### Theory:

We can perform subtraction of rational numbers like the addition. All we have to keep in mind is the sign conversion.
Example:
Subtract $\frac{2}{3}$ and $\frac{3}{2}$

As the denominator is not the same, we have to take LCM.

Here LCM is 6.

$\begin{array}{l}\frac{2}{3}-\frac{3}{2}\\ =\frac{\left(2×2\right)-\left(3×3\right)}{6}\\ =\frac{4-9}{6}\\ =\frac{-5}{6}\end{array}$
Let us recollect subtraction rules
We can add a negative number like

$$- 2 + (- 6) = - 8$$

$$10 + (- 6) = 4$$

But how to subtract a negative number? What is $$2 - (- 6)$$?

Let's explore what a deprivation action means.

Subtracting the second number($$b$$) from the first number($$a$$) means finding the difference ($$a$$ number $$x$$).

$$a - b = x$$

The result obtained can always be verified by addition: $$x + b = a$$

Let's follow an example $$6 - (-4) = x$$ (Let's deal with $$x$$ because we don't know how to subtract yet).

Write the test expression $$x + (-4) = 6.$$

Let's find the value of $$x$$. How much $$(- 4)$$ should be added to get a positive $$6$$?

We can guess that $$x = 10$$ because $$10 + (- 4) = 6.$$

So the unknown $$x$$ is $$10.$$

$$6 - (- 4) = 10$$.

It turns out that  ($-$) ($-$) $$= +$$

Since we know that $$6 + 4 = 10$$, we can conclude that subtract $$6$$ from $$(- 4)$$ means add $$6$$ to $$4$$.
Subtracting $$b$$ from the number $$a$$ means adding the opposite number of $$b$$ to $$a$$.
Remember, $$-4$$ is the opposite of $$4$$.

There is no need to use $$x$$ or any other sophisticated modifications to solve the examples, remember that $-$$$($$$-$$$) = +$$
Example:
i) $$2 - (- 6)$$ = 2 + 6 = 8\).

ii) $$- 12 - ( - 3) = - 12 + 3 = - 9$$.

iii) $$0.4 - ( - 0.6) = 0.4 + 0.6 = 1$$.