Long Beach Unified School District Properties Becky Afghani Long Beach Unified School District rafghani@lbusd.k12.ca.us 2006 Reflexive Property

Properties Menu Reflexive Property Additive Identity Symmetric Property Multiplicative Identity Transitive Property Add’n Property of Equality Commutative Property (+) Sub’n Property of Equality Commutative Property (x) Mult’n Property of Equality Associative Property (+) Div’n Property of Equality Associative Property (x) Inverse Property of Add’n Distributive Property Inverse Property of Mult’n

Any quantity is equal to itself. Reflexive Property Any quantity is equal to itself.

“Reflexive” is like a “reflection” in a mirror. Reflexive Property “Reflexive” is like a “reflection” in a mirror.

“Reflexive” is like a “reflection” in a mirror. Reflexive Property x = x “Reflexive” is like a “reflection” in a mirror.

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Symmetric Property You can flip an equation around the equal sign. All the contents from each side can be moved to the opposite side.

Symmetric Property a b An equation is like a balance. You can exchange what’s in the two pans.

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Transitive Property If a first quantity is equal to a second quantity, and the second quantity is equal to a third quantity, then the first quantity is equal to the third quantity.

If Spongebob is the same height as Mr. Crabs, Transitive Property = If Spongebob is the same height as Mr. Crabs,

And Mr. Crabs is the same height as Squidward, Transitive Property = And Mr. Crabs is the same height as Squidward,

Then Spongebob is the same height as Squidward. Transitive Property = Then Spongebob is the same height as Squidward.

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Commutative Property of Addition When you are adding, you can change the order of the numbers.

Commutative Property of Addition Think of “commuting” from home to school…

Commutative Property of Addition It’s the same drive from school to home.

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Commutative Property of Multiplication When you are multiplying, you can change the order of the numbers.

Commutative Property of Multiplication The commutative property applies to both ADDING and MULTIPLYING.

Commutative Property of Multiplication Does the commutative property apply to subtracting or dividing? 4 - 2 = 2 2 - 4 = -2

Commutative Property of Multiplication Does the commutative property apply to subtracting or dividing? 2  1 = 2 1  2 = 2 1

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Associative Property of Addition When you are adding, you can change the grouping of the numbers.

Associative Property of Addition + + = You are just regrouping the numbers so “friends” can be together.

Associative Property of Addition + + = Remember: friends associate in groups.

Associative Property of Addition Often, regrouping can make the math easier. not easy

Associative Property of Addition Often, regrouping can make the math easier. much easier

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Associative Property of Multiplication When you are multiplying, you can change the grouping of the numbers.

Associative Property of Multiplication The associative property applies to both ADDING and MULTIPLYING.

Associative Property of Multiplication Does the associative property apply to subtracting or dividing? (20 – 15) - 5 = 0 20 – (15 – 5) = 10

Associative Property of Multiplication Does the associative property apply to subtracting or dividing? (32  8)  2 = 2 32  (8  2) = 8

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Distributive Property and A term that multiplies the parenthesis multiplies every term within the parenthesis.

Distributive Property and + 5 5 = + Think of a teacher distributing something to every student in the class.

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Additive Identity Property When you add zero to a term, you get the same term.

Additive Identity Property It’s still me! x x + 0 = An identity is something that won’t change the identity of the number.

Additive Identity Property It’s still me! x x + 0 = The additive identity is zero, because that’s the only number you can add without changing the identity of the number.

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Multiplicative Identity Property When you multiply a term by one, you get the same term.

Multiplicative Identity Property It’s still me! x x • 1 = An identity is something that won’t change the identity of the number.

Multiplicative Identity Property It’s still me! x x • 1 = The multiplicative identity is one, because that’s the only number you can multiply without changing the identity of the number.

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Addition Property of Equality If you add something to one side of an equation, you must add the same thing to the other side of the equation.

Addition Property of Equality c a b If you add something to one side of an equation, you must add the same thing to the other side of the equation.

Addition Property of Equality c a c b If you add something to one side of an equation, you must add the same thing to the other side of the equation.

Addition Property of Equality b c If you add something to one side of an equation, you must add the same thing to the other side of the equation. a c

Addition Property of Equality What you add to one side… You add to the other a c b c

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Subtraction Property of Equality If you subtract something from one side of an equation, you must subtract the same thing from the other side of the equation.

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Multiplication Property of Equality If you multiply one side of an equation by something, you must multiply the other side of the equation by the same thing.

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Division Property of Equality If you divide one side of an equation by something, you must divide the other side of the equation by the same thing.

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Inverse Property Of Addition The sum of a number and its opposite is zero.

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Inverse Property Of Multiplication The product of a number and its inverse is one. (x ≠ 0)

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