# distributive property

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## dis·trib·u·tive property

(dĭ-strĭb′yə-tĭv)
The property which states that for certain mathematical operations, applying an operation (such as multiplication) to a set of quantities combined by another operation (such as addition) yields the same result as applying the first operation to each quantity individually and then combining those results by the second operation (in this case addition). Thus 2 × (3 + 4) is equivalent to (2 × 3) + (2 × 4), meaning that multiplication is distributive relative to addition. See also associative property, commutative property.
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For example, when attempting to multiply a single-digit number by a double-digit number, students should be considering other strategies, such as applying the distributive property, and exercising their understanding of place value (e.g., 17 x 6 is 10 x 6 which is 60 and 7 x 6 which is 42 so 17 x 6 is 60 + 42 = 102), which allows them to complete these calculations mentally.
A more complete approach includes first multiplying these binomials using the distributive property as such:
Appendices include: (1) Additional Item Analysis Results; (2) 6th Grade, Teacher Handbook, Properties of Arithmetic: The Distributive Property; (3) Sample Alternative Professional Development Materials; (4) Examples of Professional Development Website Materials; (5) Transfer Measure Items and Sources; (6) Transfer Measure Alignment: Standards and Focal Points; (7) Teacher Surveys; and (8) Interview and Observation Measures.
The distributive property of the histogram presents the distribution of the pixels at the gray level.
Use the distributive property to multiply polynomials.
For example, eight-year-old Isaiah's explanation for 10 x 11 = 110 was, "If 10 x 10 = 100, then one more 10 added to that would be 110." He implicitly uses 10 x (10 + 1) = 10 x 10 + 10 x 1, the distributive property of multiplication over addition.
Partitioning is the recognition that a number can be split into smaller parts--an important concept in effectively using the distributive property of multiplication.
In addition, students in the POWERSOURCE[C] group significantly outperformed control group students on distributive property items and the effect was larger as pretest scores increased.
The distributive property is much more visible, as is the place value of all the numbers involved in the problem:
Specific focus areas were students' ability to reason and explain their knowledge and their understanding and use of arrays, the commutative property, the distributive property, and the inverse relationship between multiplication and division.
To gauge such effects the authors have developed teacher measures that focus on three key mathematical principles that are central to POWERSOURCE: the distributive property, solving equations, and rational number equivalence.
This composition nicely illustrates the distributive property: 10 x 10 (5 + 5) x 10 = (5 x 10) + (5 x 10).

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