Elementary arithmetic, with brief notices of its history... by Robert Potts.

21 to 3 and 6 factors each equal to 5. Sometimes 34x50 is more briefly denoted by 34.56. 7. PROB. To find the quotient of two numbers which consist of one or of two digits. Let it be required to find the quotient arising from 15 divided by 5. The quotient denotes the number of times the divisor is contained in, or can be subtracted from, the dividend. Let 5 be subtracted successively from 15. First. 5 subtracted from 15 leaves 10. Secondly. 5 from 10 leaves 5. Thirdly. 5 from 5 leaves 0. So that 5 can be subtracted 3 times from 15, or 5 is; contained 3 times in 15, or 15 divided by 5 gives 3 for the quotient. This will also appear from the fact that division being the reverse of multiplication, since 3 times a is 15, it follows that 5 is contained 3 times in 15. The following statements exhibit how many times each of the nine digits is exactly contained in numbers consisting of one or two digits: 1 divided by 1 gives 1 2,,, 2 3,,,, 3 4,,,, 4 5,,,, 5 6,,,, 6 7,,,, 8,,,, 8 9,,,, 9 4 divided by 4 gives 1 8,,,, 2 12,,,, 3 16,,,, 4 20,,, 5 24,,,, 6 28,,,, 7 32,,,, 8 36,,,, 9 7 divided by 7 gives 1 14,,,, 2 21,,,, 3 28,,,, 4 35,,,, 5 42,,,, 6 49,, 7 56,,,, 8 63,,,, 9 2 divided by 2 gives 1 4,,,, 2 6,,,, 3 8,,,, 4 10,,,, 5 12,,, 6 14,,, 7 16,,,, 8 18, 9 5 divided by 5 gives 1 10,,,, 2 15,,,, 3 20,,,, 4 25,,,, 5 30,,,, 6 35,,,, 7 40,,,, 8 45,,,, 9 8 divided by 8 gives 1 16,,,, 2 24,,,, 3 32,,,, 4 40,,,, 5 48,,,, 6 56,,, 7 64,,,, 8 72,,, 9 3 divided by 3 gives 1 6,,,, 2 9,,,, 12,,,, 4 15,,,, 5 18,,,, 6 21,,,, 7 24,,,, 8 27,,,, 9 6 divided by 6 gives 1 12,,,, 2 18,,,, 3 24,,,, 4 30,,,, 5 36,,,, 6 42,,,, 7 48,,,, 8 54,,,, 9 9 divided by 9 gives 1 18,,,, 2 27,,,, 3 36,,,, 4 45,,, 5 54,,,, 6 63,,,, 7 72,,,, 8 81,,,, 9 8. PROB. To divide any number by a number of one digit. The process depends on the following Axiom. One number is contained in another as many times as the former is contained in the several parts into which the latter can be divided.

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Title
Elementary arithmetic, with brief notices of its history... by Robert Potts.
Author
Potts, Robert, 1805-1885.
Canvas
Page 8
Publication
London,: Relfe bros.,
1876.
Subject terms
Arithmetic

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"Elementary arithmetic, with brief notices of its history... by Robert Potts." In the digital collection University of Michigan Historical Math Collection. https://name.umdl.umich.edu/abu7012.0001.001. University of Michigan Library Digital Collections. Accessed June 7, 2025.
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