Final Exam Flashcards
(24 cards)
Divisibility rule: 2 only if
if the last digit is even (ends in 0, 2, 4, 6, 8…)
Divisibility rule: 3
The sum of the digits is divisible by 3
Divisibility rule: 4
The last 2 digits are divisible by 4
Divisibility rule: 5
The last digit is a 0 or 5
Divisibility rule: 6
The number is divisible by 2 and 3
Divisibility rule: 8
The last 3 digits are divisible by 8
Divisibility rule: 9
The sum of digits is divisible by 9
Divisibility rule: 10
The last digit is a 0
Divisibility rule: 11
if the difference of the sum of digits is 0 or 11
Arithmetic sequence formula
an = a1 + (n-1)d
Proper subset
a subset that contains all the elements of another set, but is not the same set itself (ex. If A = {1, 2, 3} and B = {1, 2}, then B is a proper subset of A because all elements of B are in A, but A has an additional element (3) not present in B.)
(written out answer ex. 2^6 - 1)
Improper subset:
a subset of a set that contains all the elements of the original set, meaning it is essentially the original set itself; every set only has one improper subset, which is the set itself.
(Ex. if set A = {1, 2, 3}, then the only improper subset of A is A itself, {1, 2, 3}.) (Written out answer ex. 2^6)
Closure property of addition of whole numbers
the sum of two whole numbers is a unique whole number; for example, 5+2 is a unique whole number, and that number is 7
Closure property of multiplication of whole numbers
when two numbers from a set are multiplied, the product is also in that set
Prime numbers
natural numbers that are divisible by only 1 and the number itself.
examples: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, …
Composite numbers
any positive integers or natural numbers that have more than two factors. examples: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, …
Geometric sequence formula
an = a (r^n - 1) / r-1
12|4
“does 4 divide 12” (is saying 4 divided by 12, so it is false)
0|8
“does 8 divide 0” (is saying 8 divided by 0, but we don’t get a real whole number b/c it’s undefined, so it’s false)
8|0
“does 0 divide 8” (is saying 0 divided by 8, which is true b/c it equals 0)
LCM
Least Common Multiple: lowest possible number that can be divisible by both numbers.
GCD/GCF
Greatest Common Divisor/Factor: the largest positive integer that divides each of the integers.
Comparing fractions
To compare fractions with different denominators, you need to first find a common denominator by finding the least common multiple (LCM) of the denominators, then convert each fraction to an equivalent fraction with that common denominator, and finally compare the numerators of the new fractions; the fraction with the larger numerator is the larger fraction
Arithmetic sequence sum formula
Sum = n/2 (n1+last term)
