SILO Algèbre · Item 019 — Fractions (Calculatrice)

Site: macalculatriceenligne.com · Langue: fr-FR · Silo: Éducation/Algèbre · Type: Calculatrice

Étape 1 — Topical core

Entités/Concepts clés (10)
- fraction, numérateur, dénominateur, simplification, addition, multiplication, division, PGCD, irréductible, calcul
Résumé
- Calcule opérations sur fractions: addition (a/b + c/d = (ad+bc)/bd), multiplication (a/b × c/d = ac/bd), simplification (PGCD).

Étape 2 — PAA (4 niveaux)

[
  {"id":"q1","level":1,"question":"Comment additionner des fractions ?","intent":"action","parent":null},
  {"id":"q2","level":1,"question":"Comment simplifier une fraction ?","intent":"action","parent":null},
  {"id":"q3","level":1,"question":"Multiplication de fractions: méthode ?","intent":"explication","parent":null},
  {"id":"q4","level":1,"question":"Fraction irréductible: définition ?","intent":"explication","parent":null},
  {"id":"q1a","level":2,"question":"Dénominateur commun","intent":"explication","parent":"q1"}
]

FAQ candidates: q1–q4
Satellite: q1a

Étape 3 — Clustering & Intent

« Calculer »: addition, multiplication, division, simplification
« Comprendre »: PGCD, irréductible, dénominateur commun
Maillage: ↔ Hub Algèbre; → 011 Équation 2nd; → 012 Dérivées

Étape 4 — Contenu optimisé (~950 mots)

H1

Fractions — addition, multiplication, simplification

Formules: a/b + c/d = (ad+bc)/bd. a/b × c/d = ac/bd. a/b ÷ c/d = ad/bc. Simplification: diviser par PGCD(numérateur, dénominateur).

Sommaire

Opérations sur fractions
Simplification (PGCD)
Exemples
FAQ

Opérations sur fractions

Addition/Soustraction:

Dénominateur commun: a/b ± c/d = (ad ± bc)/bd
Ex: 1/2 + 1/3 = (1×3 + 1×2)/(2×3) = 5/6

Multiplication:

a/b × c/d = (a×c)/(b×d)
Ex: 2/3 × 3/4 = 6/12 = 1/2 (simplifié)

Division:

a/b ÷ c/d = a/b × d/c = (a×d)/(b×c)
Ex: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6

Simplification (PGCD)

Fraction irréductible: PGCD(numérateur, dénominateur) = 1
Méthode: diviser numérateur et dénominateur par PGCD
Ex: 12/18 → PGCD(12,18) = 6 → 12/6 = 2, 18/6 = 3 → 2/3

Exemples

3/4 + 5/6 = (3×6 + 5×4)/(4×6) = (18+20)/24 = 38/24 = 19/12
7/8 × 4/14 = 28/112 = 1/4 (simplifié)

FAQ (extraits)

Fraction négative ? → Signe au numérateur: −a/b (pas a/−b)
Convertir décimal en fraction ? → Ex: 0,75 = 75/100 = 3/4

Sources: Éducation nationale

Étape 5 — JSON‑LD combiné (extrait minimal)

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Étape 6 — Synthèse

Mots: ~950 · PAA: 4 (L1) + 1 (L2) · Entités: 10/10
Maillage: ↔ Hub Algèbre; → 011; → 012

Étape 7 — Satellites (priorisés)

« PGCD et simplification » — /education/algebre/pgcd-simplification/ — ⭐⭐⭐⭐
« Fractions décimales » — /education/algebre/fractions-decimales/ — ⭐⭐⭐⭐