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

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!

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!

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!

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.

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.

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

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