# Lesson 7

 Additive Axiom f equals are added to equals, then the sums are equal according to the additive axiom.If a = b and c = d, then a + c = b + dIf a = 3 and a = b, then b = 3. If c = 5 and c = d, then d = 5. Therefore,if a = b, that means 3 = 3 and if c = d, that means 5 = 5, soa + c = b + d in this case is 3 + 5 = 3 + 5 Multiplicative Axiom The multiplicative axiom states that if a = b and c = d, then ac = bd. In other words, if equals are multiplied by equals, the answer should be equal. If a = b and c = d, then ac = bdLet's look at an example.If a = 6 and a = b, then b = 6. And if c = 8 and c = d, then d = 8.Therefore, we can say a = 6 and c = 8, so ac = (6)(8) or 6c = (6)(8). Commutative property he commutative property tells us that the order in which two numbers are added does not affect their sum. a + b = b + aWe can add 3 + 2 to get 5 or we can add 2 + 3 and get 5. The commutative property also works with multiplication.ab = baWe can multiply 3 x 15 and get 45 or we can multiply 15 x 3 and get 45. Associative property he associative property extends this by saying that the grouping of numbers under addition does not affect their sum.(a + b) + c = a + (b + c)For example, (8 + 2) + 5 = 8 + (2 + 5)Which gives 10 + 5 = 8 + 7 (both of which equal 15)If we have a string of numbers such as 4 + 6 + 3 + 4 + 2 + 1, we could add them in order: 4 + 6 = 10 + 3 = 13 + 4 = 17 + 2 = 19 + 1 = 20.Or we could quickly see that 4 + 6 is 10 and 3 + 2 is 5 and 4 + 1 is 5 and then add 10 + 5 + 5 to get 20. Distributive property he distributive property of multiplication over addition tells us that the product of a number and the sum of two numbers is the same as the sum of the products of the first number and each of the others.a(b + c) = ab +acFor example, 5(3 + 8) = 5(3) + 5(8)In other words, 5(11) = 15 + 40Which is 55 = 55This shows us that we can distribute the multiplier that is outside the parenthesis to each of the numbers inside the parenthesis. Authortaloggains ID116312 Card SetLesson 7 DescriptionOperations and Properties Updated2011-11-12T22:03:46Z Show Answers