Powerpoint of Notes
... What is the Multiplication Multiplication Property of -1: A number times -1 is equal to the Property of -1? opposite of the original number [In other words, the original number becomes negative if it was positive or positive if it was negative.] Examples: -1 x (-5) = 5 n x -1 = -n ...
... What is the Multiplication Multiplication Property of -1: A number times -1 is equal to the Property of -1? opposite of the original number [In other words, the original number becomes negative if it was positive or positive if it was negative.] Examples: -1 x (-5) = 5 n x -1 = -n ...
Rules of Divisibility
... Let’s say there are two cakes, one chocolate, and the other vanilla. The chocolate is cut into thirds and the vanilla into fourths as shown below. Ashton eats one piece of chocolate cake and one piece of vanilla cake, as shown by the gray pieces. ...
... Let’s say there are two cakes, one chocolate, and the other vanilla. The chocolate is cut into thirds and the vanilla into fourths as shown below. Ashton eats one piece of chocolate cake and one piece of vanilla cake, as shown by the gray pieces. ...
Full text
... and so on. It is clear that when n ∈ N is large, the probability that a number chosen at random from {0, 1, 2, . . . , n} will end in 1 when written in binary is approximately onehalf. In fact, by taking n sufficiently large, the probability that a randomly-chosen number from {0, 1, 2, . . . , n} wi ...
... and so on. It is clear that when n ∈ N is large, the probability that a number chosen at random from {0, 1, 2, . . . , n} will end in 1 when written in binary is approximately onehalf. In fact, by taking n sufficiently large, the probability that a randomly-chosen number from {0, 1, 2, . . . , n} wi ...
Tiling Proofs of Recent Sum Identities Involving Pell Numbers
... connection with the order of certain simple groups. The interested reader should consult Sloane [4, A002315] for more information on these numbers. Theorem 9. For all n ≥ 0, pn−1 + pn = ...
... connection with the order of certain simple groups. The interested reader should consult Sloane [4, A002315] for more information on these numbers. Theorem 9. For all n ≥ 0, pn−1 + pn = ...
Grade 5 Common Core Math Scope and Sequence Draft
... and evaluate expressions with these symbols. Write and interpret numerical expressions. 5.OA 2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 ...
... and evaluate expressions with these symbols. Write and interpret numerical expressions. 5.OA 2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 ...
rational number
... cream. A dish with two scoops can have any two flavors, including the same flavor twice. How many different double-scoop combinations are possible? ...
... cream. A dish with two scoops can have any two flavors, including the same flavor twice. How many different double-scoop combinations are possible? ...
Full text
... case. For example, for b = 10, we get p = 24, which is not coprime to b-l = 9. Thus, if we constructed a similar table for 6 = 10, we would expect to get some simultaneous congruences without solutions. This is in fact the case, i.e., the pair of congruences k = 2 (mod 24) and k = F2 = l (mod 9) has ...
... case. For example, for b = 10, we get p = 24, which is not coprime to b-l = 9. Thus, if we constructed a similar table for 6 = 10, we would expect to get some simultaneous congruences without solutions. This is in fact the case, i.e., the pair of congruences k = 2 (mod 24) and k = F2 = l (mod 9) has ...