Property indicating a special way in which multiplication is applied to addition of two (or more) numbers. For example, 5 x 23 = 5 x (20 + 3) = 5 x 20 + 5 x 3 = 100 + 15 = 115.
An algebraic property of how two operations relate to one another. The statements ( + ) = ab + ac and ( + ) = ba + ca describe how multiplication distributes over addition.
the product of a number and a sum is equal to the sum of the products of the number with each of the addends in the sum. That is, for all real numbers a, b, and in a given set, ( b + c) = ab + ac. For example, 4(45 + 8) = (4 • 45) + (4 • 8).
for any real numbers a, b, and x, x(a + b) = ax + bx.
adding two numbers and then multiplying by another yields the same result as multiplying each one by the number and then adding the products. i.e. a(b + c) = ab + ac, or (a+b)c = ac + bc. E.g. 2(3 + 5) = 2x3 + 2x5.
Summing two numbers and then multiplying by another number yields the same value as multiplying both values by the other value and then adding. In mathematical terms, for all real numbers a, b, and c, a(b+c) = ab+ac
When factor is a sum, multiplying each addend before adding does no change the product.
When one of the factors of a product is a sum, multiplying each addend before adding does not change the product. For example: 6x (2+3)=(6x2)+(6x3)
A property which establishes a relationship between multiplication and addition such that multiplication distributes across the addition [i.e., a(b+c) = ab + ac].
A property that relates two operations on numbers, usually multiplication and addition, or multiplication and subtraction. Distributive property of multiplication over addition: a * (x + y) = (a * x) + (a * Distributive property of multiplication over subtraction: a * (x – y) = (a * x) – (a * This property gets its name because it “distributes” the factor outside the parentheses over the two terms within the parentheses.
The process of distributing a number on the outside of the parentheses to each number on the inside; a(b + c) = ab + ac.
For any numbers a,b, and c, a(b + c) = ab + ac and a(b - c) = ab - bc.
A property of real numbers that states that the product of the sum or difference of two numbers is the same as the sum or difference of their products. Example: 6x(2+3)=(6x2)+(6x3) -- Multiplication over addition. Example 2: 5 x 23 = 5 x (20 + 3) = 5 x 20 + 5 x 3 = 100 + 15 = 115.
