Answer
a.) ab = ba; Commutative Property
b.) a+(b+c) = c+(a+b); Associative Property
c.) a(b+c) = ab+ac; Distributive Property
Work Step by Step
a.) As the Commutative Property states, the order in which two numbers are added (or multiplied) does not matter. So the multiplication of ab is the same as ba
Ex.) 3x5=5x3 (which both ends come out to be 15)
b.)The Associative Property states when adding multiple numbers, it doesn't matter which two are added first.
Therefore, a+(b+c) = c+(a+b)
Ex.) 1+(5+7) = 5+(7+1) = 7+(1+5) [They all equal 13]
c.) The Distributive Property states When we multiply a number by a sum of two numbers, we get the same result as we get if we multiply the number by each of the terms and then add the results. Therefore a(b+c) = ab+ac
Ex.) 2(8+3) = 2x8+2x3 (They both come out to be 22)
