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1.2 – The Commutative & Identity Properties Commutative Properties Addition For any numbers a and b, a b b a . (We can change the order when adding without affecting the sum.) Multiplication For and numbers a and b, ab ba . (We can change the order when multiplying without affecting the product.) Expressions such as 2 x and x 2 , which always result in the same number when we substitute any value for their variables, are called equivalent expressions. Identity Properties Addition For any number a, a 0 a and 0 a a . (Adding 0 to any number gives that number.) Multiplication For any number a, 1 a a and a 1 a . (Multiplying a number by 1 gives that number.) Dividing a Number by Itself For any number a, a 0 , a 1. a Example 1 – Write an equivalent expression for Use 3 for 1. 3 6 by multiplying by 1. 7 Example 2 – Write an equivalent expression for Use a for 1. a x by multiplying by 1. 2 When two or more numbers are multiplied to form a product, each number is called a factor of the product. For example, 3 5 15 , so 3 and 5 are factors of 15. When the only common factor of the numerator and the denominator of a fraction is 1, the fraction is in simplest form. The process of finding the simplest form is called simplifying. Example 3 – Simplify. a. 21 14 b. L2 – pg 14 (11-29 odd) 40 60 c. 4ab 8a d. y 3 xy