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In mathematics education at the primary school level, chunking (sometimes also called the partial quotients method) is an elementary approach for solving simple division questions by repeated subtraction. It is also known as the hangman method with the addition of a line separating the divisor, dividend, and partial quotients. [1]
The process of adding one more partial quotient to a finite continued fraction is in many ways analogous to this process of "punching a hole" in an interval of real numbers. The size of the "hole" is inversely proportional to the next partial denominator chosen – if the next partial denominator is 1, the gap between successive convergents is ...
In cases where one or more of the b terms has more than two digits, the final quotient value b cannot be constructed simply by concatenating the digit pairs. Instead, each term, starting with b 1 , {\displaystyle b_{1},} should be multiplied by 100, and the next term added (or, if negative, subtracted).
Thought of quotitively, a division problem can be solved by repeatedly subtracting groups of the size of the divisor. [1] For instance, suppose each egg carton fits 12 eggs, and the problem is to find how many cartons are needed to fit 36 eggs in total.
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Here, the partial dividend is 9. The first number to be divided by the divisor (4) is the partial dividend (9). One writes the integer part of the result (2) above the division bar over the leftmost digit of the dividend, and one writes the remainder (1) as a small digit above and to the right of the partial dividend (9).
The badly approximable numbers are precisely those with bounded partial quotients. [6] Equivalently, a number is badly approximable if and only if its Markov constant is finite and its simple continued fraction is bounded.
Suppose the game of Nim is played as usual with heaps of objects, but that at the start of play, every heap is restricted to have either one or two objects in it. In the normal-play convention, players take turns to remove any number of objects from a heap, and the last player to take an object from a heap is declared the winner of the game; in Misere play, that player is the loser of the game.
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