Addition properties serve to facilitate calculations. In the set of natural numbers, there are four: associative, commutative, neutral element and closure. In the set of whole numbers, there is also the property of the inverse element.
The addition operation is the first one we learn, even before school. Joining, joining and adding are actions that we perform by adding.
associative property
Used in sums with more than two installments.
We can associate the parcels in order to facilitate the calculation, that is, add the parcels in an order that makes the operation easier.
Example
75 + 50 + 13 + 25 = 163
Another order could be:
75 + 25 = 100 (completing whole hundreds or tens can make the calculation easier)
Then add the 50.
100 + 50 = 150
Finally, add the 13.
150 + 13 = 163
It is common to use parentheses to prioritize the order in which we will add.
27 + 75 + 25 + 33 = 160
We can associate the parcels as it suits us and use parentheses to indicate the order in which we are adding.
(75 + 25) + (33 + 27) = 160
100 + 60 = 160
Commutative Property
The order of the parcels does not change the result.
3 + 2 = 5
It's the same as adding:
2 + 3 = 5
Neutral Element Property
In addition, the neutral element is zero. Every number added to zero results in the number itself.
Example:
273 + 0 = 273
Adding zero does not change the result.
Closure property
Two or more natural numbers added together result in a natural number.
The natural numbers are the positives counting with zero (0, 1, 2, 3, 4, …), advancing from unit to unit.
Examples:
17 + 25 = 42
3 + 6 = 9
154 + 26 = 180
Learn it natural numbers.
Opposite element property
The opposite of a positive number is its negative. The opposite of any number b is -b. So, to know the opposite of a number, just put the minus (minus) sign to its left.
A number added to its opposite always results in zero.
Examples:
-3 + 3 = 0
8 + (-8) = 8 - 8 = 0
87 + (-87) = 87 - 87 = 0
This property includes the set of integer numbers, which includes negative and positive ones (-4, -3, -2, -1, 0, 1, 2, 3, 4, ...).
learn about whole numbers.
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