Math equations Flashcards
definitions
Sum: addition
Difference: subtraction
Product: multiplication
Quotient: division
Integers
positive and negative whole numbers, and zero (…, –2, –1, 0, 1, 2, …)
zero as an integer
Zero is an even integer, neither positive nor negative
Digits
Digits: the integers from 0 through 9 (ten digits total)
ABCD.EFGH:
A = thousands
B = hundreds
C = tens
D = ones = units;
E = tenths
F = hundredths
G = thousandths
H = ten-thousandths
Prime
numbers with exactly two factors (so 1 is not prime)
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97 are prime
Prime numbers are numbers that have only 2 factors: 1 and themselves.
By contrast, numbers with more than 2 factors are call composite numbers.
“Can the positive integer p be expressed as the product of two integers, each of which is greater than 1”
is the same as asking “is p NOT prime”
Through or inclusive: including the endpoints
Through or inclusive: including the endpoints
(to count consecutive integers through: last number – first number + 1)
including endpoints- what is the sum of the multiples of 3 between 1 and 99 or 2 3 adn 99, does not include 3 adn 99, first 3 last 96, how many multiples of 3 are there from 3 to 99 inclusive, then includes both 3 adn 99 so then 99-3 plus 1 divided by 2 but rounding up
Between: excluding the endpoints
Between: excluding the endpoints
(to count consecutive integers between: last number – first number – 1)
Factors or divisors
when listing factors/divisors, always list them in pairs beginning with 1 and the number itself
ex: 24 = 1 × 24, 2 × 12, 3 × 8, 4 × 6
add 1 to each exponent of prime factorization, then multiply all of those numbers = total # of factors
ex: 144 = 24
2^4 X 3^2 → (4+1)(2+1) = 15 → 144 has 15 total factors
lets take a number 12 numbers are made up of prime factors every number has its unique set of prime factors what makes a number distinct, and in fact as we have discussed think about numbers not as numbers but as composites of their dna. governs every aspect of the that number, governs the entire identity of that number, it is also the case that numbers have a set of factor pairs factor pairs of 12, 1, 12, 2, 6, 3,4 - if you want to know how many factors that number has you can caluclate it using its prime factorization is using process on sheet so 12 2^2 x 3, circle exponents 2 and 1 we add 1 to each exponent then multiply the result 2+1=3 and 1+1= 2, 3x2 6 12 has 6 factors, 1, 12, 2, 6, 3, 4 and thats what it means
Multiples
Multiples: the multiples of 5 are 5, 10, 15, 20, 25, …
Distinct
Distinct: different
Reciprocal
the reciprocal of x is 1/x
the reciprocal of a/b is b/a
Mean
average ([Sum] Total = Average × Number of Numbers)
Median
Median: middle number or the average of the two middle numbers, when numbers are arranged in order (equivalent to the 50th percentile)
Mode
Mode: the most commonly occurring number
Range
Range: greatest number – smallest number
Standard deviation
a measure of how spread out a set of numbers is
- adding a constant to every number in a set does not change the SD
- multiplying by a constant will change the SD by the absolute value of that same constant
-if all the numbers in a set are the same, the SD will be 0 - in a normal distribution, within 1 SD = 68%; within 2 SDs = 95%; within 3 SDs = 99.7%
** question was if X, Y, Z haev same sd as 10, 15, 20? z-x=10 and 2. z-y=5. yes C Because the standard deviation is unaffected when the same number is added to each member of a data set, the standard deviation of the data set consisting of the numbers z – 10, z – 5, and z is the same as the standard deviation of the data set consisting of the numbers 10, 15, and 20;***
Divisibility
3: if the sum of the digits is divisible by 3, the number is also divisible by 3
9: if the sum of the digits is divisible by 9, the number is also divisible by 9
4: if the last two digits as a number are divisible by 4, the number is also divisible by 4
Divisibility 2
8: if the last three digits as a number are divisible by 8, the number is also divisible by 8
6: must be divisible by 2 and 3
15: must be divisible by 3 and 5
- Any integer divided by any power of 2 or 5 (or combination of those two numbers, such as 10 or 20) will be a terminating decimal; anything else in the denominator has the potential to make a repeating decimal
Fractions 1
Fractions 2
Cross multiplying
Odd/Even Rules
Counting
Equally spaced Lists 1
