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At the same time the student is generating a list of the multiples of the small number (i.e., partial quotients) that have so far been taken away, which when added up together would then become the whole number quotient itself. For example, to calculate 132 ÷ 8, one might successively subtract 80, 40 and 8 to leave 4:
If there is a remainder in solving a partition problem, the parts will end up with unequal sizes. For example, if 52 cards are dealt out to 5 players, then 3 of the players will receive 10 cards each, and 2 of the players will receive 11 cards each, since = +.
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 ...
For example, 93,−12 denotes 9288, while −16,32 denotes −1600 + 32 or −1568. (Note: 45,−16,32 denotes 448432.) ... Partial quotients with more than two digits
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
For example, the constant ... Infinitely many partial quotients are 4 or 5, and infinitely many partial quotients are greater than or equal to 50. [110]
An example spangram with corresponding theme words: PEAR, FRUIT, BANANA, APPLE, etc. Need a hint? Find non-theme words to get hints. For every 3 non-theme words you find, you earn a hint.
For example, can be expanded to the periodic continued fraction [;,,,...]. This article considers only the case of periodic regular continued fractions . In other words, the remainder of this article assumes that all the partial denominators a i ( i ≥ 1) are positive integers.