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The division with remainder or Euclidean division of two natural numbers provides an integer quotient, which is the number of times the second number is completely contained in the first number, and a remainder, which is the part of the first number that remains, when in the course of computing the quotient, no further full chunk of the size of ...
The other problems on the tablets were computed by the same technique. The scribe used the identity 1 hekat = 320 ro and divided 64 by 7, 10, 11 and 13. For instance, in the 1/11 computation, the division of 64 by 11 gave 5 with a remainder 45/11 ro. This was equivalent to (1/16 + 1/64) hekat + (4 + 1/11) ro. Checking the work required the ...
7 divided by 10 yields 2/3 + 1/30. After these two tables, the papyrus records 91 problems altogether, which have been designated by moderns as problems (or numbers) 1–87, including four other items which have been designated as problems 7B, 59B, 61B and 82B. Problems 1–7, 7B and 8–40 are concerned with arithmetic and elementary algebra.
For example, if s=2, then ๐(s) is the well-known series 1 + 1/4 + 1/9 + 1/16 + …, which strangely adds up to exactly ๐²/6. When s is a complex number—one that looks like a+b๐, using ...
36/10 = 3 + 1/2 + 1/10 (g18 & h34) Chace and Shute had noted the Reisner Papyrus division by 10 method, also applied in the RMP. Chace, nor Shute, clearly cite the quotients and remainders that were used by Ahmes.
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.
The text of problem 10 runs like this: "Example of calculating a basket. You are given a basket with a mouth of 4 1/2. What is its surface? Take 1/9 of 9 (since) the basket is half an egg-shell. You get 1. Calculate the remainder which is 8. Calculate 1/9 of 8. You get 2/3 + 1/6 + 1/18. Find the remainder of this 8 after subtracting 2/3 + 1/6 ...
The remainder, as defined above, is called the least positive remainder or simply the remainder. [2] The integer a is either a multiple of d, or lies in the interval between consecutive multiples of d, namely, q⋅d and (q + 1)d (for positive q). In some occasions, it is convenient to carry out the division so that a is as close to an integral ...