Solve 19/1014/10-13/10,11/10

$$1 \frac { 9 } { 10 } 1 \frac { 4 } { 10 } - 1 \frac { 3 } { 10 } , 1 \frac { 1 } { 10 }$$

Sort

$$\frac{11}{10},\frac{34}{25}$$

Solution Steps

Multiply 1 and 10 to get 10.

$$sort(\frac{10+9}{10}\times \frac{1\times 10+4}{10}-\frac{1\times 10+3}{10},\frac{1\times 10+1}{10})$$

Add 10 and 9 to get 19.

$$sort(\frac{19}{10}\times \frac{1\times 10+4}{10}-\frac{1\times 10+3}{10},\frac{1\times 10+1}{10})$$

Multiply 1 and 10 to get 10.

$$sort(\frac{19}{10}\times \frac{10+4}{10}-\frac{1\times 10+3}{10},\frac{1\times 10+1}{10})$$

Add 10 and 4 to get 14.

$$sort(\frac{19}{10}\times \frac{14}{10}-\frac{1\times 10+3}{10},\frac{1\times 10+1}{10})$$

Reduce the fraction \frac{14}{10} to lowest terms by extracting and canceling out 2.

$$sort(\frac{19}{10}\times \frac{7}{5}-\frac{1\times 10+3}{10},\frac{1\times 10+1}{10})$$

Multiply \frac{19}{10} times \frac{7}{5} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{19\times 7}{10\times 5}-\frac{1\times 10+3}{10},\frac{1\times 10+1}{10})$$

Do the multiplications in the fraction \frac{19\times 7}{10\times 5}.

$$sort(\frac{133}{50}-\frac{1\times 10+3}{10},\frac{1\times 10+1}{10})$$

Multiply 1 and 10 to get 10.

$$sort(\frac{133}{50}-\frac{10+3}{10},\frac{1\times 10+1}{10})$$

Add 10 and 3 to get 13.

$$sort(\frac{133}{50}-\frac{13}{10},\frac{1\times 10+1}{10})$$

Least common multiple of 50 and 10 is 50. Convert \frac{133}{50} and \frac{13}{10} to fractions with denominator 50.

$$sort(\frac{133}{50}-\frac{65}{50},\frac{1\times 10+1}{10})$$

Since \frac{133}{50} and \frac{65}{50} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{133-65}{50},\frac{1\times 10+1}{10})$$

Subtract 65 from 133 to get 68.

$$sort(\frac{68}{50},\frac{1\times 10+1}{10})$$

Reduce the fraction \frac{68}{50} to lowest terms by extracting and canceling out 2.

$$sort(\frac{34}{25},\frac{1\times 10+1}{10})$$

Multiply 1 and 10 to get 10.

$$sort(\frac{34}{25},\frac{10+1}{10})$$

Add 10 and 1 to get 11.

$$sort(\frac{34}{25},\frac{11}{10})$$

Least common denominator of the numbers in the list \frac{34}{25},\frac{11}{10} is 50. Convert numbers in the list to fractions with denominator 50.

$$\frac{68}{50},\frac{55}{50}$$

To sort the list, start from a single element \frac{68}{50}.

$$\frac{68}{50}$$

Insert \frac{55}{50} to the appropriate location in the new list.

$$\frac{55}{50},\frac{68}{50}$$

Replace the obtained fractions with the initial values.

$$\frac{11}{10},\frac{34}{25}$$

Evaluate

$$\frac{34}{25},\frac{11}{10}$$