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If 'a', 'b' and 'c' are any three numbers, then the properties of addition are:
* Associative: the value of a + (b + c) is the same as (a + b) + c;
* Additive identity: there exists zero (0) such that a + 0 = a;
* Additive inverse: for every number a there is an additive inverse, denoted by (-a), such that a + (-a) = (-a) + a = 0;
* Commutative: the value of a + b is the same as b + a;
* Closed: the value of a + b is another number in the original set of a and b, for example, if aand b are both integers, then a + b will also be an integer.
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How can addition properties help you add whole numbers?
Because addition properties allow you to add them in the first place and without them, you couldn't add!
What are properties of addition?
There are two properties of addition. The COMMUTATIVE property states that the order in which the addition is carried out does not matter. In symbolic terms, a + b = b + a The ASSOCIATIVE property states that the order in which the operation is carried out does not matter. Symbolically, (a + b) + c = a + (b + c) and so, without ambiguity, either can be written as a + b + c. That is IT. No more! The DISTRIBUTIVE property is a property of multiplication over addition (OR subtraction), not a property of addition. The existence of of an IDENTITY and an ADDITIVE INVERSE are properties of the set over which addition is defined; again not a property of addition. For example, you can define addition on all positive integers which will have the commutative and associative properties but the identity (zero) and additive inverses (negative numbers) are undefined as far as the set is concerned.
Explain how to use the associative properties of addition and multiplication to find sums mentally?
use mental math
What is the typical effect of the addition of an interstitial element on the properties of a metal?
Increase in hardness and strength, decrease in ductility.
What are commutative and associative properties of addition?
Commutative Law: a + b = b + a Associative Law: (a + b) + c = a + (b + c)
