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### 34 Cards in this Set

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 WHAT ARRE THE 4 KEY WORDS TO REMEMBER OF APPLICAIONS OF NUMBER THEORY MENTAL MATH TECHNIQUES PERMUTATIONS COMBINATIONS PROPRTIES OF REAL NUMBERS MENTAL MATH TECHNIQUES PERMUTATIONS COMBINATIONS PROPERIES OF REAL NUMBERS THE FIRST OF THE TWOD DISCRIPTORS OF APPS OF NUMBER THEORY-DISCRIPTOR 1 USE PRINCIPLES OF NUMBER THEORY AND PROPERTIES OF OR DECIMAL BASED SYSTEM TO PERFORM ARITHEMTIC OPERATIONS MENTALLY OR QUICKLY THE FIRST OF THE TWOD DISCRIPTORS OF APPS OF NUMBER THEORY-DISCRIPTOR 2 USE PERMUTATIONS AND COMBINATIONS TO SOLVE PROBLEMS THE FIRST OF THE TWOD DISCRIPTORS OF APPS OF NUMBER THEORY-DISCRIPTOR 3 APPS PROBLEMS REQUIRING THE USE OF NUMBERS TO QUANTIFY MEASURES PRIME NUMBERS TWO FACTORS 1 AND ITSELF THE PRIME NUMBERS BEGIN WITH 2 ZERO AND ONE ARE NOT PRIME NUMBERS EXAMPLE OF A PRIME NUMBER 11 IS PRIME: HAS EXACTLY TOW FACTORS 1 AND 11 11 AND ? COMPOSITE NUMBER: MORE THAN TWO FACTORS EXAMPLE OF A COMPOSITE NUMBER 24 IS A COMPOSITE HAS MOULTIPLE FACTORS- (1,2,3,4,5,6,7,8,12,24) COMPOSITE OF WHAT NUMBER? EVEN NUMBERS INTERGERS DIVISABLE BY 2 IF N=ANY INTERGER, THEN 2N+1 IS AN ODD NUMBER EN ODD NUMBERS OR INTERGERS INTEGERS DIVISABLE BY 2 IF N=ANY INTERGER, THEN 2N+1 IS AN ODD NUMBER ON PRIME FACTORIZATION, GCF FACTORZATION OR FACTORING PROCESS USED TO REWRITE A COMPOSTIE NUMBER AS THE PRODUCT OF TWO OR MORE FACTORS PRIME FACTORIZATION, GCF FACTORZATION OR FACTORING EXAMPLES ALL OF THESE ARE WAYS THE NUMBER 24 CAN BE FACTORED 24=1(24) OR 2(12) OR 3(8) PR 4(6)_- PRIME FACTORING FACTORZATION OR FACTORING EXAMPLES-EXAMPLES 24=(2)(2)(2)(2) GCF DEFINE LARGEST FACTOR BY WHICH TWO DIFFRIENT NUMBERS ARE DIVISIBLE GCF EXAMPLES-WHAT IS THE GCF OF 24 AND 32? MAKE A NUMBER TREE 24-BRANCH 1 (1,24) 24-BRANCH 2 (3,12) 24-BRANCH 3 (3,8) 24 BRANCH 4 (4.6) BANCH 2 BRANCH 1 (1<32) BRANCH 2 (2,16) BRANCH 3 (4,16) MENTAL ARITHMATIC DIVISIBILTY RULES DIVISIBLE BY 2: NUMBER IS EVEN DIVISIBLE BY 3: SUM OF DIGITS DIVISIBLE BY 3 DIVISIBLE BY 5: NUMBER ENDS IN 0 OR 5 DIVISIBLE BY 6: EVEN NUMBER DIVSIBLE BY 3 DIVIISBLE BY 9: SUM OF DIGITS DIVISIBLE BY 9 DIVISIBLE BY 10: NUMBER ENDS IN 0 QUICK ARITHIMATIC: N20 ARROW X2,X10 0n*25 100/4*100 17*25=/4, X100 Nx50=>/2, *100 QUICK ARITHIMATIC:DIVISION N/20=> X2, X10 PERCENTS AND FRACTIONS LEARN THE UNIT PERCENTS AND THEIR FRACTIONAL EQUIVALENTS AND THEN JUST USE MULTUIPLES unit prcent unit fraction unit percent unit fraction 1% 1/100 100% 1 unit prcent unit fraction unit percent unit fraction 2% 1/50 50% 1/2 unit prcent unit fraction unit percent unit fraction 4% 1/25 25% 1/4 unit prcent unit fraction unit percent unit fraction 5% 1/20 20% 1/5 unit prcent unit fraction unit percent unit fraction 33 1/3% 1/3 10% 1/10 Lenth, area, Volume, capacity, density-LENTH MEASURS OF 1 DIEMENSION SUCH AS FET, INCHES, METERS, KILOMETERS, MILES Lenth, area, Volume, capacity, density-AREA MEASURE OF TWO DIMENSIONS OR PART OF SURFACE, SUCH AS FT^2, M^2, IN^3, CM^3 Lenth, area, Volume, capacity, density-VOLUME MEASURE OF 3 DIMIENSIONS OR OCCUPIED BY SPACE, SUCH AS FT^3, m^3, CM^3 Lenth, area, Volume, capacity, density-CAPACITY A MEASURE BASED ON THREE DIMENESIONS OR HOW MUCH SOMETHING WILL GOLD SUCH AS GALLONS, LITERS, PINTS, QUARTS, OUNCES Lenth, area, Volume, capacity, density-DENSITY DESITY IS PHYSICAL PROPERTY OF MATTER RELATED TO MASS AND VOLUME-DENSITY=MAS/VOL DURING TESTING YOU ARE PROVIDED WITH A CHART THAT HAS THE FOLLOWING FORMULAS CIRCUM CIRCLE AREA: CIRCLE TRAINGLE, RHOMBUS, TRAPZOID, SURFACE AREA:SPHERE LATERAL AREA: CYLINDER vOLUME CLYINDER, CONE, SPHRE PRISM WHICH OF THE 3 SHAPES ARE U UNSURE OF? RHOMBUS TRAPEZOID SO STUDY AND UNDERSTAND THEM! COUNTING TECHNIQUES:PERMUTATIONS AN ARRANGEMENT FO THE ELEMENTS FORM A GIVEN SENT IN A DEFINATE ORDER-GIVE {A, B. c} THERE ARE 6 DIFFIENT ARRANGEMENTS ABC, ACB, BAC, BCA, CZB, CBA-DO EXAMPLB PROMBEM ON PAGE 52 COMBINATIONS COUNTING TECHNIQUES COMBINATIONS ARE UNIQUE SUBSETS OF THE ELEMENTS SET, REGARDLESS HOW THEY ARE ARRANGED-GIVEN {A,b,c} THERE IS 1 UNIQUE ARRANGEMENT BECAUSE EACH ARRANGEMENT HAS THE SAME LETTERS**DO THE EXAMPLE ON THE BOTTEM OF PAGE 52*****AND TOP OF 53*** A FOURTH GRADE TEACHER WANTED T BUILD A SANDBOX FOR HER ROOM THAT SHE COULD USE TO TEACH STUDENTS ABOUT ARTIFACTS. THE bOX WAS TO BE FILLED TO A DEPTH O F15 INCHES AND HAD DIMENSITONS OF 5 FT BY 4 FT BY 3 FT BY 2 FT. iF ABOUT 1/4 A CUBIC FOOT WEITHS 10 POUNDS, HOW MANY POUNDS OF SAND ARE NEED TO FILL THE SANDBOX? DRAW A SANDBOX 5 ON THE BOTTEM LENGTH, 4 ON THE BOTTEM SIDE LENGTH, AND 2 ON THEH HIGHT =A 1000PDS FIRST CONVERT THE 15 INCHES TO FEET, 15/12=5/4 FOOT, v=BH=5 (4) =25FT^2 VOLUME =B * h 1/4FT^3=10 POUNDS SO 1 FT=40 POUN-SO THE AMOUNT OF SAND NEED IS 25(40) OR 1000 POUNDS OF SAND