NEWCOLORs basic math rev - Student Affairs & Diversity

1 123 basic Math ReviewNumbersNATURAL NUMBERS{1, 2, 3, 4, 5, ..}WHOLE NUMBERS{0, 1, 2, 3, 4, ..}INTEGERS{.., 3, 2, 1, 0, 1, 2, ..}RATIONAL NUMBERSAll numbers that can be written in the form , where aand bare integers NUMBERSReal numbers that cannot be written as the quotient of twointegers but can be represented on the number NUMBERSI nclude all numbers that can be represented on the numberline, that is, all rational and irrational NUMBERSA prime number is a number greater than 1 that has onlyitself and 1 as examples:2, 3, and 7 are prime NUMBERSA composite number is a number that is not prime.

2 Forexample,8 is a composite number #2#2=23 Rational NumbersReal Numbers23, , 21 , 0, , 1, 23, 22, 21, 0, 1, 2, 3, pIntegers0, 1, 2, 3, pWhole NumbersNatural Numbers1, 2, 3, p3,2, p, >b 5 5 4 4 3 3 Negative integersNegative integersPositive integersThe Number LineZero 2 2 1 1012345 ISBN-13:ISBN-10:978-0-321-39476-70-321-3 9476-39 780321 39476790000 Integers (continued)MULTIPLYING AND DIVIDING WITH NEGATIVESSome examples:FractionsLEAST COMMON MULTIPLEThe LCM of a set of numbers is the smallest number that is amultiple of all the given example,the LCM of 5 and 6 is 30, since 5 and 6 have nofactors in COMMON FACTORThe GCF of a set of numbers is the largest number that canbe evenly divided into each of the given example,the GCF of 24 and 27 is 3, since both 24 and27 are divisible by 3, but they are not both divisible by anynumbers larger than are another way to express division.

3 The top num-ber of a fraction is called the numerator, and the bottomnumber is called the AND SUBTRACTING FRACTIONSF ractions must have the same denominator before they canbe added or subtracted., with ., with .If the fractions have different denominators, rewrite them asequivalent fractions with a common denominator. Then addor subtract the numerators, keeping the denominators thesame. For example,.23+14=812+312=1112dZ0ad-bd=a-bd dZ0ad+bd=a+bdor362 18 2 3618 1-242>1-82=3 1-721-62=42 -3#5=-15-a,b=- ab-a-b=ab-a#-b=ab-a#b=-abImportant PropertiesPROPERTIES OF ADDITIONI dentity Property of Zero:Inverse Property:Commutative Property:Associative Property:PROPERTIES OF MULTIPLICATIONP roperty of Zero:Identity Property of One:, when.

4 Inverse Property:,when .Commutative Property:Associative Property:PROPERTIES OF DIVISIONP roperty of Zero:, when .Property of One:, when .Identity Property of One:Absolute ValueThe absolute value of a number is always , .If , .For example, and . In each case, theanswer is positive. 5 =5 -5 =5 a =aa60 a =aa70a1=a#1aZ0aa=1aZ00a=0a#1b#c2=1a#b2#c a#b=b#aaZ0a#1a=1aZ0a#1=aa#0=0a+1b+c2=1a+ b2+ca+b=b+aa+1-a2=0a+0=aKey Words and SymbolsThe following words and symbols are used for the operations , total, increase, plusaddend addend = sumSubtractionDifference, decrease, minusminuend subtrahend = differenceMultiplicationProduct, of, timesfactor factor = productDivisionQuotient, per, divided bydividend divisor = quotientOrder of Operations1st:ParenthesesSimplify any expressions inside :ExponentsWork out any.

5 Multiplication and DivisionSolve all multiplication and division, working from left to :Addition and SubtractionThese are done last, from left to example,.IntegersADDING AND SUBTRACTING WITH NEGATIVESSome examples: -19+4=4-19=-15 -3-17=1-32+1-172=-20 a-1-b2=a+b -a+b=b-a -a-b=1-a2+1-b2 =12=15-6+3=15-2#3+27,915-2#3+130-32,32a b ab a>b b aa*b, a#b, 1a21b2, abmore Rates, Ratios, Proportions,and PercentsRATES AND RATIOSA rateis a comparison of two quantities with different example, a car that travels 110 miles in 2 hours is mov-ing at a rate of 110 miles/2 hours or 55 ratio is a comparison of two quantities with the sameunits.

6 For example, a class with 23 students has astudent teacher ratio of 23:1 or .PROPORTIONSA proportion is a statement in which two ratios or rates exampleof a proportion is the following statement:30 dollars is to 5 hours as 60 dollars is to 10 is typical proportion problem will have one unknown quantity, such can solve this equation by cross multiplying as shown:.So, it takes 60 minutes to walk 3 percent is the number of parts out of 100. To write a per-cent as a fraction, divide by 100 and drop the percent sign. For example.

7 To write a fraction as a percent, first check to see if thedenominator is 100. If it is not, write the fraction as anequivalent fraction with 100 in the denominator. Then thenumerator becomes the percent. For example,.To find a percent of a quantity, multiply the percent by example, 30% of 5 #5=150100=3245=80100=80%57%=57100x=6020= 320x=60 #11 mile20 min=x miles60 min$305 hr=$6010 hr231 Fractions (continued)Equivalent fractionsare found by multiplying the numeratorand denominator of the fraction by the same number. In theprevious example, AND DIVIDING FRACTIONSWhen multiplying and dividing fractions, a commondenominator is not needed.

8 To multiply, take the product of the numerators and the product of the denominators:To divide fractions, invert the second fraction and then multiply the numerators and denominators:Some examples:REDUCING FRACTIONSTo reducea fraction, divide both the numerator and denom-inator by common factors. In the last example,. mixed NUMBERSA mixed number has two parts: a whole number part and afractional part. An example of a mixed number is . Thisreally represents,which can be written , an improper fraction can be written as a mixednumber. For example,can be written as ,since 20 divided by 3 equals 6 with a remainder of 23203408+38=4385+385 381012=10,212,2=56512,12=512#21=1012=563 5#27=635ab,cd=ab#dc=adbcab#cd=a#cb#d=acb d14=1#34#3=31223=2#43#4=812more NEWCOLORs_basic_math_rev 3/31/08 3:52 PM Page 1-123 basic Math ReviewNumbersNATURAL NUMBERS{1, 2, 3, 4, 5.}

9 }WHOLE NUMBERS{0, 1, 2, 3, 4, ..}INTEGERS{.., 3, 2, 1, 0, 1, 2, ..}RATIONAL NUMBERSAll numbers that can be written in the form , where aand bare integers NUMBERSReal numbers that cannot be written as the quotient of twointegers but can be represented on the number NUMBERSI nclude all numbers that can be represented on the numberline, that is, all rational and irrational NUMBERSA prime number is a number greater than 1 that has onlyitself and 1 as examples:2, 3, and 7 are prime NUMBERSA composite number is a number that is not prime.

10 Forexample,8 is a composite number #2#2=23 Rational NumbersReal Numbers23, , 21 , 0, , 1, 23, 22, 21, 0, 1, 2, 3, pIntegers0, 1, 2, 3, pWhole NumbersNatural Numbers1, 2, 3, p3,2, p, >b 5 5 4 4 3 3 Negative integersNegative integersPositive integersThe Number LineZero 2 2 1 1012345 ISBN-13:ISBN-10:978-0-321-39476-70-321-3 9476-39 780321 39476790000 Integers (continued)MULTIPLYING AND DIVIDING WITH NEGATIVESSome examples:FractionsLEAST COMMON MULTIPLEThe LCM of a set of numbers is the smallest number that is amultiple of all the given example,the LCM of 5 and 6 is 30, since 5 and 6 have nofactors in COMMON FACTORThe GCF of a set of numbers is the largest number that canbe evenly divided into each of the given example,the GCF of 24 and 27 is 3, since both 24 and27 are divisible by 3, but they are not both divisible by anynumbers larger than are another way to express division.