting and canceling out 3.

$$sort(\frac{5}{4},\frac{51}{4}-\frac{35}{4})$$

Since \frac{51}{4} and \frac{35}{4} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{5}{4},\frac{51-35}{4})$$

Subtract 35 from 51 to get 16.

$$sort(\frac{5}{4},\frac{16}{4})$$

Divide 16 by 4 to get 4.

$$sort(\frac{5}{4},4)$$

Convert decimal numbers in the list \frac{5}{4},4 to fractions.

$$\frac{5}{4},4$$

Evaluate

$$\frac{5}{4},\ 4$$