Math 2008 Module 2 Flashcards

Terms Definitions
Closure property of addition
For whole numbers a and b, a + b is a whole number
Identity property of addition
There exists a unique whole number, 0, such that 0 + a = a for every whole number a. Zero is the additive identity element
Additive identity element of addition
Zero is the
Commutative property of addition
For whole numbers a and b, a + b = b + a
Associative property
For whole numbers a, b, and c, (a +b) + c = a + (b + c)
Definition of less than and greater than for whole numbers
Given whole numbers a and b, a is less than b, (a < b) if and only if there is a whole number k > 0 such that a + k = b. Also, b is greater than a ( b > a) whenever a < b.
Taking Away in subtraction
Ex. How much string is left on a 33 yrd spool if 21 yards have already been used (Taken away)
Separating in subtraction
Ex. How must carpet is needed to finish capering a room when you both the total amount and also the amount in the part of the room that is already carpeted.
Comparing in subtraction
Ex. How much wider a living room window is than a bedroom window
Definition of Subtraction of whole numbers
In the subtraction of the whole numbers a and b a -b = c if and only if c is a unique whole number such that c + b = a. In the equation, a - b = c, a is the minuend, b is the subtrahend, and c is the difference.
Rectangular array of multiplication
when sets are arranged in equal rows and columns
Area model of multiplication
the two numbers being multiplied represent the dimensions of a rectangle
Definition of multiplication as repeated addition
In the multiplication of whole numbers, if there a rem sets with n objects in each set, then the total of objects ( n + n + n+ ....) where n is used as an added m times) can be represented by m x m where m and n are factors and m x n is the product.
Closure property of multiplication
For whole numbers a and b a x b is a unique whole number
Identity property of multiplication
There exists a unique whole number 1 such that 1 x a = a x 1 = a for every whole number a. Thus is the multiplicative identity element
multiplicative identity element
1 is the
Commutative property of multiplication
For whole numbers a and b, a x b = b x a
Associative property
For whole numbers a, b, and c (a x b) x c =a x (b x c)
Zero property
For each whole number a, a x 0 = 0 x a = 0
Distributive property of multiplication over addition
for whole numbers a, b, and c, a x(b +c ) = (a x b) + (a x c)
Partitioning model of division
Separating and finding how many in each subset. Ex. Total of 300 envelopes, with 25 bundles. How many in each bundle?
Measurement model
Separating and finding how many subsets. Ex. total of 300 envelopes, with 25 in each bundle. How many bundles?
Definition of division
in the division of whole numbers and b, b is not equal to 0, a/b=c if and only if c is a unique whole number such that c x b = a. In the equation a/b=c, a is the dividend, b is the divisor, and c is the quotient.
The division algorithm
For any two whole numbers a and b, b does not equal 0, a division process for a/b can be used to find unique whole numbers q (quotient) and remainder such that a=bq +r and 0 is less than or equal to r and r is less than b. For a = 25, b =4, q=6, and r =1, 25 = (4x6) + 1 using whole number division
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