Chapter 1.1, 1.2

Properties of Real NumbersChapter One1.1 ORDER OF OPERATIONSPARENTHESES (GROUPING SYMBOLS)EXPONENTSMULTIPLICATION AND DIVISIONADDITION AND SUBTRACTION *PERFORM THESE OPERATIONS AS THEY OCCUR FROM LEFT TO RIGHTPLEASE EXCUSE MY DEAR AUNT SALLYOrder of OperationsSimplify:[384-3(7-2)3]/33S-T(s2-t) if s=2 and t=3.4-0.048xy+z3 y2+5if x = 5, y = -2, z=-1-9Order of OperationsFind the area of a trapezoid with base lengths of 13 meters and 25 meters and a height of 8 meters.A = *h*(b1+b2)A = *8*(25+13)A = 152m21.2 REAL NUMBERSRATIONAL #S (Q) M/N; where N is not 0FRACTION, TERMINATING, REPEATINGINTEGERS (Z) -2, -1, 0, 1, 2, WHOLE #S (W) 0, 1, 2, NATURAL #S (N) 1, 2, 3, IRRATIONAL #S (I)NOT RATIONAL, NON-TERMINATING, NON-REPEATINGExamples:Pi, .010001001000001023..

Real Number Venn Diagram

NaturalsNAME THE SETS OF #S TO WHICH EACH BELONG

Q, RQ, RI, RN, W,Z,Q,RQ, RPROPERTIES of Real NumbersCOMMUTATIVE (2 + 3) + 4 = 4 + (2 + 3)ASSOCIATIVE - 2 (3X) = (- 23) XIDENTITYa + 0 = 0 + aINVERSEADDITIVE INVERSE OF 7 IS -7MUSTIPLICATIVE INVERSE OF 7 IS 1/7DISTRIBUTIVE

Distributive Propertya(b + c)=ab + ac and (b + c)a=ba + caLike terms have the same variables and same exponents

Ex: Simplify 4(3a b) + 2(b + 3a)1.3 Verbal ExpressionsThree more than a numberX+3Six times the cube of a number6X3The square of a number decreased by the product of 5 and the same numberX2-5XTwice the difference of a number and six2(X-6)Verbal Expressions14+9=23The sum of 14 and 9 is 23.6=-5+XSix is equal to -5 plus a number7Y-2=19Seven times a number minus 2 is 9.Properties of EqualityReflexive a=aSymmetricIf a =b, then b = aTransitiveIf a = b and b = c, then a = cSubstitutionIf a = b, then a may be replaced by b and b may be replaced by a.12Solving One Step EquationsS-5.48=0.02S=5.5Make sure to check solution!18= 1 t 2T=3613Solving Multi Step Equations2(2x+3)-3(4x-5)=22X=-1/853=3(y-2)-2(3y-1)X = -1914Solve for a VariableS=RL + R2; Solve for LL =S- R2 RRe-write the formula for area of a trapezoid for h.A = *h*(b1+b2)H= 2A .b1+b215More equations.If 3n-8=9/5, what is the value of 3n-3?What are two ways we can solve this problem?Solve for n and then plug into second equationMake left hand side look like 3n-3How do we do that?Add Five to both sidesAnswer = 34/5If 4g+5=4/9, what is the value of 4g-2?Subtract 7 from both sidesAnswer = -59/9

More equations.Josh and Pam have bought an older home that needs some repair. After budgeting a total of $1685 for home improvements, they started by spending $425 on small improvements. They would like to replace six interior doors next. What is the maximum amount they can afford to spend on each door?Let C represent the cost to replace each door.6c+425=1685They can spend $210 on each door.More equations.Basketball GameWarm Up1. Draw the Venn Diagram we used to review the relationship of the different sets of numbers (R, I, W, Q, Z,N)2. Reflect on one (or more) concepts that you feel you need to review before the quiz tomorrow.1.4 Solving Absolute ValuesAbsolute ValueFor any real number a, if a is positive or zero, the absolute value of a is a. If a is negative, the absolute value of a is the opposite of a.For any real number a, |a| = a, if a 0, |a| = -a if a