There are two properties of addition which apply here. They are the commutative and associative properties.
Commutative property: When two numbers are added, the sum is the same regardless of the order of the addends. For example 4 + 2 = 2 + 4
Associative Property: When three or more numbers are added, the sum is the same regardless of the grouping of the addends. For example (2 + 3) + 4 = 2 + (3 + 4)
Commutative property: When two numbers are added, the sum is the same regardless of the order of the addends. For example 4 + 2 = 2 + 4
Associative Property: When three or more numbers are added, the sum is the same regardless of the grouping of the addends. For example (2 + 3) + 4 = 2 + (3 + 4)
There is subtraction property which applies here, namely the subtraction of whole numbers is not commutative, that is, if a and b are two whole numbers, then in general a – b is not equal to (b – a).
Given those properties, we can simplify the expression
23 + (-49) + 12 + (-23) + (-4) + (-8) + 49 + (-33)
first, we group like terms, which gives us
23 +12 +49 + (-49) + (-23) + (-4) + (-8) + (-33)
we can then add the like terms, which gives us
84 + (-117) = -33
Grouping the terms is not required, but it makes the solution easier to understand.
