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词条 Multiple (mathematics)
释义

  1. Examples

  2. Properties

  3. References

  4. See also

{{wiktionary|multiple|submultiple}}

In science, a multiple is the product of any quantity and an integer.[1][2][3] In other words, for the quantities a and b, we say that b is a multiple of a if b = na for some integer n, which is called the multiplier. If a is not zero, this is equivalent to saying that b/a is an integer.[4][5][6]

In mathematics, when a and b are both integers, and b is a multiple of a, then a is called a divisor of b. One says also that a divides b. If a and b are not integers, mathematicians prefer generally to use integer multiple instead of multiple, for clarification. In fact, multiple is used for other kinds of product; for example, a polynomial p is a multiple of another polynomial q if there exists third polynomial r such that p = qr.

{{anchor|Submultiple}}In some texts, "a is a submultiple of b" has the meaning of "b being an integer multiple of a".[7][8] This terminology is also used with units of measurement (for example by the BIPM[9] and NIST[10]), where a submultiple of a main unit is a unit, named by prefixing the main unit, defined as the quotient of the main unit by an integer, mostly a power of 103. For example, a millimetre is the 1000-fold submultiple of a metre.[9][10] As another example, one inch may be considered as a 12-fold submultiple of a foot, or a 36-fold submultiple of a yard.

Examples

14, 49, –21 and 0 are multiples of 7, whereas 3 and –6 are not. This is because there are integers that 7 may be multiplied by to reach the values of 14, 49, 0 and –21, while there are no such integers for 3 and –6. Each of the products listed below, and in particular, the products for 3 and –6, is the only way that the relevant number can be written as a product of 7 and another real number:

  • is a rational number, not an integer
  • is a rational number, not an integer.

Properties

  • 0 is a multiple of everything ().
  • The product of any integer and any integer is a multiple of . In particular, , which is equal to , is a multiple of (every integer is a multiple of itself), since 1 is an integer.
  • If and are multiples of then and are also multiples of .

References

1. ^{{MathWorld|urlname=Multiple|title=Multiple}}
2. ^WordNet lexicon database, Princeton University
3. ^WordReference.com
4. ^The Free Dictionary by Farlex
5. ^Dictionary.com Unabridged
6. ^Cambridge Dictionary Online
7. ^{{cite web |url=https://www.merriam-webster.com/dictionary/submultiple |title=Submultiple |author= |date=2017 |website=Merriam-Webster Online Dictionary |publisher=Merriam-Webster |access-date=2017-02-01}}
8. ^{{cite web |url=https://en.oxforddictionaries.com/definition/us/submultiple |title=Submultiple |author= |date=2017 |website=Oxford Living Dictionaries |publisher=Oxford University Press |access-date=2017-02-01}}
9. ^1 {{SIbrochure8th}}
10. ^1 {{cite web |url=http://physics.nist.gov/Pubs/SP811/sec04.html |title=NIST Guide to the SI}} Section 4.3: Decimal multiples and submultiples of SI units: SI prefixes

See also

  • Unit fraction
  • Ideal (ring theory)
  • Decimal and SI prefix
  • Multiplier (linguistics)
{{DEFAULTSORT:Multiple (Mathematics)}}

2 : Arithmetic|Multiplication
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