Fractions
Understand, compare, calculate: from the meaning of a part to the technique of the calculation.
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What this volume contains
A complete manual on fractions: what a fraction measures, how it is read, how it is placed on a number line, how it is compared, how it is added, and how a part of a quantity is taken from it. Every chapter carries its exercises, and every exercise its reasoned answer.
What the volume assumes you already know Able to count, add, subtract, multiply and divide whole numbers, quotient and remainder included, and to share an object into two or into four parts. No knowledge of fractions is assumed.
The contents
- 1Before you beginWhy this book exists, what it covers and what it does not cover, how to work through it, and what it owes to the texts it teaches from.
- 2Chapter 1. Sharing a whole into equal partsA fraction is born of a sharing into equal parts: this chapter settles the reference whole, the part, and the two numbers that write a fraction.
- 3Chapter 2. Counting with partsThe part becomes a counting unit: it is repeated, it goes beyond the whole, and every fraction is bracketed between two consecutive whole numbers.
- 4Chapter 3. A fraction is a numberPlacing a fraction on a number line gives it its standing as a number, and reveals three habits of whole numbers that stop being true.
- 5Chapter 4. Two ways of writing, one numberOne and the same point on the line carries an endless number of writings: this chapter settles equivalent fractions, simplifying, and the move from one denominator to another.
- 6Chapter 5. Comparing two fractionsFour methods of comparison, from the fastest to the most general, and the rule that says which one to use according to what you have in front of you.
- 7Chapter 6. Adding and subtractingOnly parts of the same size are added: this chapter settles addition over equal denominators, then the move to a common denominator.
- 8Chapter 7. Taking a fraction of a quantityA fraction acts on a quantity: this chapter settles the calculation of a fraction of a number and the multiplication of a fraction by a whole number.
- 9Chapter 8. Decimal fractions and decimal notationFractions with denominator ten, one hundred or one thousand give decimal notation: this chapter makes the move in both directions.
- 10Chapter 9. Solving problems with fractionsRecognising the meaning at work, estimating before calculating, then checking: the method that makes the eight previous chapters usable.
- 11Answers to the exercisesAll the answers of the volume, in the order of the chapters: what we are looking for, what we use, why, and then the result.
- 12GlossaryEvery technical word used in this volume, defined in the terms of the book and arranged in alphabetical order.
- 13Reference tablesFour tables: the names of the parts, the common fractions with their decimal notation, the first multiples, and the place of this volume in four French-language school systems.
- 14SourcesThe public documents this volume rests on, with their address and the date on which each one was consulted.
The volume in detail
- Shelf
- Mathematics
- Stage in the progression
- Foundations
- What the volume assumes you already know
- Able to count, add, subtract, multiply and divide whole numbers, quotient and remainder included, and to share an object into two or into four parts. No knowledge of fractions is assumed.
- Chapters
- 14
- Estimated pages in print
- ≈ 89
- Formats served
- Reading online
- Languages published
- 2
- Licence of the text
- CC BY 4.0
- Checked on
The caveat about mistakes
Every volume from this house is read by someone who did not write it. Double checking reduces mistakes, it does not remove them: this volume may therefore still contain some. Report what you find to labibliotheque@odersa.org, with the chapter and the exact sentence; ODERSA corrects it, redates the volume and says what changed. This work informs, and it replaces neither an official curriculum, nor a teacher, nor a professional in the field: it says how fractions work, it prescribes no progression to a class or to a school.
The colophon
- Written by
- L'ODERSA
- Checked by
- An ODERSA reader who did not write this volume: the reasoning taken up again chapter by chapter, and the exercises worked afresh with nothing but the knowledge the book has already given.
- Typeset
- Typeset in Source Serif 4 and Public Sans, two typefaces under the OFL, by the house generator, with no outside dependency.