Solve {l}{(16,3-13-1/9)*1/11+2,2(3/33-1/11)+3frac{2}{11}}{(1frac{1}{7}-frac{23}{49}):frac{22}{147}-(0,6:3frac{3}{4})*2frac{1}{2}}

$$\left. \begin{array} { l } { ( 16,3 - 13 - \frac { 1 } { 9 } ) \cdot \frac { 1 } { 11 } + 2,2 ( \frac { 3 } { 33 } - \frac { 1 } { 11 } ) + 3 \frac { 2 } { 11 } } \\ { ( 1 \frac { 1 } { 7 } - \frac { 23 } { 49 } ) : \frac { 22 } { 147 } - ( 0,6 : 3 \frac { 3 } { 4 } ) \cdot 2 \frac { 1 } { 2 } } \end{array} \right.$$

Sort

$$\frac{3437}{990},\ 4,1$$

Solution Steps

Subtract 13 from 16,3 to get 3,3.

$$sort(\left(3,3-\frac{1}{9}\right)\times \frac{1}{11}+2,2\left(\frac{3}{33}-\frac{1}{11}\right)+\frac{3\times 11+2}{11};\frac{\frac{1\times 7+1}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2})$$

Convert decimal number 3,3 to fraction \frac{33}{10}.

$$sort(\left(\frac{33}{10}-\frac{1}{9}\right)\times \frac{1}{11}+2,2\left(\frac{3}{33}-\frac{1}{11}\right)+\frac{3\times 11+2}{11};\frac{\frac{1\times 7+1}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2})$$

Least common multiple of 10 and 9 is 90. Convert \frac{33}{10} and \frac{1}{9} to fractions with denominator 90.

$$sort(\left(\frac{297}{90}-\frac{10}{90}\right)\times \frac{1}{11}+2,2\left(\frac{3}{33}-\frac{1}{11}\right)+\frac{3\times 11+2}{11};\frac{\frac{1\times 7+1}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2})$$

Since \frac{297}{90} and \frac{10}{90} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{297-10}{90}\times \frac{1}{11}+2,2\left(\frac{3}{33}-\frac{1}{11}\right)+\frac{3\times 11+2}{11};\frac{\frac{1\times 7+1}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2})$$

Subtract 10 from 297 to get 287.

$$sort(\frac{287}{90}\times \frac{1}{11}+2,2\left(\frac{3}{33}-\frac{1}{11}\right)+\frac{3\times 11+2}{11};\frac{\frac{1\times 7+1}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2})$$

Multiply \frac{287}{90} times \frac{1}{11} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{287\times 1}{90\times 11}+2,2\left(\frac{3}{33}-\frac{1}{11}\right)+\frac{3\times 11+2}{11};\frac{\frac{1\times 7+1}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2})$$

Do the multiplications in the fraction \frac{287\times 1}{90\times 11}.

$$sort(\frac{287}{990}+2,2\left(\frac{3}{33}-\frac{1}{11}\right)+\frac{3\times 11+2}{11};\frac{\frac{1\times 7+1}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2})$$

Reduce the fraction \frac{3}{33} to lowest terms by extracting and canceling out 3.

$$sort(\frac{287}{990}+2,2\left(\frac{1}{11}-\frac{1}{11}\right)+\frac{3\times 11+2}{11};\frac{\frac{1\times 7+1}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2})$$

Subtract \frac{1}{11} from \frac{1}{11} to get 0.

$$sort(\frac{287}{990}+2,2\times 0+\frac{3\times 11+2}{11};\frac{\frac{1\times 7+1}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2})$$

Multiply 2,2 and 0 to get 0.

$$sort(\frac{287}{990}+0+\frac{3\times 11+2}{11};\frac{\frac{1\times 7+1}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2})$$

Add \frac{287}{990} and 0 to get \frac{287}{990}.

$$sort(\frac{287}{990}+\frac{3\times 11+2}{11};\frac{\frac{1\times 7+1}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2})$$

Multiply 3 and 11 to get 33.

$$sort(\frac{287}{990}+\frac{33+2}{11};\frac{\frac{1\times 7+1}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2})$$

Add 33 and 2 to get 35.

$$sort(\frac{287}{990}+\frac{35}{11};\frac{\frac{1\times 7+1}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2})$$

Least common multiple of 990 and 11 is 990. Convert \frac{287}{990} and \frac{35}{11} to fractions with denominator 990.

$$sort(\frac{287}{990}+\frac{3150}{990};\frac{\frac{1\times 7+1}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2})$$

Since \frac{287}{990} and \frac{3150}{990} have the same denominator, add them by adding their numerators.

$$sort(\frac{287+3150}{990};\frac{\frac{1\times 7+1}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2})$$

Add 287 and 3150 to get 3437.

$$sort(\frac{3437}{990};\frac{\frac{1\times 7+1}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2})$$

Multiply 1 and 7 to get 7.

$$sort(\frac{3437}{990};\frac{\frac{7+1}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2})$$

Add 7 and 1 to get 8.

$$sort(\frac{3437}{990};\frac{\frac{8}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2})$$

Least common multiple of 7 and 49 is 49. Convert \frac{8}{7} and \frac{23}{49} to fractions with denominator 49.

$$sort(\frac{3437}{990};\frac{\frac{56}{49}-\frac{23}{49}}{\frac{22}{147}}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2})$$

Since \frac{56}{49} and \frac{23}{49} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{3437}{990};\frac{\frac{56-23}{49}}{\frac{22}{147}}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2})$$

Subtract 23 from 56 to get 33.

$$sort(\frac{3437}{990};\frac{\frac{33}{49}}{\frac{22}{147}}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2})$$

Divide \frac{33}{49} by \frac{22}{147} by multiplying \frac{33}{49} by the reciprocal of \frac{22}{147}.

$$sort(\frac{3437}{990};\frac{33}{49}\times \frac{147}{22}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2})$$

Multiply \frac{33}{49} times \frac{147}{22} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{3437}{990};\frac{33\times 147}{49\times 22}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2})$$

Do the multiplications in the fraction \frac{33\times 147}{49\times 22}.

$$sort(\frac{3437}{990};\frac{4851}{1078}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2})$$

Reduce the fraction \frac{4851}{1078} to lowest terms by extracting and canceling out 539.

$$sort(\frac{3437}{990};\frac{9}{2}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2})$$

Divide 0,6 by \frac{3\times 4+3}{4} by multiplying 0,6 by the reciprocal of \frac{3\times 4+3}{4}.

$$sort(\frac{3437}{990};\frac{9}{2}-\frac{0,6\times 4}{3\times 4+3}\times \frac{2\times 2+1}{2})$$

Multiply 0,6 and 4 to get 2,4.

$$sort(\frac{3437}{990};\frac{9}{2}-\frac{2,4}{3\times 4+3}\times \frac{2\times 2+1}{2})$$

Multiply 3 and 4 to get 12.

$$sort(\frac{3437}{990};\frac{9}{2}-\frac{2,4}{12+3}\times \frac{2\times 2+1}{2})$$

Add 12 and 3 to get 15.

$$sort(\frac{3437}{990};\frac{9}{2}-\frac{2,4}{15}\times \frac{2\times 2+1}{2})$$

Expand \frac{2,4}{15} by multiplying both numerator and the denominator by 10.

$$sort(\frac{3437}{990};\frac{9}{2}-\frac{24}{150}\times \frac{2\times 2+1}{2})$$

Reduce the fraction \frac{24}{150} to lowest terms by extracting and canceling out 6.

$$sort(\frac{3437}{990};\frac{9}{2}-\frac{4}{25}\times \frac{2\times 2+1}{2})$$

Multiply 2 and 2 to get 4.

$$sort(\frac{3437}{990};\frac{9}{2}-\frac{4}{25}\times \frac{4+1}{2})$$

Add 4 and 1 to get 5.

$$sort(\frac{3437}{990};\frac{9}{2}-\frac{4}{25}\times \frac{5}{2})$$

Multiply \frac{4}{25} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{3437}{990};\frac{9}{2}-\frac{4\times 5}{25\times 2})$$

Do the multiplications in the fraction \frac{4\times 5}{25\times 2}.

$$sort(\frac{3437}{990};\frac{9}{2}-\frac{20}{50})$$

Reduce the fraction \frac{20}{50} to lowest terms by extracting and canceling out 10.

$$sort(\frac{3437}{990};\frac{9}{2}-\frac{2}{5})$$

Least common multiple of 2 and 5 is 10. Convert \frac{9}{2} and \frac{2}{5} to fractions with denominator 10.

$$sort(\frac{3437}{990};\frac{45}{10}-\frac{4}{10})$$

Since \frac{45}{10} and \frac{4}{10} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{3437}{990};\frac{45-4}{10})$$

Subtract 4 from 45 to get 41.

$$sort(\frac{3437}{990};\frac{41}{10})$$

Least common denominator of the numbers in the list \frac{3437}{990};\frac{41}{10} is 990. Convert numbers in the list to fractions with denominator 990.

$$\frac{3437}{990};\frac{4059}{990}$$

Evaluate

$$\frac{3437}{990},\ 4,1$$