We will use the annihilation model to give meaning to the addition of directed numbers. To refresh how we use the model, let's look at how some integers are represented. This model is introduced in Meaning and Models. Recall that any number can be represented in many ways.
The operation of addition is modelled by combining the collections of chips.
Example 1: 5 + 3
5 + 3 can be represented as 5 positive chips plus 3 positive chips, which when combined, gives 8 positive chips.
Example 2: (-5) + 3
(-5) + 3 is represented as a collection of 5 negative chips combined with a collection of 3 positive chips. When we put the collection together we can see that 3 positive chips and 3 negative chips will annihilate each other, leaving 2 negative chips.
Example 3: 5 + (-3)
When we add -3 to 5 we can see that 3 positive chips and 3 negative chips annihilate each other, and we are left with 2 positive chips.
example shows how the addition of a negative number is the same as
subtraction of a positive number. We have added 3 negative chips which
is the same as taking away 3 positive chips. We can show this using
the model below:
Example 4: 5 - +3
Example 5: (-5) + (-3)
Basic Addition Facts
We can draw a table of basic addition facts to show the patterns that form when we add positive and negative integers.
down some more patterns that you can see.
When we are adding and subtracting many directed numbers we sometimes put brackets around the negative numbers so that the example is easier to read.
-6 + -7 - -9 + -21 - -4 - 3 + -12 is better written as,
-6 + (-7) - (-9) + (-21) - (-4) - 3 + (-12)
Grouping the number with its negative sign makes it clearer to see what is going on and leaves less chance to make mistakes.
Example 6: movie - using the annihilation model, (-10) + 6
Example 7: movie - using the annihilation model, -14 + 11 + (-6) + (-7) + 5
Example 8: movie - using the number line model, 2 + 3 + (-3) = 2
To view the quiz answers, click here.
'Talking through' questions
The 'talking through' questions and answers below have been provided to enable you to see how an 'expert' might tackle these questions. The annihilation model has been used in the explanations where appropriate.
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