Subtraction of Rational numbers — lesson. Mathematics State Board, Class 8.

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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).

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

Did you find an error?

2. Subtraction of Rational numbers