1. CET ReviewTIU Math Session 1

2. TODAY:Sets & Number Theory Sets The Set of Real Numbers Divisibility Rules GCF and LCM, Prime & Composite 3. SETS 4. Application of SETSIn a class, every student participates in thesoccer team or the debate team. 10students participate only in the debateteam, 29 students participate only in thesoccer team, and 12 students participatein both teams.QUESTION: How many students are there in the class? 5. Venn diagram:Soccer & Debate teamsDebate Soccer10 12 29 How many participate in Debate ONLY? 10 How many participate in Debate? 22 Why is the answer 22? 6. EXERCISE 1.1 part I (page 2)I. GivenU = {0,1,2,3,4,5,6} universal setA = {0,2,4,6}subset AB = {0,3,6}subset BC = {1,3,5}subset CFind A U B.Set anygroup orB collection of0 2 A objects C 1 3 4(elements)56 7. Operations on Sets: UnionFind A U B.unionA = {0,2,4,6} subset AB = {0,3,6} subset BUnion marriageof familiesAUB=?- set containingA U B = {0, 2, 3, 4, 6} ALL elements ofboth sets 8. Using a Venn DiagramShown: Set A A U B (union)A = {0,2,4,6} subset AB = {0,3,6} subset B 2 0Show: A U B 3 4 6A U B = {0, 2, 3, 4, 6} 9. Operations on Sets:Intersection Find A C.intersectionIntersection the partcommon to both roads - set containing common elements 10. Using a Venn DiagramShown:Intersection of 2 JOINT sets A C (intersection) A = {0,2,4,6}subset A C = {1,3,5}subset C2 01When two sets have NOTHING in4 635 common: DISJOINT AC=An empty intersectionmeans that set A and set phi = emptyC have NOTHING incommon. or null set 11. Using a Venn Diagram(Summary of Operations) 12. Operations on Sets: Complement Find C. complement or primeU complement of C- set containing Celements of theuniversal set Uthat are not C found in C 13. Complement Find C.U = {0,1,2,3,4,5,6} universal setC = {1,3,5} subset C C = not in C but in U C = {0, 2, 4, 6} C = A 14. THE SET OF REAL NUMBERS 15. The Set of Real Numbers 16. Prime vs. Composite PRIME NUMBERS COMPOSITENUMBERS2, 3, 5, 7, 11, 13, 17, 4, 6, 8, 9, 10, 12, 14, 16, Numbers whose only factors are just 1 Numbers whose and itselffactors are more than just 1 and itselfEx. Factors of 4: 1, 2, 4 17. (Book: Read page 6, Do page 5 even #s)PROPERTIES OF THE SET OFREAL NUMBERS 18. Answer page 8 Exercise1.4 I Seatwork II Even numbers(Book: page 7)DIVISIBILITY RULES 19. GCF & LCM 20. Question:In an ongoing TELUS project, there are18 men and 21 women. They are to bedivided into smaller exclusive groups(all-men or all-women groups) suchthat there are the same number ofpeople in each small group.How many members should there be ineach group? 21. Answer:3 people in each small group.(3 is the Greatest Common Factor of `8 and 21.)18 MEN 21 WOMEN3 33 3 3 3 33 33 3 3 3 Two ways to answer:1.) List all factors of each number.2.) Use prime factorization. 22. Difference of FACTOR &MULTIPLE2 36 6 is a MULTIPLE of2. 2 and 3 are6 is also aFACTORS of 6MULTIPLE of 3. 23. The greatest common factor (GCF) of 18 and 21:METHOD 1:List all factors of 18 and 21. Factors of 18: 1, 2, 3, 6, 9,18 Factors of 21: 1, 3, 7, 211 and 3 are the common factors of 18 and21, but the GREATEST is 3.Therefore, the GCF or 18 and 21 is 3. 24. Method 2: Prime factorization Prime Factor Tree represents the numberin terms of its prime factors 18 21 18 = 2 x 3 x 3Do page 10 Exercise 1.5, 21 = 3x 7 Seatwork GCF only. GCF =3 25. Question:In a Palawan seaport,two lighthouses guardthe shores at night.One lighthouse flashesevery 16 seconds, andthe other flashes every24 seconds. If they litup at the same time atexactly 12 midnight,after how manyseconds will they flashtogether again? 26. Answer:At 12:00:48, or 48 seconds after midnight.METHOD 1:List all MULTIPLES of 16 and 24. Multiples of 16: 16, 32, 48, 64, 80, 96, Multiples of 24: 24, 48, 72, 96, 120, 48 is the smallest or LEAST commonmultiple, so our answer is 48. 27. Method 2: Prime factorization Prime Factor Tree of 16 and 24: 1624Do page 10Exercise 1.5, 16 = 2 x 2 x 2 x 2Seatwork LCM 24 = 2 x 2 x 2 x3part. LCM = 2 x 2 x 2 x 2 x 3 = 48 28. GCF vs. LCM of two numbersGCFLCM Method 1: Listing Method 1: Listing List FACTORS List MULTIPLES Method 2: Prime Method 2: PrimeFactorizationFactorization Include in the GCF only Include in the LCM all the the COMMON prime prime factors factorsDo page 10 Challenge 29. (Book page 11)FRACTIONS 30. 84Reduce to lowest terms: 16Lowest terms is when the numerator & denominatorhave no common factor other than 1.84 2 42 Is this fraction in lowest16 2 8terms already?42 2 21 Is this fraction in lowestterms already? 8 24 Do page 12 Exercise 1.6,Seatwork Reduce. 31. Arranging fractions Same NumeratorSame denominator(SIMILAR FRACTIONS) Which has greatervalue: 7 3 ? or 8 8 32. Arranging fractions By using Equivalent Fractions 28 7? 33. 3Convertto decimal form.8 0 .3 7 5 Solution: Divide 3 by 8.8 3 .0 0 0 TIPS 2 4 Numerator INSIDE divisionhouse.6 0 The remainder is thedifference left at the 5 6bottom. 4 0 4 00 34. (Book page 14)RATIO & PROPORTION 35. Question: Two boxes of macaroons costP120. How much do 7 boxes ofmacaroons cost?DIRECT ProportionAs the number of boxes increases, the price increases too.27 1 720pcrei P042120 price2no os no osof x . be of x . beperi cperi c 36. Question: It takes Kevin 20 minutes to ride hisbicycle at 20kph from home to thegrocery store. To shorten his travel timeto 16 minutes for the same distance, how fast should his speed be?INVERSE ProportionAs Kevins speed increases, thetime to reach destinationDECREASES.2n 00s k m p 6 s p2 i 2h1n em ei s d 37. Question: Eighteen liters of milk is transferredinto 3 containers in the ratio 2 : 3 : 4.How much water is in each container?PARTITIVE ProportionThe whole is divided into more than two parts.2 : 3 : 4 38. 2+3+4=92 : 3 : 4liters (total)2x2 3x2 4x2Multiplier: 9 x ? = 184 __ : ____: 6818 liters 39. (Book pages 15 & 16)EXERCISES ON RATIO &PROPORTION 40. Page 19 Exercise 1.8 (see hint on top)SeatworkFraction to decimal: 4640decimal percent Divide 4640 by 300. 1 0.2525 % 300 4 14.5 2 5 300 4640.0 7 9Decimal to percent:11200.43 = 43 %513 41. -% Increase/Decrease - Finance Interest - Discounts - Commissions - Mixtures / Solutions - Parts of a WholePRB(PERCENTAGE RATE BASE) 42. THANK YOU!