Theory:

To add the decimal fractions \(33.142\) and \(5.6\). First, we'll equalize the number of digits after the decimal point by attributing to the second decimal value with two zeros on the right: \(5.6 = 5.600\).
 
We write the decimal fractions as mixed numbers:
  
Write the digits after the decimal in fraction with denominator \(10, 100, 1000\), etc., depending on the number of digits after the decimal.
 
33.142=331421000;5.6=56001000.
 
Add mixed numbers and convert the result into decimal:
 
 33.142+5.6=331421000+56001000=38142+6001000=387421000=38.742
 
We can also write the addition in a "column":

33.142+5.600¯38.742
 
Similarly, we can find the difference between numbers \(19.4 - 3.15\):
 
19.43.15=19.403.15=1940100315100=164015100=1625100=16.25
 
We can also write the subtraction "column":

19.403.15¯16.25
To add or subtract decimal fractions, you need to:
1. Equalize the number of decimal places in the fractions;
2. Write them under each other so that the point is written under the point;
3. Perform addition or subtraction, don't pay attention to the point;
4. Place the point under the point in these fractions in the answer.