fraction
Let an agent explain fractions and their arithmetic, distinguish fractions as notation from rational numbers as values, support learning and calculation, and route specialised uses to their entries.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify
Researched by: Claude
Purpose and description
Let an agent explain fractions and their arithmetic, distinguish fractions as notation from rational numbers as values, support learning and calculation, and route specialised uses to their entries.
A number expressing a part of a whole or a ratio of two integers, written as a numerator over a denominator, such as three quarters; fractions represent rational numbers, are taught as a foundation of arithmetic, and appear as proper, improper and mixed forms, in unit subdivisions such as monetary subunits, and in notation across mathematics.
What it is for: Expressing parts and ratios exactly.
It can be explain notation and kinds of fraction; perform and explain fraction arithmetic; convert between fractions, decimals and percentages; support teaching and common misconceptions.
Distinguishing features
Exact representation of ratios
Notation distinct from value
Equivalent forms with different denominators
Foundation of arithmetic
What it looks like
Not visible in itself; written as one number over another with a bar or slash.
How it is recognised
Numerator over denominator
Proper, improper and mixed forms
A ratio, a decimal and a percentage express related ideas differently
Related models
is a kind of - a way of writing numbers
represents - the value
is related to - another representation
is related to - a comparison of quantities
In practice
Families and kinds
proper and improper fractions
mixed numbers
unit fractions
equivalent and simplified fractions
continued fractions and generating fractions
fractions in units such as monetary subunits
Standards and regulation
Mathematics curricula and standards for teaching fractions
ISO 80000-2 notation conventions
Failure modes and hazards
Adding numerators and denominators separately
Confusing fraction notation with division or ratio contexts
Rounding errors when converting to decimals
Also called
+2
Where this came from
wikidata · CC0 1.0
Also registered as vr.tr.fraction-quantity
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.
Concept What a fraction is.
Definition.
Definition
Definition.
Definition
Definition.
- What does a fraction represent, and how do numerator and denominator work? definition
- Is the question about fraction notation, rational numbers or ratios? boundary
Kinds
Kinds.
Kinds
Kinds.
- What kinds of fractions exist, and how are they converted between forms? definition
- Which entry fits rational numbers? action
Compute Arithmetic.
Computation.
Operations
Operations.
Operations
Operations.
- How are fractions added, subtracted, multiplied, divided and simplified? action
- What is the result for the calculation in question? measurement
Conversion
Conversion.
Conversion
Conversion.
- How are fractions converted to decimals and percentages, and when is exactness lost? action
- Which entry fits decimals? action
Learn Teaching.
Education.
Teaching
Teaching fractions.
Teaching
Teaching.
- How are fractions taught, and which models and representations help? provenance
- Which references are standard? provenance
Misconceptions
Misconceptions.
Misconceptions
Misconceptions.
- Which misconceptions are common, and how are they addressed? provenance
- Which entry fits mathematics education? action
Context History and uses.
Context.
History
History.
History
History.
- How did fraction notation develop from Egyptian unit fractions to modern notation? provenance
- Which entry fits the history of mathematics? action
Uses
Uses.
Uses
Uses.
- How are fractions used in measurement, music, finance and units? provenance
- Which entry fits a specific use? action
What the second pass must settle
- Should rational number be the primary entry?
- How should curricula be linked?
- The registry entry has merged aliases for monetary subunits; should they be split off?