### 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.

$\begin{array}{l}33.142\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}33\frac{142}{1000};\\ \\ 5.6\phantom{\rule{0.147em}{0ex}}=5\frac{600}{1000}.\end{array}$

Add mixed numbers and convert the result into decimal:

$\begin{array}{l}33.142\phantom{\rule{0.147em}{0ex}}+\phantom{\rule{0.147em}{0ex}}5.6\phantom{\rule{0.147em}{0ex}}\\ \\ =\phantom{\rule{0.147em}{0ex}}33\frac{142}{1000}+5\frac{600}{1000}\phantom{\rule{0.147em}{0ex}}\\ \\ =38\frac{142+600}{1000}\\ \\ =38\frac{742}{1000}=38.742\end{array}$

We can also write the addition in a "column":

$\begin{array}{l}\underset{¯}{\begin{array}{l}{}_{+}33.142\\ \phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}5.600\end{array}}\\ \phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}38.742\end{array}$

Similarly, we can find the difference between numbers $$19.4 - 3.15$$:

$\begin{array}{l}19.4\phantom{\rule{0.147em}{0ex}}-\phantom{\rule{0.147em}{0ex}}3.15\phantom{\rule{0.147em}{0ex}}\\ \\ =19.40\phantom{\rule{0.147em}{0ex}}-\phantom{\rule{0.147em}{0ex}}3.15\\ \\ =19\frac{40}{100}-3\frac{15}{100}\\ \\ =16\frac{40-15}{100}\\ \\ =16\frac{25}{100}=16.25\end{array}$

We can also write the subtraction "column":

$\begin{array}{l}\underset{¯}{\begin{array}{l}{}_{-}19.40\\ \phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}3.15\end{array}}\\ \phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}16.25\end{array}$
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.