@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr: a skos:ConceptScheme .
psr:-XJWLBZKZ-8
  skos:prefLabel "elementary arithmetic"@en, "arithmétique élémentaire"@fr ;
  a skos:Concept ;
  skos:narrower psr:-MGLXLR0P-9 .

psr:-MGLXLR0P-9
  skos:prefLabel "casting out nines"@en, "preuve par neuf"@fr ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Preuve_par_neuf>, <https://en.wikipedia.org/wiki/Casting_out_nines> ;
  dc:modified "2024-10-18"^^xsd:date ;
  a skos:Concept ;
  skos:broader psr:-XJWLBZKZ-8 ;
  dc:created "2023-07-18"^^xsd:date ;
  skos:definition """Casting out nines is any of three arithmetical procedures :
<br/>- Adding the decimal digits of a positive whole number, while optionally ignoring any 9s or digits which sum to a multiple of 9. The result of this procedure is a number which is smaller than the original whenever the original has more than one digit, leaves the same remainder as the original after division by nine, and may be obtained from the original by subtracting a multiple of 9 from it. The name of the procedure derives from this latter property.
<br/>- Repeated application of this procedure to the results obtained from previous applications until a single-digit number is obtained. This single-digit number is called the "digital root" of the original. If a number is divisible by 9, its digital root is 9. Otherwise, its digital root is the remainder it leaves after being divided by 9.
<br/>- A sanity test in which the above-mentioned procedures are used to check for errors in arithmetical calculations. The test is carried out by applying the same sequence of arithmetical operations to the digital roots of the operands as are applied to the operands themselves. If no mistakes are made in the calculations, the digital roots of the two resultants will be the same. If they are different, therefore, one or more mistakes must have been made in the calculations. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Casting_out_nines">https://en.wikipedia.org/wiki/Casting_out_nines</a>)"""@en, """En arithmétique, la preuve par neuf est une technique permettant de vérifier un calcul mental ou effectué « à la main ». Malgré son nom, cette technique n'est pas une preuve mathématique, car elle peut montrer qu'un résultat est erroné, mais si la technique ne trouve pas d'erreur, elle ne permet pas de conclure que le résultat est correct. Le principe général est de refaire le calcul beaucoup plus simplement, en remplaçant chaque nombre supérieur ou égal à 10 par la somme de ses chiffres, de façon répétée.
<br/>Cette technique est en fait une application des propriétés de l'arithmétique modulaire puisqu'elle revient à calculer modulo 9. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Preuve_par_neuf">https://fr.wikipedia.org/wiki/Preuve_par_neuf</a>)"""@fr ;
  skos:inScheme psr: .