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Cycle 3

Cours : Cycle 3 > Chapitre 6 

Leçon 6: Décomposer une fraction
Mathématiques
Cycle 3
Nombres et calculs - Les fractions
Décomposer une fraction
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Décomposer une fraction - ce qu'il faut comprendre et savoir

Google Classroom
Revoir comment on décompose une fraction en somme de plusieurs fractions et faire quelques exercices d'application

Décomposer une fraction

Pour décomposer un nombre, on le sépare en "plus petits morceaux".
Les fractions, comme les nombres entiers, peuvent être décomposées de différentes façons.

Exemple 1 : avec un schéma

Décomposer start fraction, 5, divided by, 9, end fraction.
A tape diagram divided into 9 equal parts. Five parts are shaded.
start fraction, 5, divided by, 9, end fraction peut se décomposer en start color #e07d10, start fraction, 2, divided by, 9, end fraction, end color #e07d10, plus, start color #1fab54, start fraction, 3, divided by, 9, end fraction, end color #1fab54 :
A tape diagram divided into 9 equal parts with 5 parts shaded. The first two parts are shaded orange. The next three parts are shaded green.
start color #e07d10, start fraction, 2, divided by, 9, end fraction, end color #e07d10, plus, start color #1fab54, start fraction, 3, divided by, 9, end fraction, end color #1fab54, equals, start fraction, start color #e07d10, 2, end color #e07d10, plus, start color #1fab54, 3, end color #1fab54, divided by, 9, end fraction, equals, start fraction, 5, divided by, 9, end fraction
Mais start fraction, 5, divided by, 9, end fraction peut aussi être décomposée en start color #7854ab, start fraction, 1, divided by, 9, end fraction, end color #7854ab, plus, start color #e84d39, start fraction, 2, divided by, 9, end fraction, end color #e84d39, plus, start color #01a995, start fraction, 2, divided by, 9, end fraction, end color #01a995:
A tape diagram divided into 9 equal parts with 5 parts shaded. The first part is shaded purple. The next two parts are shaded pink. The next two parts are shaded green.
start color #7854ab, start fraction, 1, divided by, 9, end fraction, end color #7854ab, plus, start color #e84d39, start fraction, 2, divided by, 9, end fraction, end color #e84d39, plus, start color #01a995, start fraction, 2, divided by, 9, end fraction, end color #01a995, equals, start fraction, start color #7854ab, 1, end color #7854ab, plus, start color #e84d39, 2, end color #e84d39, plus, start color #01a995, 2, end color #01a995, divided by, 9, end fraction, equals, start fraction, 5, divided by, 9, end fraction

Exemple 2 : avec la demi-droite graduée

Décomposer start fraction, 6, divided by, 4, end fraction.
A number line labeled 0 to 2 with tick marks every one-fourth unit. Tick marks 0, 1, and 2 are labeled. A point labeled six-fourths appears two tick marks to the right of 1.
On peut décomposer start fraction, 6, divided by, 4, end fraction en start color #7854ab, start fraction, 1, divided by, 4, end fraction, end color #7854ab, plus, start color #7854ab, start fraction, 1, divided by, 4, end fraction, end color #7854ab, plus, start color #7854ab, start fraction, 1, divided by, 4, end fraction, end color #7854ab, plus, start color #7854ab, start fraction, 1, divided by, 4, end fraction, end color #7854ab, plus, start color #7854ab, start fraction, 1, divided by, 4, end fraction, end color #7854ab, plus, start color #7854ab, start fraction, 1, divided by, 4, end fraction, end color #7854ab :
A number line labeled 0 to 2 with tick marks every one-fourth unit. Tick marks 0, 1, and 2 are labeled. A point labeled six-fourths appears two tick marks to the right of 1. An arrow begins at 0 and moves right one tick mark six times, ending two tick marks to the right of 1. The arrow is labeled one-fourth plus one-fourth plus one-fourth plus one-fourth plus one-fourth plus one-fourth.
start color #7854ab, start fraction, 1, divided by, 4, end fraction, end color #7854ab, plus, start color #7854ab, start fraction, 1, divided by, 4, end fraction, end color #7854ab, plus, start color #7854ab, start fraction, 1, divided by, 4, end fraction, end color #7854ab, plus, start color #7854ab, start fraction, 1, divided by, 4, end fraction, end color #7854ab, plus, start color #7854ab, start fraction, 1, divided by, 4, end fraction, end color #7854ab, plus, start color #7854ab, start fraction, 1, divided by, 4, end fraction, end color #7854ab, equals, start fraction, start color #9d38bd, 1, end color #9d38bd, plus, start color #9d38bd, 1, end color #9d38bd, plus, start color #9d38bd, 1, end color #9d38bd, plus, start color #9d38bd, 1, end color #9d38bd, plus, start color #9d38bd, 1, end color #9d38bd, plus, start color #9d38bd, 1, end color #9d38bd, divided by, 4, end fraction, equals, start fraction, 6, divided by, 4, end fraction
Mais on peut aussi décomposer start fraction, 6, divided by, 4, end fraction en start color #11accd, start fraction, 3, divided by, 4, end fraction, end color #11accd, plus, start color #11accd, start fraction, 3, divided by, 4, end fraction, end color #11accd :
A number line labeled 0 to 2 with tick marks every one-fourth unit. Tick marks 0, 1, and 2 are labeled. A point labeled six-fourths appears two tick marks to the right of 1. An arrow begins at 0 and moves right three tick marks and then moves right three tick marks, ending two tick marks to the right of 1. The arrow is labeled three-fourths plus three-fourths.
start color #11accd, start fraction, 3, divided by, 4, end fraction, end color #11accd, plus, start color #11accd, start fraction, 3, divided by, 4, end fraction, end color #11accd, equals, start fraction, start color #11accd, 3, end color #11accd, plus, start color #11accd, 3, end color #11accd, divided by, 4, end fraction, equals, start fraction, 6, divided by, 4, end fraction

À vous !

Exercice 1
  • Actuelle
Laquelle de ces sommes est égale à start fraction, 14, divided by, 10, end fraction, space, question mark
Choisissez toutes les réponses possibles :

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