2Do you remember these Properties of Addition? Commutative Property of AdditionThe numbers move arounda + b = b + aAssociative Property of AdditionGrouping with parentheses(a + b) + c = a + (b + c)Identity Property of AdditionThe identity of the problem does not changea + 0 = a
3In multiplication, you will see these same properties, plus 2 more…
4Five Properties of Multiplication These are the basically the same as additionCommutativeAssociativeIdentityThese belong to multiplication onlyZeroDistributive
5Multiplicative (Do you see most of the word “multiply” in this word? Let’s review the addition properties— from the multiplicative perspective…Multiplicative (Do you see most of the word “multiply” in this word?
7The Commutative Property BackgroundThe word commutative comes from the verb “to commute.”Definition on dictionary.comCommuting means changing, replacing, exchanging, switching places, trading placesPeople who travel back and forth to work are called commuters.
8Here are two families of commuters. Hi!Remember us?Commuter BCommuter ACommuter A & Commuter B changed lanes.Remember… commute means to switch places.Commuter ACommuter B
14The Associative Property BackgroundThe word associative comes from the verb “to associate.”Definition on dictionary.comAssociate means connected, joined, or relatedPeople who work together are called associates.They are joined together by business, and they have to talk to one another.
15Let’s look at another hypothetical situation Three people work together.Associate B needs to call Associates A and C to share some news.Does it matter who he calls first?
16Here are three associates. BB calls A firstHe calls C lastACIf he called C first, then called A, would it have made a difference?NO!
17(The Role of Parentheses) In math, we use parentheses to show groups.In the order of operations, the numbers and operations in parentheses are done first. (PEMDAS)So….
18The Associative Property The parentheses identify which two associates talked first.(A B) C = A (B C)BBACTHENATHENC
20The Identity PropertyI am me!You cannot changeMy identity!
21One is the only number you can multiply something by and see no change.
22Identity Property of Multiplication x 1 =a x 1 = a
23Identity Property of Multiplication x 1 =x 1 =x 1 =a x 1 = a
24These are 3 of the Properties of Multiplication Commutative Property of MultiplicationThe numbers move arounda • b = b • aAssociative Property of MultiplicationGrouping with parentheses(a • b) • c = a • (b • c)Identity Property of MultiplicationThe identity of the problem does not changea • 1 = a
25There are two more properties which are unique to multiplication The Zero PropertyThe Distributive Property
27The Zero Property of Multiplication This looks like a mixture of the identity property of addition and the identity property of multiplication…Be careful not to mix them up!
28If I have 2 pockets with NO money in them, then I have NO money! The Zero PropertyAny time you multiply a number by zero, your answer is zero!If I have 2 pockets with NO money in them, then I have NO money!2 • 0 = 0The End
30The Distributive Property BackgroundThe word distributive comes from the verb “to distribute.”Definition on dictionary.comDistributing refers to passing things out or delivering things to people
31The Distributive Property a(b + c) = (a • b) + (a • c)A times the sum of b and c = a times b plus a times cLet’s plug in some numbers first.Remember that to distribute means delivering items, or handing them out.Here is how this property works:5(2 + 3) = (5 • 2) + (5 • 3)
32You have sold many items for the RCMS fundraiser! You went to two houses on one street and three houses on a different street. Every family bought 5 items!5(2 + 3) = (5 • 2) + (5 • 3)You went to two houses on one street and three houses on a different street. Every family bought 5 items!
33You will be distributing 5 items to each house. 23541
345(2 + 3) = (5 • 2) + (5 • 3)You distributed (delivered) these all in one trip.There are (2+3) five houses all together.You need to deliver 5 gifts to each house.You need to put 25 items on your wagon at one time.5 items x 5 houses = 25 items all together
355(2 + 3) = (5 • 2) + (5 • 3)and10You distributed your items in two trips (+).On the first trip you distributed 5 items to each of 2 houses (5 x 2 = 10).On the second trip you distributed 5 items to each of 3 houses (5 x 3 = 15).That means you distributed (delivered) 10 items plus 15 items. That makes 25 items altogether.+1525
36The Distributive Property Make 1 trip. You have 5 houses. You need to bring 5 items to each house. You need 25 items on your wagon.DISTRIBUTION CENTER5(2 + 3)
37The Distributive Property Make 2 trips. You have 2 houses for your first trip and you need to bring 5 items to each house. You have 3 houses on your second trip and need to bring 5 items to each house. When your second trip is over, you will have distributed 25 items.DISTRIBUTION CENTER(5 • 2) + (5 • 3)
38How do I tell the properties apart? CommutativeNumbers switch placesAssociativeParentheses on both sidesOnly multiplication on each sideIdentityMultiply by 1Zero PropertyMultiply by zeroDistributiveParentheses on each sideOne side has a multiplication sign AND a plus sign
39Let’s practice ! Look at the problem. Identify which property it represents.
40The Distributive Property 4(5 + 6) = (4 • 5) + (4 • 6)The Distributive Propertyof Multiplication3 numbers on one side—4 on the otherMultiplication AND addition3 sets of parentheses