### 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.

**$\begin{array}{l}\frac{2}{3}-\frac{3}{2}\\ =\frac{(2\times 2)-(3\times 3)}{6}\\ =\frac{4-9}{6}\\ =\frac{-5}{6}\end{array}$**

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).

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 \(a\).

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)**\(0.4 - ( - 0.6) = 0.4 + 0.6 = 1\).