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Year 8 Interactive Maths - Second Edition


Addition and Subtraction of Integers

Addition of Positive Integers

Consider the addition of 2 + 3.

The plus sign, +, tells us to face the positive direction.
So, to evaluate 2 + 3, start at 2, face the positive direction and move 3 units forwards.


This suggests that:

Positive integers can be added like natural numbers.


Addition of Negative Integers

Consider the addition of (2) + (3).

The plus sign, +, tells us to face the positive direction.
So, to evaluate (2) + (3), start at 2, face the positive direction and move 3 units backwards.


Note: 

We can write (2) + (3) as 2 + 3


Subtracting a Positive Integer from a Negative Integer

Consider the value of (2) (3).

The minus sign, , tells us to face the negative direction.
So, to evaluate (2) (3), start at 2, face the negative direction and move 3 units forwards.

We notice that:

That is:


This suggests that:

Adding a negative integer is the same as subtracting a positive integer.


From the above discussion, we can state that:

Negative integer are added like natural numbers; but place a minus sign, , in front of the sum.


Example 7

Find the value of:

Solution:


Addition of a Positive Integer and a Negative Integer

Consider the addition of 3 + (7).

The plus sign, +, tells us to face the positive direction.
So, to evaluate 3 + (7), start at 3, face the positive direction and move 7 units backwards.


Note:

3 + (7) is often written as 3 7.

To find the value of 3 7, first ignore the signs and subtract the smaller number, 3, from the larger number, 7, and put the sign, , of the larger number, 7, in front of the difference.  That is:


Example 8

Find the value of:

Solution:


Subtracting a Negative Integer from a Positive Integer

Consider the subtraction of 2 (3).

The minus sign, , tells us to face the negative direction.
So, to evaluate 2 (3), start at 2, face the negative direction and move 3 units backwards.


This suggests that:

To take away a negative integer, add its opposite which is a positive integer.


Example 9

Find the value of:

Solution:


Note:

If two minus signs are side by side, then the two minus signs become a plus sign (i.e. a positive).


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