Algebra is the first exposure to abstract thinking in mathematics. It serves as the foundation for so many other math courses students will face in their journey through the world of abstractions. The word "Algebra" comes from the Arabic language which when translated means "reunion of broken parts". My first course in algebra was in ninth grade and the one thing that helped me most was looking at all the little charts that the teacher had set up on the top of the walls of the classroom. The 9 most influential rules were as follow:
Commutative Property of Addition: a + b = b + a Commutative Property of Multiplication: a * b = b * a (Order doesn't matter)
Associative Property of Addition a+(b+c) = (a+b)+c Associative Property of Multiplication: a(bc) = (ab)c (Grouping doesn't matter)
Distributive Property: a( b + c ) = ab + ac ( pass the number outside parentheses onto the two numbers inside the parentheses)
Identity Property of Addition: 0 Is the identity a + 0 = a Identity Property of Multiplication: 1 Is the identity a * 1 = a
Both identity properties I like to think of them as the do nothing properties. Apply the identity You always return to the original number
Inverse Property of Addition a + (-a) = 0 Inverse Property of Multiplication a * 1/a = 1
Inverse properties return you back the identity. This happens for both addition and the multiplication properties.
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