Math Unit 1 A Flashcards
(20 cards)
Real Numbers
any # you can thing of
symbol is a R with a extra line
Natural Numbers
all positive courting numbers and whole numbers [not 0}
Symbol is N with extra line
Whole Numbers
Positive courting numbers and whole numbers including zero
Symbol is W with two extra lines
Integers
Positive and Negative whole numbers + zero
Symbol is a z with a extra line
Rational Numbers
Numbers that can be written in the form of a fraction. In decimal form these are termination (decimals that end ex 1/5 = 0.2) and non termination/repeating decimals (0.3333… = 1/3) note rational numbers do not have to be in fraction form but has to be able to be a fraction
Symbol is Q with a l inside
A set is a …
A set is a collection of numbers or objects. Numbers are categorized into different types of sets. Curly Brackets are used to list the numbers of a set with each number separated by a comma. ex {1,2,3,4,5}
Irrational numbers
Numbers that cannot be written in the form of a fraction. In decimals they do not terminate or repeat ex; pi and squared numbers that do not equal an exact number.
Symbol is Q with a l inside and dash over it
Empty set/null set
Set that contains no elements can be represented by squiggly brackets of a zero with a cross. Always can be a proper subset and subset
Scientific Notation
Involves writing any given number as a positive number between 1 and 10 multiplied by a power of 10 example ( A * 10 ^ k where A is greater than or equal to 1 and less than 10 And K is an integer)Example 23, 600, 0000 equals 2.36 * 10 ^ 7 ( if negative go to left if positive go the right)
Infinity, limits, and density:
Density and dense refer to a measure of how much of something exists within a fixed amount example which set is a denser set of numbers.
Density property - the number line - The density property tells us that we can always find another real number that lies between any two real numbers
Sequences:
Sequences can at times get closer and closer to a specific number AKA limit/turning towards example 1,4,9,16, 36, 49 tends towards Infinity.
E reads
“is a member of” or “is in”
ex -5 e Z - in other words -5 is a member of a integer set
E with a cross reads
“is not a element of” or “is not in”
ex Pi E cross is not a Q - in other words Pi is no a element of a rational number set
C underlined reads
C reads
is a subset of
is a proper subset of
Ex if A= {3,9,14} than {3} C set A
Fractions
A fraction is an expression written in the form a/b where be is not equal to zero
top is numerator bottom is denominator
reciprocal of a/b is b/a
numerator less than denominator = proper fraction
numerator greater than denominator = improper fraction
2 4/7 is a mixed number
1/3 and 3/9 is equivalent
formula for converting mixed number to improper fractions if A B/C than A x C + B
-4/-9 = 4/9 - dividing two negatives makes positive
-2/3 = 2/-3 - when - on just numerator or just denominator it just goes to whole thing
when comparing fractions:
find common denominator
for negative greater fractions mean less
for improper fraction turn to mixed number if whole number is not the same
Fraction of quantities
of = times (x)
126 = 126/1
Powers
2 to the power of 3 is qual to to 2x2x2
-2 to the power of 3 is like (-1) (2 to the power of 3)
very important to keep brackets -2 to the power of 3 is not equal to (-2) to the power of 3
now the 5 to the power of 4 divided by 5 is 5 to the power of 3
Fraction Calculations
adding and subtracting fractions
Common denominator and if needed make proper fraction mixed number
Add or subtract
Simplify
Multiplication
Multiply denominators and multiply numerators
Division
proper fraction
flip second fraction therefore reciprocal
multiply fractions
simplify if needed
*practice word problems from lesson 5
Proportional relationships (direct variation + partial variation)
When a relationship between two variables is described as proportional it means that as one variable changes the other changes in a constant manner. Therefore in a proportional relationship the ratio of the two variables remains constant. Example: distance and time or cost in quantity.
Direct variation is a relationship between two variables and which one variable is a constant multiple of the other in a graph it is a straight line that passes through the origin. Always starts with 0 and 0 and both X and Y variables.
Partial variation is a relationship between two variables and which the dependent variable is a sum of a constant number and a constant multiple of independent variables and a graph looks like a straight line that is not passed through the origin.
^unite conversion is a example of proportional relationship (12 in = 1 ft)
Unite Rate, Converting Fractions + Decimals to a percent, and calculate the percent of something
Unit rate = rate for one of something helps us to make meaningful comparisons in calculations involving different quantities.
Converting fractions and decimals to a percent.
Multiply by 100
Calculate the percent of something
Put percent in decimal than multiply
Ex - 10% of 45 is 0.1 x 45 = 45
25% of 120 25 is 1/4 so 120 / 4 = 30
Therefore put percent into fraction
To add the percent to the number do 1.13 for 13 percent therefore put into decimal
+ 1 to get amount of percent and og number
Redo questions *redo test? for practice