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Meaning & use

distributive property

noun·Academicmathematics

Last updated

UK/dɪˈstrɪbjətɪv ˈprɒpəti/
US/dɪˈstrɪbjətɪv ˈprɑːpərti/

Meaning

  1. nounsingularmathematics

    The rule that multiplying a sum by a number gives the same result as multiplying each part separately and then adding.

    Grammar: Usually used with 'the'; it is a singular noun and takes a singular verb.

    Patterns

    • the distributive property of multiplication over addition
    • use the distributive property
    • apply the distributive property

    The distributive property says that 3 × (4 + 5) = 3 × 4 + 3 × 5.

    We used the distributive property to expand 2(x + 7) into 2x + 14.

    Understanding the distributive property makes it easier to do mental math.

Common combinations

the distributive property of multiplication over addition
The distributive property of multiplication over addition lets you multiply a sum by a factor.
use the distributive property
You can use the distributive property to simplify 5(2x + 3).
apply the distributive property
Apply the distributive property first, then combine like terms.
the distributive law
In some textbooks, the distributive property is called the distributive law.

Synonyms and how they differ

distributive law
A more formal term used in some textbooks, especially in algebra and logic.

Word family

distribute verb
To multiply a term across the parts inside parentheses.
distribution noun
The act of spreading something out, as in the distribution of multiplication over addition.
distributive adjective
Relating to distribution; used in phrases like 'distributive property'.

Commonly confused: distributive property or commutative property? distributive property or associative property?

distributive property vs commutative property

The commutative property says order does not matter (a + b = b + a), while the distributive property connects multiplication and addition.

distributive property vs associative property

The associative property says grouping does not matter ((a + b) + c = a + (b + c)), which is different from distributing a factor.

Practice

Which expression shows the distributive property applied to 4(x + 2)?

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