# Distributive Property

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The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Distributive Property

(distributive law), the property of multiplication expressed by the identities c(a + b) = ca + cb and (a + b)c = ac + be. In a more general sense, the distributive property of the operator F(x) with respect to some operation x * y is referred to as a property expressed by the equality F(x *y) = F(x) * F(y). For example, the equality (ab)n = anbn shows that the operator of involution is distributive with respect to the operation of multiplication but not with respect to the operation of addition, since, generally speaking, (a + b)nan + bn.

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Algorithms need to be developed through a thorough understanding of the distributive property, gradually increasing the size of the numbers and developing the grid or area representation for multiplication.
A student should be tasked with multiplying several pairs of binomials in this way to support the concept of polynomial multiplication using the distributive property. Through several examples, the student can then start to look for patterns as final answers are recorded:
Knowing the technical vocabulary, such as distributive property, is not as important as realizing how such a property is used.
One property of multiplication that can be powerfully demonstrated with the array, is the distributive property.
The distributive property seems to underlie both their solutions.
In particular, different tasks were chosen in order to present particular concepts in different ways, such as those tasks about the distributive property (a critically important understanding that numbers can be partitioned to make operating with them easier, for example 34 x 7 can be considered as [30 x 7] + [4 x 7]) and inverse relationship (another important understanding that sometimes it is easier and more efficient to use division even though the problem appears to be a multiplication one, for example, 24 x ?
They appropriately applied the distributive property of multiplication to calculate 48 by 11 ("48 by 10 equals 480, plus another 48 equals 528"), and then added 48 more to work out the total number of Smarties if 12 were the average (576), and another 48 to work out the total number if 13 were the average (624).
The distributive property of multiplication is shown whe n fifty eggs are split into sets of 6 x 5 and 4 x 5.
Furthermore, multiplicative thinking involves an understanding of and ability to apply the distributive property of numbers in order to solve problems.
Trevor used the distributive property to find his answer.
Due to the limited scope of this article, we are only able to present findings related to parts of the interview based on the theme of algorithms, the distributive property, and linking to place value.
Their solutions for solving these different recipe problems illustrate an implicit understanding of the distributive property.

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