Lesson 7

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Author:
taloggains
ID:
116312
Filename:
Lesson 7
Updated:
2011-11-12 17:03:46
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Operations Properties
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Description:
Operations and Properties
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  1. 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 + d
    • If 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, so
    • a + c = b + d in this case is 3 + 5 = 3 + 5
  2. 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 = bd
    • Let'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).
  3. Commutative property
    • he commutative property tells us that the order in which two numbers are added does not affect their sum.
    • a + b = b + a
    • We can add 3 + 2 to get 5 or we can add 2 + 3 and get 5.
    • The commutative property also works with multiplication.
    • ab = ba
    • We can multiply 3 x 15 and get 45 or we can multiply 15 x 3 and get 45.
  4. 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.
  5. 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 +ac
    • For example, 5(3 + 8) = 5(3) + 5(8)
    • In other words, 5(11) = 15 + 40
    • Which is 55 = 55
    • This
    • shows us that we can distribute the multiplier that is outside the
    • parenthesis to each of the numbers inside the parenthesis.

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