Addition
what is the definition of "addition of whole numbers"?
Let a and b be any two whole numbers. If A and B are disjoint sets with A=N(A) and b=n(b) then a+b=n(AuB).
What is the take away approach for subtraction?
Let a and b be any whole numbers and A and B be sets such that a=n(A), b= n(B), and B subset A. then a-b= n(A-B).
what are decimals used for?
to represent fractions in our usual base ten place value notation.
is every fraction a rational number?
yes
what is "distributivity of multiplication over addition of integers"?
let a, b and c be any integers. then a(b+c)= ab+ac
what is the "closure property for whole number addition"?
The sum of any two whole numbers is a whole number
What is "missing addend approach to subtraction of whole numbers"?
let a and b be any whole numbers. Then a-b=c if and only if a=b+c for some whole number c.
where is the decimal point located in the number 3457.968?
between the ones column and the tenths column to show where the whole number portion ends and where the decimal portion begins
what is the equality of rational numbers definition used for?
to find equivalent representations of rational numbers (1) to simplify rational numbers and (2) to obtain common denominators to facilitate addition, subtraction, comparing rational numbers
what is the "multiplicative cancellation property"?
let a, b, c be any integers with c not equal to 0. if ac=bc, the a=b
what is the "commutative property for whole-number addition"?
Let a and b be any whole numbers. Then a+b=b+a
what are two models that can be used to represent the take away approach of subtraction?
set model and measurement model
what are two visual ways to represent decimals
hundreds square and number line
when is a rational number said to be in simplest form?
if a and b have no common prime factors and b is positive
what is the "zero divisors" property?
let a and b be integers. then ab=0 if and only if a=0 or b=0 or a and b both equal zero
what is the "associative property for whole number addition"?
Let a, b, c be any whole numbers. Then (a+b)+c=a+(b+c).
in "a-b" which is the "minuend" and which is the "subtrahend"?
a is the minuend and b is the subtrahend
what are terminating decimals?
a finite of non zero digits to the right of the decimal point
do rational numbers have an additive property?
yes
what is the definition for division of integers?
what is the "Identity property for whole number addition" ?
There is a unique whole number, namely 0, such that for all whole numbers a, a+0=a=0+a
what are two possible approaches to subtraction?
take away approach and missing addend approach
how can we order decimals?
by using a hundreds square, a number line, comparing them in fraction form, or comparing place value one at a time from left to right
when is a rational number positive?
if both a and b are both positive or both negative integers
what are two approaches to order integers?
number line approach and addition approach