Properties of Multiplication of Integers Multiplication of two integers is a specific operation that involves multiplying the two integers' numerical values...
Properties of Multiplication of Integers
Multiplication of two integers is a specific operation that involves multiplying the two integers' numerical values. This operation follows specific rules and principles that determine the result of the multiplication.
Associative Property:
(a * b) * c = a * (b * c)
This property states that the order in which the numbers are multiplied does not affect the result. For example, 3 * (4 * 5) = (3 * 4) * 5, which is equal to 60.
Distributive Property:
a * (b + c) = (a * b) + (a * c)
This property states that the multiplication of a number with a sum can be calculated by multiplying the number with each addend and then adding the results together. For example, 3 * (4 + 5) = 3 * 9 = 27.
Cancellation Property:
a * (b - c) = a * b - a * c
This property states that the multiplication of a number with a difference can be calculated by multiplying the number with the addend and then subtracting the result from the original number. For example, 3 * (4 - 5) = 3 * (-1) = -3.
Identity Property:
The identity property states that the multiplication of any number with itself is equal to the original number. For example, 3 * 3 = 9.
Example:
Let's apply these properties to the following multiplication:
(2 + 3) * 4 = 2 * 4 + 3 * 4
= 8 + 12
= 20
Therefore, 2 + 3 * 4 = 20