distributive law: meaning, definition, pronunciation and examples
Technical TermTechnical/Formal (Academic Mathematics, Computer Science, Logic)
Quick answer
What does “distributive law” mean?
A mathematical law stating that multiplication distributes over addition, expressed as a × (b + c) = a×b + a×c.
Audio
Pronunciation
Definition
Meaning and Definition
A mathematical law stating that multiplication distributes over addition, expressed as a × (b + c) = a×b + a×c.
A fundamental principle in arithmetic, algebra, set theory, and other formal systems where one binary operation distributes over another. It governs how operations interact when applied to sums or unions.
Dialectal Variation
British vs American Usage
Differences
No significant difference in meaning or usage. Spelling follows regional conventions for 'law' within a text. In pedagogy, the mnemonic acronyms FOIL (First, Outer, Inner, Last) and BODMAS/BIDMAS are more common in US/UK contexts respectively, but both reference the distributive property.
Connotations
None beyond its technical meaning.
Frequency
Identical frequency in relevant academic or technical fields. Rare to non-existent in general discourse.
Grammar
How to Use “distributive law” in a Sentence
[Subject: operation/ring/lattice] + [verb: obeys/follows/satisfies] + the distributive law (over [object: another operation])Applying the distributive law to [mathematical expression]Vocabulary
Collocations
Examples
Examples of “distributive law” in a Sentence
verb
British English
- To solve this, you need to *distribute* the 3 across the terms in the brackets.
- First, *multiply out* the expression using the distributive law.
American English
- You should *distribute* the coefficient to each term inside the parentheses.
- Remember to *apply* the distributive property before combining like terms.
Usage
Meaning in Context
Business
Extremely rare. Might appear in highly technical financial modelling discussions.
Academic
Primary context. Found in textbooks and lectures on mathematics, abstract algebra, logic, set theory, and computer science.
Everyday
Virtually never used.
Technical
Core term in mathematics, formal logic, computer architecture (Boolean algebra), and engineering.
Vocabulary
Synonyms of “distributive law”
Vocabulary
Antonyms of “distributive law”
Watch out
Common Mistakes When Using “distributive law”
- Confusing it with the associative or commutative laws. Applying it incorrectly from right to left without checking if the operation is right-distributive. Misapplying it to operations that are not distributive, e.g., exponentiation over addition.
FAQ
Frequently Asked Questions
FOIL is a specific mnemonic for applying the distributive law to the multiplication of two binomials. The distributive law is the general principle behind it.
Yes, because subtraction can be viewed as adding a negative number. So, a × (b - c) = a×b - a×c.
No, it is not. (a + b) / c = a/c + b/c, but a / (b + c) is NOT equal to a/b + a/c. The distributive law only holds in one direction for multiplication over addition/subtraction.
It is a defining axiom in abstract algebraic structures like rings and fields, crucial in set theory (intersection over union), propositional logic, and the design of digital logic gates in computing.
A mathematical law stating that multiplication distributes over addition, expressed as a × (b + c) = a×b + a×c.
Distributive law is usually technical/formal (academic mathematics, computer science, logic) in register.
Distributive law: in British English it is pronounced /dɪˈstrɪb.jʊ.tɪv lɔː/, and in American English it is pronounced /dɪˈstrɪb.jə.t̬ɪv lɑː/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “There are no idioms for this technical term.”
Learning
Memory Aids
Mnemonic
The number outside the parentheses is a 'distributor' who gives copies of itself (multiplies) to each term inside the parentheses before they are added together.
Conceptual Metaphor
FAIR SHARING: The multiplier outside the brackets fairly shares itself with each addend inside the brackets.
Practice
Quiz
In which of these pairs does the first operation distribute over the second?