{"id":10931,"date":"2025-04-02T19:10:09","date_gmt":"2025-04-02T19:10:09","guid":{"rendered":"https:\/\/editionsjfd.com\/backup\/produit\/arithmetique-elementaire-pour-la-formation-des-enseignants-tome-ii-les-nombres-rationnels\/"},"modified":"2025-05-16T19:55:17","modified_gmt":"2025-05-16T19:55:17","slug":"elementary-arithmetic-for-teacher-training-tome-ii-rational-numbers","status":"publish","type":"product","link":"https:\/\/jfd.virtualgx.com\/en\/produit\/arithmetique-elementaire-pour-la-formation-des-enseignants-tome-ii-les-nombres-rationnels\/","title":{"rendered":"Elementary arithmetic for teacher training - Volume II: Rational numbers"},"content":{"rendered":"
\n

In Mesopotamia and Egypt, the first societies in which traces of writing can be found, fractions appeared as part of the social practices of measuring, sharing and distributing material goods.<\/p>\n

Chevallard (1989) emphasizes that: \u00abthe problem is not simply the empirical sharing of goods, as might be achieved by an individual, or a restricted group of individuals - whose action is primary and self-sufficient - but a higher managerial authority that must decide on the terms of sharing, the procedures to be followed, even before the action is carried out\u00bb.<\/p>\n

For the Greeks, the notion of fraction appeared in the context of ratios and proportions, and was not associated with a type of number comparable to today's rational numbers.<\/p>\n

The development of fractions continued in Arab-Islamic civilization and spread to medieval Europe through trade. Towards the end of the Middle Ages, the theory of ratios and proportions evolved towards an arithmetization of these concepts, which encouraged calculations and the development of fraction arithmetic.<\/p>\n

The theory of proportions continued to play a fundamental role in the development of Vi\u00e8te's algebra (in the 17th century), and fractions were linked to division. Towards the end of the 16th century, Stevin succeeded in spreading the use of decimal fractions and decimal numbers, enabling Descartes, a few years later, to base his algebra on the idea of measurement (Kibindigiri, 1995).<\/p>\n

In this text, we present various uses (internal or external to mathematics) of rational numbers, both in their fractional and decimal representations, and their relationship to other mathematical concepts for which this type of number plays a fundamental role.<\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"

Dans la Mésopotamie et dans l’Égypte, premières sociétés dans lesquelles on retrouve des traces d’écritures, les fractions apparaissent dans le cadre de pratiques sociales de mesure, de partage et de distribution de biens matériels. Chevallard (1989) souligne bien que : « le problème n’est pas le seul partage empirique de biens, tel que pourrait le […]<\/p>\n","protected":false},"featured_media":10932,"comment_status":"open","ping_status":"closed","template":"","meta":{"_acf_changed":false},"product_brand":[],"product_cat":[1030],"product_tag":[],"class_list":["post-10931","product","type-product","status-publish","has-post-thumbnail","author-gustavo-barallobres","product_cat-sciences-de-leducation","product_shipping_class-book","first","instock","taxable","shipping-taxable","purchasable","product-type-variable"],"acf":[],"yoast_head":"\nArithm\u00e9tique \u00e9l\u00e9mentaire pour la formation des enseignants - Tome II : Les nombres rationnels - Les \u00c9ditions JFD<\/title>\n<meta name=\"robots\" content=\"noindex, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Arithm\u00e9tique \u00e9l\u00e9mentaire pour la formation des enseignants - Tome II : Les nombres rationnels - Les \u00c9ditions JFD\" \/>\n<meta property=\"og:description\" content=\"Dans la Mésopotamie et dans l’Égypte, premières sociétés dans lesquelles on retrouve des traces d’écritures, les fractions apparaissent dans le cadre de pratiques sociales de mesure, de partage et de distribution de biens matériels. Chevallard (1989) souligne bien que : « le problème n’est pas le seul partage empirique de biens, tel que pourrait le […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/jfd.virtualgx.com\/en\/product\/elementary-arithmetic-for-teacher-training-tome-ii-rational-numbers\/\" \/>\n<meta property=\"og:site_name\" content=\"Les \u00c9ditions JFD\" \/>\n<meta property=\"article:modified_time\" content=\"2025-05-16T19:55:17+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/jfd.virtualgx.com\/wp-content\/uploads\/2025\/04\/10623-preview.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"315\" \/>\n\t<meta property=\"og:image:height\" content=\"472\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/jfd.virtualgx.com\\\/produit\\\/arithmetique-elementaire-pour-la-formation-des-enseignants-tome-ii-les-nombres-rationnels\\\/\",\"url\":\"https:\\\/\\\/jfd.virtualgx.com\\\/produit\\\/arithmetique-elementaire-pour-la-formation-des-enseignants-tome-ii-les-nombres-rationnels\\\/\",\"name\":\"Arithm\u00e9tique \u00e9l\u00e9mentaire pour la formation des enseignants - 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