distributive property: meaning, definition, pronunciation and examples
C1Academic/Technical (mathematics)
Quick answer
What does “distributive property” mean?
A fundamental mathematical principle stating that multiplying a number by a sum of numbers gives the same result as multiplying each addend separately and then adding the products.
Audio
Pronunciation
Definition
Meaning and Definition
A fundamental mathematical principle stating that multiplying a number by a sum of numbers gives the same result as multiplying each addend separately and then adding the products.
A concept used primarily in arithmetic and algebra, expressed as a(b + c) = ab + ac, which allows for the simplification and reorganization of calculations. It can extend to other mathematical structures like sets or matrices that follow similar distribution rules.
Dialectal Variation
British vs American Usage
Differences
No lexical or conceptual differences. Spelling of related words follows standard conventions ('property' vs. no difference). The term is identical in both varieties.
Connotations
None beyond its strict mathematical definition.
Frequency
Frequency is identical, as it is a core technical term in the global mathematical lexicon.
Grammar
How to Use “distributive property” in a Sentence
The distributive property [allows/proves/states] that X.We [apply/use] the distributive property to [simplify/expand] Y.Vocabulary
Collocations
Examples
Examples of “distributive property” in a Sentence
verb
British English
- You must distribute the multiplication over the terms inside the brackets.
American English
- Distribute the 3 across the terms in the parentheses to simplify.
adjective
British English
- The distributive law is essential for expanding algebraic expressions.
American English
- Understanding the distributive principle is key to factoring polynomials.
Usage
Meaning in Context
Business
Virtually never used in standard business discourse.
Academic
Primary context. Used in mathematics textbooks, lectures, and problem-solving from secondary school to university level.
Everyday
Extremely rare outside of helping children with maths homework.
Technical
Core term in pure and applied mathematics, computer science (in Boolean algebra), and formal logic.
Vocabulary
Synonyms of “distributive property”
Watch out
Common Mistakes When Using “distributive property”
- Applying it incorrectly to other operations, e.g., thinking a/(b + c) = a/b + a/c.
- Confusing it with the associative or commutative properties.
- Writing 'distributive property' as 'distributive *propriety*' (spelling error).
FAQ
Frequently Asked Questions
FOIL (First, Outer, Inner, Last) is a specific mnemonic for applying the distributive property to multiply two binomials. The distributive property is the general rule that FOIL is based on.
Yes. Since subtraction is the same as adding a negative number, the property holds: a(b - c) = ab - ac.
Only in one direction: (a + b) / c = a/c + b/c. It does NOT work as a / (b + c) = a/b + a/c. This is a very common mistake.
It is a foundational tool for simplifying algebraic expressions, solving equations, factoring polynomials, and is a defining axiom in more advanced algebraic structures like rings and fields.
A fundamental mathematical principle stating that multiplying a number by a sum of numbers gives the same result as multiplying each addend separately and then adding the products.
Distributive property is usually academic/technical (mathematics) in register.
Distributive property: in British English it is pronounced /dɪˈstrɪb.jə.tɪv ˈprɒp.ə.ti/, and in American English it is pronounced /dɪˈstrɪb.jə.t̬ɪv ˈprɑː.pɚ.t̬i/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
The number outside the parentheses is like a postman; he must DISTRIBUTE his letters (the multiplication) to each house inside the parentheses separately.
Conceptual Metaphor
OPERATIONS ARE AGENTS (Multiplication acts as an agent that distributes itself across a sum).
Practice
Quiz
Which of the following correctly demonstrates the distributive property?