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.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