Meaning & use
the associative property
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Meaning
nounsingularmathematics
In math, the rule that when you add or multiply three or more numbers, the way you group them does not change the result.
Grammar: Used with 'the'; it is a singular noun and takes a singular verb: 'The associative property holds for addition.'
Patterns
- the associative property of addition
- the associative property of multiplication
- the associative property holds
The associative property tells us that (2 + 3) + 4 equals 2 + (3 + 4).
Because of the associative property, we can add 5 + 7 + 3 in any order we like.
Multiplication also has the associative property: (2 × 3) × 4 = 2 × (3 × 4).
Common combinations
- the associative property of addition
- The associative property of addition lets you group addends in different ways.
- the associative property of multiplication
- The associative property of multiplication means (a × b) × c = a × (b × c).
- the associative property holds
- The associative property holds for both addition and multiplication.
Synonyms and how they differ
- associativity
- A shorter, more technical term used mainly in advanced math; 'the associative property' is the full phrase taught in school.
Word family
- associative adjective
- Describing an operation that follows this rule.
- associate verb
- To connect or group things together in your mind.
Commonly confused: the associative property or the commutative property?
the associative property vs the commutative property
The commutative property says you can swap the order of numbers (a + b = b + a). The associative property is about regrouping, not swapping.
Practice
Which equation shows the associative property?
Choose one answer.
The associative property involves regrouping with parentheses: (2 + 3) + 4 = 2 + (3 + 4). Option 0 shows the commutative property, option 1 shows the identity property, and option 3 shows the zero property.
Make it your own
Write a sentence using “the associative property”, then check it and compare it with the examples above.