Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
The Properties of Addition & Multiplication As shown in different types of algebraic equations. Yes yes. Notes for November 14th 11/14/2012 Do Now 1. (-10) + (-8) = 2. (-3) + 12 = 3. -5 – 2 = 4. 7 – (-6) = 2 5 5. 3 6 6. -1.5 – 0.2 = 7. The temperature at 6:00 a.m. was -5 ºF. At 2:00 p.m. the temperature had increased 14 ºF. What was the temperature at 2:00 p.m.? 8. -8 x 9 = 11/14/2012 Do Now 1. (-10) + (-8) = -18 2. (-3) + 12 = 9 3. -5 – 2 = -7 4. 7 – (-6) = 13 2 5 1 5. 3 6 6 6. -1.5 – 0.2 = -1.7 7. The temperature at 6:00 a.m. was -5 ºF. At 2:00 p.m. the temperature had increased 14 ºF. What was the temperature at 2:00 p.m.? 9 -8 x 9 = -72 Announcements Make sure name is on homework; turn it in Tonight's HOMEWORK ACE 1, 2, 7 and 8-25 page 69 and 70 of Accentuate the Negative There is an assessment on Tuesday 11/20/12 Things you will need to know Adding integers, fractions and decimals Subtracting integers, fractions and decimals Multiplying integers, fractions and decimals Dividing integers, fractions and decimals Order of Operations Answering real world math problems like last nights homework Concept of a ledger (withdrawals, deposits, balance, etc.) ARE YOU READY! •Commutative Property •Identity Property •Associative Property •Inverse Property What is a property? What do we mean by property? Something that a person owns Ex. This is Chuck’s cow. It is his property. What is a property? The other definition of property A distinctive attribute or quality of something Ex. What are the properties of water? The Properties of Addition An addition property is “A distinctive quality unique to problems involving addition.” Commutative Property Commutative Property The order in which two numbers are added does not change the sum Ex. 5 + 6 = 6 + 5 Commutative Property How will I remember? Commute = move from one place to another (like when you commute to school every morning) With addition, numbers can commute (move around), and we still get the same answer. Associative Property Associative Property The way three numbers are grouped when adding does not change the sum The parentheses are used to show groups In the order of operations, the numbers in parentheses are done first (PEMDAS) Ex. (4 + 3) + 9 = 4 + (3 + 9) Associative Property How will I remember? Associate = to hang out with someone (like when you associate with your homies) With addition, numbers can associate (be grouped with other numbers), and we still get the same answer. Identity Property Identity Property The sum of a number and zero (0) is the number. Ex. 14 + 0 = 14 How will I remember? 0 has no identity (poor guy). So there is no way that this nothing can change a number. He is worthless. Inverse Property Inverse Property The sum of a number and its opposite is zero (0). Ex. 24 + -24 = 0 How will I remember? What’s the opposite of… Let’s Practice Which property is represented in the equation below? 8 + (-8) = 0 Which property is represented in the equation below? 8 + (-8) = 0 Inverse Property Which property is represented in the equation below? (12 + 4) +13 = 12 + (4 +13) Which property is represented in the equation below? (12 + 4) +13 = 12 + (4 +13) Associative Property Which property is represented in the equation below? 1234 + 4321 = 4321 + 1234 Which property is represented in the equation below? 1234 + 4321 = 4321 + 1234 Commutative Property Which property is represented in the equation below? 98765 + 0 = 98765 Which property is represented in the equation below? 98765 + 0 = 98765 Identity Property This addition stuff is boring. Can’t we do multiplication now? Yes yes young grasshopper. We can embark on the wonderful journey of multiplication properties!!! •Distributive Property •Commutative Property •Identity Property •Associative Property •Inverse Property Commutative Property Commutative Property The order in which two numbers are multiplied does not change the product Ex. 5 x 6 = 6 x 5 Commutative Property How will I remember? Commute = move from one place to another (like when you commute to work) With addition, numbers can commute (move around), and we still get the same answer. Associative Property Associative Property The way three numbers are grouped when multiplying does not change the product Ex. (4 x 3) x 9 = 4 x (3 x 9) Ex. (ab)c = a(bc) Associative Property How will I remember? Associate = to hang out with someone (like when you associate with your homies) With mutliplication, numbers can associate (be grouped with other numbers), and we still get the same product. Identity Property Identity Property The product of a number and 1 is the number. 15 1 15 Ex. How will I remember? 1 I am worthles s Just like 0 in addition, 1 really serves no purpose in multiplication. It is worthless and has no effect on the number. It is the 0 of multiplication. Inverse Property Inverse Property The product of a number and its reciprocal is 1. 1 15 1 15 Ex. How will I remember? When you are inverted, you are flipped over. Let’s Practice Which property is represented in the equation below? 31(5) = 5(31) Which property is represented in the equation below? 31(5) = 5(31) Commutative Property Which property is represented in the equation below? 1 39 1 39 Which property is represented in the equation below? 1 39 1 39 Inverse Property Which property is represented in the equation below? 56342 x 1 = 56342 Which property is represented in the equation below? 56342 x 1 = 56342 Identity Property Which property is represented in the equation below? (983 x 3)17 = 983(3 x 17) Which property is represented in the equation below? (983 x 3)17 = 983(3 x 17) Associative Property Distributive Property Distributive Property A number outside parenthesis must be multiplied by everything inside Ex. Distributive Property Distributive Property A number outside parenthesis must be multiplied by everything inside Ex. How will I remember? Distribute means “to share.” The outside number must be distributed (shared) with every other number. Distributive Property Think of it like this… Ex. 3(5 + 2) = ??? ** 3 is the candy. We must share the candy with everyone. That is, we must share 3 with 5 & 2. 3 3 Distributive Property Think of it like this… Ex. 6(2 + 7) = ??? There is too much of a spotlight on 6. The spotlight must be shared with 2 and 7 6 (2 + 7) 6(2) + 6(7) 12 + 42 54 Distributive Property Think of it like this… Ex. -10(3 + 9) = ??? Uh oh! Don’t lose the negative sign as you distribute the spotlighted number!! -10(3 + 9) -10(3) + -10(9) -30 + -90 -120 Distributive Property Think of it like this… Ex. -5(4 – 7) = ??? Make sure you know where your negative signs are in this problem!!!!! -5 (4 – 7) -5(4) - -5(7) -20 – (-35) 15 Here is the same distributive property written … symbolically: a × (b + c) = a × b+ a × and pictorially (rectangular array area model): b a a c × b a × c c An example: 6 x 13 using your mental math skills . . . symbolically: 6 × (10 + 3) = 6 × 10 + 6 and pictorially (rectangular array area model): 10 6 6× 10 3 6 × 3 × 3 And now it’s time for … No!! It can’t be!! Say it ain’t so!! Yes class. It’s time for variables!!! Mwahahaha!!! Distributive Property Think of it like this… Ex. 3(x + 4) = ??? There is too much of a spotlight on 3. The spotlight must be shared with x and 4 3 (x + 4) 3(x) + 3(4) 3x + 12 Distributive Property Think of it like this… Ex. -11(x + 5) = ??? Uh oh! Don’t lose the negative sign as you distribute the spotlighted number!! -11 (x + 5) -11(x) + -11(5) -11x + -55 Distributive Property Think of it like this… Ex. -5(2x – y) = ??? Make sure you know where your negative signs are in this problem!!!!! -5 (2x – y) -5(2x) - -5(y) -10x – (-5y) Let’s Practice Distributive Property 1. 4(6 + 5) 2. 6(3 + 8) 3. 15(12 + t) 4. -6(x + 12) 5. -12(3 + r) 6. -15(4 + t) 7. -9(6 + p) 8. -5(7 + t)