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).
