1-8 Properties of Real NumbersAlgebra I

By PresenterMedia.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

• 3 + 2 = 2 + 3

• 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 PropertyCommute 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 PropertyParentheses 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 + 0 = 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 PropertyYou 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

• 3 + -3 = 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 PropertyFor 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 + 12

•5. Distributive PropertyYou 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 -1

•6. 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