Math for Elementary Teachers 1 WGU

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complement

the elements that are NOT in the stated set Example: E' is read ''complement of E'' and means all the elements that are NOT in E but in Universal set A' = not in A or B

intersection of sets

the elements that are common to two or more sets

Exponent Rules

x + x = x² x⁻ⁿ = 1/xⁿ x⁰ = 1 x¹x² = x¹⁺² (x²)⁴ = x⁸ x⁴/x² = x⁴⁻²

point slope form

y - y₁ = m(x - x₁)

intersect

∩ A∩B = A and B A∩0=0

Ways to identify sets

1. A written description A is the set of calendar months beginning with the letter J. 2. List or roster method A=(January, June, July) 3. Set-builder notation A=(xIx is a calendar month beginning with the letter J)

LCM (Least Common Multiple)

1st GCD (divide until no remainder) 2nd multiply the first 2 #s 3rd divide by the number from 1st step GCD (a,b)*LCM (a,b)= ab

equivalent fractions

2 fractions with the same value ½ and 2/4. Multiply or divide top & bottom by the same number ie x 2

equivalent sets

2 sets are equivalent if they contain the same # of elements A= (1,2,5,6,8) B= (5,7,8,9,10) C= (6,8,10) A and B are equivalent because they have 5 elements each If 2 sets are equivalent we write A∼B

Theorem

A mathematical statement which we can prove to be true

Negative Exponent Rule

A negative exponent is the reciprocal of that number with a positive exponent; x⁻⁴ = 1/x⁴ 2⁻³=1/8 2³=8

empty or null set

A set with no elements { } or ∅

Arithmetic Sequence Formula

A=a₁+(n-1)d A= Last term a₁=1st term n=which term you want to know d= common difference

standard form of a linear equation

Ax + By = C, where A, B, and C are real numbers, and A and B are NOT both zero In standard form, the equation y = 4/3x - 1 is 4x + (-3)y = 3

Anything that isn't in A or B

A∩⁻B

Union

A∪B = A either/or B A∪0=A

Find the first five terms of the sequence whose nth term is given

EXP: 9n+10 replace the n with the term # you want to know 9*1+10=19 9*2+10=28 so on until you have done 5 terms

Multiplication Rule for Probabilities for Tree Diagrams

For all multistage experiments, the probability of the outcome along any path of a tree diagram is equal to the product of all the probabilities along the path.

divisible by 4 test

If the last 2 digits are divisible by 4

divisible by 8 rule

If the last 3 digits are divisible by 8

divisible by 6 test

If the sum of the digits is divisible by 2 & 3

divisible by 9 test

If the sum of the digits is divisible by 9

Interest Formula

Interest = principal × rate* × time** *expressed as a decimal **expressed in years

Front-end with adjustment

Round the front end of each number & then check to see if the sum of the other numbers will create another of the front #'s 965 =1000 215 =200 142 =100 65+15+42=100

multipicative inverse

Same as Reciprocal flip numerator & denominator 2/3 to 3/2

Sum of any series

Sn=n(a₁+an)/2 Sn= sum of n terms n= # of terms a₁=1st term an=last term

Commutative Property

The order in which numbers are added or multiplied does not change the sum or product. Change places a+b=b+a a*b=b*a

Associative Property

The way in which numbers are grouped does not change their sum or product (2+3)+4=2+(3+4) or (2*3)*4=2*(3*4)

Probability

To figure the probability... # of desired/# of possible

slope-intercept form

a form of linear equations: y = mx + b where m is the slope and b is the y-intercept

Distributive Property

a property indicating a special way in which multiplication is applied to addition of two or more numbers in which each term inside a set of parentheses can be multiplied by a factor outside the parentheses, such as a(b + c) = ab + ac

geometric sequence

an = a₁rⁿ⁻¹ an=nth term a₁=1st term r=common ratio n=nth term

The nth term of an arithmetic sequence

a₁+(n-1)d Value of any term

Divisible by 3

if the sum of the digits is divisible by 3

Find the slope.

m=y₂-y₁/x₂-x₁

cardinal numbers

number of a set is the number of elements in a set notation used (A) or IAI A=(1,2,3,5,8,9) IAI=6


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