Meaning & use
associative property
Last updated
Meanings
nounsingularmathematics
The rule that the way numbers are grouped in addition or multiplication does not change the result, so (a + b) + c equals a + (b + c).
Grammar: Usually 'the associative property', often followed by of addition or multiplication.
Patterns
- the associative property of addition
- the associative property of multiplication
The associative property of addition lets you add 3 + 4 first or 4 + 5 first.
Students used the associative property to simplify the multiplication.
Subtraction does not have the associative property.
nounsingulartechnical
More generally, a rule in algebra stating that an operation gives the same result however the terms are grouped.
Grammar: Used for operations in general: the operation has the associative property.
Matrix multiplication has the associative property, even though order matters.
Mathematicians check whether a new operation has the associative property.
A group is required to satisfy the associative property.
Common combinations
- the associative property of addition
- The associative property of addition makes mental arithmetic easier.
- apply the associative property
- Apply the associative property to regroup the terms.
- use the associative property
- We can use the associative property to speed up this sum.
- lack the associative property
- Subtraction and division lack the associative property.
- the associative property of multiplication
- The associative property of multiplication works for any three numbers.
Synonyms and how they differ
- associativity
- Is the more technical and shorter term used in higher mathematics for the same idea.
- grouping rule
- Is an informal description that teachers sometimes use for children.
- regrouping rule
- Is a plain-language description of the same idea.
Word family
- associative adjective
- Relating to the associative rule, or to association.
- associativity noun
- The quality of being associative.
- associate verb
- To connect ideas or things.
Commonly confused: associative property or commutative property?
associative property vs commutative property
Says the order of numbers does not matter, while the associative property says the grouping does not matter.
Practice
Which equation shows the associative property of addition?
Choose one answer.
The associative property changes grouping, as in the first option; the second shows the commutative property, the third the identity property and the fourth the distributive property.
Make it your own
Write a sentence using “associative property”, then check it and compare it with the examples above.