Math for Elementary Teachers 1 WGU
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