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## Multiplication Properties

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**Multiplication Properties**Lesson 2-1**Do you remember these Properties of Addition?**• Commutative Property of Addition • The numbers move around • a + b = b + a • Associative Property of Addition • Grouping with parentheses • (a + b) + c = a + (b + c) • Identity Property of Addition • The identity of the problem does not change • a + 0 = a**In multiplication, you will see these same properties, plus**2 more…**Five Properties of Multiplication**• These are the basically the same as addition • Commutative • Associative • Identity • These belong to multiplication only • Zero • Distributive**Let’s review the addition properties— from the**multiplicative perspective… Multiplicative (Do you see most of the word “multiply” in this word?**Property #1**The Commutative Property of Multiplication**The Commutative Property**• Background • The word commutative comes from the verb “to commute.” • Definition on dictionary.com • Commuting means changing, replacing, exchanging, switching places, trading places • People who travel back and forth to work are called commuters.**Here are two families of commuters.**Hi! Remember us? Commuter B Commuter A Commuter A & Commuter Bchangedlanes. Remember… commute means to switch places. Commuter A Commuter B**The Commutative Property**A • B = B • A**3 groups of 5 = 5 groups of 3**3 x 5 = 5 x 3 = = 15 kids 15 kids**Remember… in Lesson 1-11 we saidthat the word “of”**means multiply What commutative means to multiplication… 3 groups of 5 = 5 groups of 3 3 • 5 = 5 • 3 a • b = b • a**Property #2**The Associative Property of Multiplication**The Associative Property**• Background • The word associative comes from the verb “to associate.” • Definition on dictionary.com • Associate means connected, joined, or related • People who work together are called associates. • They are joined together by business, and they have to talk to one another.**Let’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?**A**C B NO! Here are three associates. B calls A first He calls C last If he called C first, then called A, would it have made a difference?**(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….**A**C B A C B The Associative Property The parentheses identify which two associates talked first. (A B) C = A (B C) THEN THEN**Property #3**The Identity Property of Multiplication**The Identity Property**I am me! You cannot change My identity!**One is the only number you can multiply something by and see**no change.**Identity Property of Multiplication**a x 1 = a x 1 =**Identity Property of Multiplication**a x 1 = a x 1 = x 1 = x 1 =**These are 3 of the Properties of Multiplication**• Commutative Property of Multiplication • The numbers move around • a •b = b • a • Associative Property of Multiplication • Grouping with parentheses • (a • b) • c = a • (b • c) • Identity Property of Multiplication • The identity of the problem does not change • a •1 = a**There are two more properties which are unique to**multiplication • The Zero Property • The Distributive Property**Property #4**The Zero Property of Multiplication**The 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!**The Zero Property**• Any 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 = 0 The End**Property #5**The Distributive Property of Multiplication**The Distributive Property**• Background • The word distributive comes from the verb “to distribute.” • Definition on dictionary.com • Distributing refers to passing things out or delivering things to people**The Distributive Property**a(b + c) = (a • b) + (a • c) A times the sum of b and c = a times b plus a times c Let’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)**You 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!**5(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**5(2 + 3) = (5 • 2) + (5 • 3)**and 10 You 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. + 15 25**The 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 CENTER 5(2 + 3)**The 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)**How do I tell the properties apart?**• Commutative • Numbers switch places • Associative • Parentheses on both sides • Only multiplication on each side • Identity • Multiply by 1 • Zero Property • Multiply by zero • Distributive • Parentheses on each side • One side has a multiplication sign AND a plus sign**Let’s practice !**Look at the problem. Identify which property it represents.**4(5 + 6) = (4 • 5) + (4 • 6)**The Distributive Property of Multiplication • 3 numbers on one side—4 on the other • Multiplication AND addition • 3 sets of parentheses**987 • 1 = 987**The Identity Property of Multiplication • Times 1**3 • 0 = 0**Zero Property of Multiplication • Times zero**(1 • 2) •3 = 1 • (2 • 3)**The Associative Property of Multiplication • Same 3 numbers • Multiplication only • 2 sets of parentheses**6 • 11 = 11 • 6**The Commutative Property of Multiplication • Same 2 numbers • Numbers switched places**9 • 7 = 7 • 9**The Commutative Property of Multiplication • Same 2 numbers • Numbers switched places**12 • 0 = 0**Zero Property of Multiplication • Times zero**(9 • 8) •7 = 9 • (8 • 7)**The Associative Property of Multiplication • Same 3 numbers • Multiplication only • 2 sets of parentheses**9(8 + 7) = (9 • 8) + (9 • 7)**The Distributive Property of Multiplication • 3 numbers on one side—4 on the other • Multiplication AND addition • 3 sets of parentheses**9 • 1 = 9**The Identity Property of Multiplication • Times 1**a • 1 = a**The Identity Property of Multiplication