Algebraic+properties+for+the+four+basic+operations

Wikiespace page 1 by: Colby Wieduwilt Mr. Morgan's algebra, 2nd period

Purpose: To inform the reader on the four basic properties of algebra and to give examples and theorems to walk through each basic process.

media type="youtube" key="Oj3zWTcaHB4" height="344" width="425"1 1-4 Theorems and Proof: Addition List Of Theorems: 1.For all Real numbers b and c, (b+c) + (-c) = b 2.For all real numbers a,b, and c, if a+c=b+c, then a=b 3. Corollary. For all real numbers a,b, and c, if c+a=c+b, then a=b 4. Cancellation Property of Addition, for all real numbers a,b, and c, a+c=b+c or c+a=c+b 5. Property of the opposite of a Sum, for all real numbers a and b, -(a+b) = (-a) + (-b) 6. cancellation property of an additive inverse, for all real numbers a, -(-a) = a

Quiz Questions:Fill in the blank so that each statement is true. Examples: 1. simplify: x + [-(x+3)] here you are simply stating the problem.( using property of opposite of a sum) -x + [-(x+3)] = x + (-x) + (-3) -0 + (-3) = -3
 * 1) 1. -(z+3) = -z + _.

2. simplify:(-y) + (-y) restating the problem. (-y) + (-y) = -(y+y) = -2y

1-5 Properties of Products List of theorems: 1.For all real numbers b and all nonzero real numbers c, (bc)1/c=b. 2.Cancellation Property of multiplication, for all real numbers a and b and all nonzero real numbers c, if ac=bc or ca=cb 3.Property of the reciprocal of a product, for all numbers a and b, 1/ab= 1/a x 1/b 4.Multiplicative Property of -1, for all real numbers a, a(-1) = -a and (-1)a=-a 5. Properties of opposites in Products, for all real numbers a and b, (-a)b=-ab a(-b)=-ab (-a)(-b)=ab

Examples: 1.5x(-3)=(-3)(5x) simply restate the problem (-1)(3)(5x) add -1 and make the three positive -15x finish working the problem

2.(-5)(7)(-12) restate the problem 420

Quiz questions: 1.-5(x)(-y) 2.(-3a)(-b)(8)

1-6 Properties of differences 1. Definition of subtraction, for all real numbers a and b, a-b= a + -b

Examples: 1.-4-(-5) restate the problem -4 + 5 =1 2.-2(x-y) restate problem -2x + 2y

Quiz Questions: 1.Is this statement true? a-b=b-a?

1-7 Properties of Quotients 1. Definition of Division a/b=a x 1/b 2.Order of Operations -simplify powers -simplify products and quotients in order from left to right -simplify sums and differences in order from left to right.

Examples: 1.13 - 2 + 18 x 2 / 4 restate problem 13-2+ 36 / 4 13 - 2+ 9 11+9 20 complete order of operations

Quiz questions: 1.(-25 - 14) / 13

Citations: Youtube: Dolciani, Mary P. __Algebra 2 and Trigonometry__. Boston, MA: Houghton Mifflin, 1986. 12-28.

[|Property of Multiplication] [|Property of Addition]