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Properties Do Now: On a piece of loose leaf please write the solution to the following problems: Remember NO calculator 3-(-7) 5-3 -10-5 S.W.B.A.T Identify the different properties Solve problems using the different properties Write their own original problem Solve a classmates original problem Distributive Property One of the most frequently used property Lets you multiply the sum by multiplying each addend separately and then add the products This might be confusing so I will show you plenty of examples Distributive Property: Examples 5(x+2)= (5x) 5(x) + 5(2) (3x+6) = 5x(3x 2 ) + 5x(6) (5)(3x 2 + 2x + 6) = 5(3x 2 )+ 5(2x)+ 5(6) Associative Property The change in grouping of three or more addends or factors does not change their sum or product Associative property holds good for both addition and multiplication, but NOT for subtraction and division Associative Property: Examples Addition (2+3)+5= 2+(3+5) Whether you add 2 and 3 first or 3 and 5 first does not matter as long as you get the same sum, which is 10, both ways Multiplication (4x5)10= 4(5x10) Whether you multiply 4 and 5 first or 5 and 10 first does not matter as long as you get the same product, which is 200, both ways Commutative Property Of It states that changing the order of addends does not change the sum a+b=b+a Of Addition Multiplication It states that changing the order of factors does not change the product axb=bxa Commutative property: More Addition and multiplication are commutative over the set of real numbers. For any two real numbers x and y, x + y = y+ x xy = yx Subtraction and division are NOT commutative Commutative property: Examples 2 4 +3=3+2 Whether you add 3 to 2 or 2 to 3, you get 5 both ways x7=7x4 Whether you multiply 4 by 7 or you multiply 7 by 4, the product is the same, 28 Laws for each property Commutative Laws You can swap numbers over and still get the same answer When a+b=b+a When you add you multiply axb=bxa Laws for Each Property Associative Laws It does not matter how you group the numbers, meaning which number you calculate first When (a+b)+c=a+(b+c) When you add you multiply (axb)xc=ax(bxc) Laws for Each Property Distributive law The best of all, but needs careful attention You get the same answer when you Multiply a number by a group of numbers added together OR Do each multiply separately and add them a x (b + c ) = a x b + a x c Careful! The commutative law does NOT work for division 12 / 3 = 4 BUT 3 / 12 = 1/4 The Associative Law does NOT work for subtraction ( 9 – 4 ) – 3 = 5 – 3 = 2 BUT 9–(4–3)=9–1=8 The Distributive Law does NOT work for division 24 / ( 4 + 8 ) = 24 / 12 = 2 BUT 24 / 4 + 24 / 8 = 6 + 3 = 9 The Identity Property Addition The sum of zero and any number or variable is the number or variable itself Example: 4 + 0 = 4 Multiplication The product of 1 and any number or variable is the number or variable itself Example: 4 x 1 = 4 Addition and multiplication property of equality Additive Property of Equality For all real numbers a, b, and c: a =ba+c=b+c We read this as a equal b is equivalent to a +c equals b + c Addition and multiplication property of equality Multiplication of Equality For all real number a and b, and for c ≠ 0 a = b ac = bc We read this as A equals b is equivalent to ac equals bc Additive and Multiplicative Inverse Additive What Inverse you add to a number to get a zero The negative of a number The additive inverse of -5 is 5 because -5 +5 = 0 The additive inverse of 5 is -5 Additive and multiplicative inverse Multiplicative Inverse The Multiplicative Inverse of a number is its reciprocal The product of a number and the reciprocal of a number is 1 Multiplicative Inverse of a number n is represented as 1 n or n -1 Homework Work on the worksheet Tomorrow I will go over any questions you might have Then I will collect the worksheets and I will pick one or two problems at random to grade Make a problem on your own, pick one of the properties and we will swap in class tomorrow to see the problems we made!
