basics Flashcards
number sequences
give an example
numbers arranged according to a rule
even by 2:2 4 6 8
even numbers
numbers that divide evenly
odd numbers
numbers that divide evenly with a remainder of one
square numbers
multiply a number by itself gives square numbers
composite numbers
numbers that can be arranged in at least two rows and two columns
prime numbers
list the first seven prime numbers
numbers that cannot be boxed
3 5 7 11 13 17 19
exponents
also called powers, multiplies a number by itself a given number (the exponent) of times
24=16
the numberline
used to represent a sequence of numbers
zero
referred to as the empty set
multiples
the results of multiplication
- fractions
- what property of numbers do fractions allow for?
- what is the name of this property?
- the numbers in between other whole numbers
- in between fractions exists more fractions
- this property is called the density of numbers
sets
groups of numbers
4 important sets
- counting numbers
- intergers
- rational numbers
- real numbers
the counting numbers set
a.k.a natural numbers because they arrise naturally from observing the world
closed under multiplication and division
what does it mean when a set is closed under an operation?
if you perform the stated operation on a number from the set with another number from the same set, you will always get another number from that same set
intergers
- encompasses zero, negative numbers, natural numbers
- closed under multiplication, addition and subtraction
rational numbers
- include intergers and fractions
- closed under multiplication, division, addition and subtraction
real numbers
- composed of rational and irrational numbers
irrational numbers
- neither whole nor fractions
- can only be written as non repeating decimals that do not fall into any pattern of number repetitions
- PI is an irrational number
digit
single numerical symbols from zero to nine
numbers
a single digit or a string of digits
place value
each digit in a number is 10 times greater than the number to its right
what number acts as a place holder?
when is a place holder significant?
- zero
- zero’s appearing to the right of a number add value and are significant
what is a leading zero?
zero’s to the left of a number which can be dropped
and
in math represents a decimal point
what is the special symbol for approximations?
≈
addition
- result: sum
- first and second: addends
multiplication
- result: product
- factors are multiplied
a. first: multiplicand; second: multiplyer
division
- result: quotient
- first: dividend; second: divisor
subtraction
- result: difference
- first: subtrahend second: minvend
inverse
give examples
operations that undo what another operation does
- addition and subtraction are inverse
- multiplication and division are inverse
commutative operations
allow for switching number order around without changing the results
multiplication and addition are commutative
associative operations
allows for grouping numbers differently without changing the results
addition and multiplication
distributive property
allows for splitting large multiplication problems into smaller ones
adding and subtracting negatives
- adding negatives results in a lower negative number
- 10+-10=-20 - subtracting negative numbers: the two negative signs cancel each other out
multiplication and division with negative numbers
- same signed numbers result in positive numbers
- opposite signs result in negatives
unit
- anything that can be counted
a. units must be identical to be added and subtracted
b. units can be multiplied and divided by numbers only if the units are objects and not abstacts
exponents
shorthand for repeated multiplication of a number
- base numbers are the numbers being multiplied
- exponents are the number of times the number is to be multiplied
squared numbers
base numbers raised to the 2’nd power or
x2
roots
the inverse operations of exponents
finding the square root of a number is the most common root operation:
use of the radical symbolizes a square root operation
absolute value
the positve value of any number
I-6I=6
shows how many numbers any given number is away from zero
equation
is a statement with an equal sign that signifies two things have the same value
two basic types: arithmetic and algebraic
two properties of equality
- reflexivity everything is equal to itself
- symmetry allows switching around the order in which things are equal
expression
string of mathematical symbols that can be placed on either side of an equation
evaluation
solving
act of finding the value of an expression
allows taking an expression and turning it into an equation with an equal sign
order of operations
evaluate an expression from left to right in this order:
- parenthesis
- exponents
- multiplication and division
- addition and subtraction
