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1 1-8 Properties of Real Numbers Algebra I By PresenterMedia.comPresenterMedia.com

2 ADDITION This basically says that you can add numbers in any order and you’ll get the same thing each time. A + B = B + A = This basically says that you can multiply numbers in any order and you’ll get the same thing each time. A times B = B times A 4 times 3 = 3 times 4 MULTIPLICATION 1. Commutative Property Commute means to go back and forth…numbers move!

3 ADDITION This basically means that you can group together any of your friends and you’ll get the same answer. (A + B) + C = A + (B + C) (3 + 2) + 4 = 3 + (2 + 4) This means the same thing…you can group together any of your friends and you’ll get the same answer. (A * B) * C = A *( B * C) (4 * 3) * 5 = 4 * (3 * 5) MULTIPLICATION 2. Associative Property Parentheses move…not the numbers!

4 ADDITION This basically means that when you add zero to anything, that number doesn’t change…you are the same person looking into a mirror. A + 0 = A = 3 This basically means that when you multiply one by anything, that number doesn’t change…you are the same person looking into a mirror. A times 1 = A 4 times 1 = 4 MULTIPLICATION 3. Identity Property You better be you when you look in a mirror!

5 ADDITION This basically means you can add the opposite to a number and get zero. A + -A = = 0 This basically means you can multiply a number by its reciprocal and get one. A times (1/A) = 1 2 times (1/2) = 1 MULTIPLICATION 4. Inverse Property For every number, there is an opposite number.

6 Distributive property means that when you have something outside of parentheses, you must multiply everything in that parentheses by what’s outside of it. A(B + C) = AB + AC -2(3m – 6) = -6m Distributive Property You have already discussed this one in earlier math classes.

7 MULTIPLICATION PROPERTY OF ZERO This basically means that when you multiply a number by zero, you get zero. A times 0 = 0 3 times 0 = 0 This basically means that when you multiply a number by -1, you get the opposite of that number. A times -1 = -A 2 times -1 = -2 MULTIPLICATION PROPERTY OF Multiplication Property

8 Let’s look at some examples… Name the property that each equation illustrates. 1m = m identity property of multiplication (-3+4) +5 = -3+(4+5) associative property of addition 3(8 times 0) = (3 times 8)0 associative property of multiplication 2+0 = 2 identity property of addition np = pn commutative property of multiplication


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