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# Math 251 Final Exam Study Guide MATH 251

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This 4 page Study Guide was uploaded by Victoria Giannini on Sunday January 31, 2016. The Study Guide belongs to MATH 251 at University of Delaware taught by Anne Morris in Spring 2015. Since its upload, it has received 108 views. For similar materials see K-8 Math: Numbers and Operations in Math at University of Delaware.

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Date Created: 01/31/16

Math 251 Final Exam Study Guide Key Terms Quantity: an amount of stuff (or other quantifiable object) Numeral: a symbolic representation of a quantity, invented by humans (ex: 3, Roman numeral= III) Numeration System: a set of symbols and a set of rules that allow humans to represent quantities symbolically Basic Symbols: each numeration system has a set of basic symbols that it uses to represent all quantities (ex: 0,1,2,3,4,5,6,7,8,9) Measuring Unit: quantities that are used to measure and represent other Quantities Basic Measuring Unit (BMU): the quantity that is assigned to the numeral ‘’1’’ Additive Property: the value of a numeral is the sum of the value of the digits Positional Property: the position of a symbol in a numeral affects the total value of the numeral Multiplicative Property: the numeration system uses a symbol or position to indicate that a particular symbol is multiplied by some constant Place Valued Property: the value of every symbol depends on its place in the numeral Zero Property: if a system has a the Zero Property, then it should have both meanings: 1) as a placeholder: zero designates “no groups” of a particular measuring unit (serves as a placeholder, ex: 780) and 2) as a quantity: zero represents a quantity, like any other quantity (ex: if 0 is added to 78, the answer is 78) Join Problem: two or more quantities are combined Take Away Problem: part of a quantity is removed from the quantity Additive Comparison Problem: the sizes of two quantities are compared Part-Part-Whole Problem: there is a part-whole relationship involved, but the quantities in the word problem are not being joined, separated or compared. No action or change is taking place Repeated Addition Problem: involve the combining of A sets of B objects and have a “for every,” “each,” or “per” idea embedded in the story Rectangular Array/Area Problem: the physical arrangement of A x B objects in a rectangular array with A rows and B columns Multiplicative Comparison Problem: involve a multiplicative comparison of two quantities in terms of a multiplicative relationship (a “times as many” or “times as much” relationship) Cartesian Product/Combination Problem: the pairing of the elements of two sets to form distinct ordered pairs where the first member of each pair belongs to the first set (which has A elements) and the second member belongs to the second set (which has B elements) Repeated Subtraction Problem: we know the size of each group, and the size of the whole, but we do not know how many groups there are. To figure out how many groups there are, we can either “repeatedly subtract” the seize of each group (take out one group at a time) from the whole to determine how many times we can subtract until we have a remainder of zero, or we can see how many copies of the quantity of size B fit into the whole C Partitioning or Equal Sharing Problem: we know the whole and the number of groups, but not the size of each group. To figure out the size of each group, we dole out or partition the whole into the known number of equal groups Missing Factor Problem: stems from the relationship between multiplication and division (we can say “? x B = C” and “C / B = ?” are equivalent elements)-the unknown is a missing factor and we have to find it. Associative Property: addition- (a + b) + c= a + (b + c) multiplication- (a x b) x c=a x (b x c) Commutative Property: addition- a + b=b + a multiplication- a x b=b x a Identity Property: addition- the identity element is 0 because a + 0=0 + a= a multiplication- the identity element is 1 because a x 1=1 x a= a Inver Property: addition- -a is the inverse of a because a + -a = -a + a = 0 multiplication- for a ≠ 0, 1/a is the inverse of a because a x 1/a = 1/a x a = 1 Distributive Property: multiplication over addition or subtraction - a x (b ± c) = (a x b) ± (a x c) division over addition or subtraction- (a ± b) ÷ c = (a ÷ c) ± (b ÷ c) Equal Additions Algorithm Intermediate Multiplication Algorithm: 28 X 37 56 (child says 7x8=56) 140 (child says 7x20=140) 240 (child says 30x8=240) + 600 (child says 30x20=600) 1036 Standard Multiplication Algorithm: 28 X 37 196 + 840 1036 3 80 ___100__ Intermediate Division Algorithm: 40 ) 7345 = 183 R 25 - 4000 3345 - 3200 145 - 120 25 Standard Division Algorithm: ___183_ R 25 40 ) 7345 - 40 êê 334 ê - 320 ê 145 - 120 25

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