Subtraction of rational numbers — lesson. Mathematics CBSE, Class 7.

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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

$6$

$\begin{array}{l} \frac{2}{3} - \frac{3}{2} \\ = \frac{(2 \times 2) - (3 \times 3)}{6} \\ = \frac{4 + 9}{6} \\ = \frac{13}{6} \end{array}$

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:

$3 - (- 10) = 3 + 10 = 13$

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

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

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4. Subtraction of rational numbers

Theory: