We can use the following colored counters to model the sum of integers with different signs.
When you add a positive integer (yellow counter) and a negative integer (red counter), the result is 0.
1 + (-1) = 0
One red and one yellow counter form a zero pair.
The value of a zero pair is 0. Adding or subtracting 0 to any number does not change its value.
Example 1 :
Find the sum of -4 and +3.
Solution :
Start with four negative counters to represent -4 and three positive counters to represent +3.
Mark the zero pairs.
In the above figure, if you remove the three zero pairs, the result will be one negative counter.
So, the answer is -1.
Therefore,
(-4) + (+3) = -1
Example 2 :
Find the sum of +5 and -2.
Solution :
Start with five positive counters to represent +5 and two negative counters to represent -2.
Mark the zero pairs.
In the above figure, if you remove two zero pairs, the result will be three positive counters.
So, the answer is +3.
Therefore,
(+5) + (-2) = +3
Example 3 :
Find the sum of +4 and -7.
Solution :
Start with four positive counters to represent +4 and seven negative counters to represent -7.
Mark zero pairs.
In the above figure, if you remove four zero pairs, the result will be three negative counters.
So, the answer is -3.
Therefore,
(+4) + (-7) = -3
Example 4 :
Find the sum of +2 and -3.
Solution :
Start with two positive counters to represent +2 and three negative counters to represent -3.
Mark zero pairs.
In the above figure, if you remove two zero pairs, the result will be one negative counter.
So, the answer is -1.
Therefore,
(+2) + (-3) = -1
Example 5 :
Find the sum of -5 and +2.
Solution :
Start with five negative counters to represent -5 and two positive counters to represent +2.
Mark zero pairs.
In the above figure, if you remove two zero pairs, the result will be three negative counters.
So, the answer is -3.
Therefore,
(-5) + (+2) = -3
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