Associative laws
The associative laws are a set of rules in mathematics that govern how to group or associate numbers or mathematical operations
The associative laws are a set of rules in mathematics that govern how to group or associate numbers or mathematical operations. These laws apply to both addition and multiplication.
For addition, the associative law states that the sum of three or more numbers is the same regardless of how the numbers are grouped. In other words, if you have three numbers a, b, and c, it doesn’t matter if you add (a + b) first and then add c, or if you add a to the sum of b and c. Mathematically, this can be expressed as:
(a + b) + c = a + (b + c)
For example, consider the numbers 2, 3, and 4. Using the associative law of addition, we can write:
(2 + 3) + 4 = 5 + 4 = 9
On the other hand:
2 + (3 + 4) = 2 + 7 = 9
The result is the same, demonstrating the associative property of addition.
Similarly, for multiplication, the associative law states that the product of three or more numbers is the same regardless of how the numbers are grouped. Mathematically, this can be represented as:
(a * b) * c = a * (b * c)
Consider the numbers 2, 3, and 4. Using the associative law of multiplication, we can write:
(2 * 3) * 4 = 6 * 4 = 24
On the other hand:
2 * (3 * 4) = 2 * 12 = 24
Again, the result is the same, demonstrating the associative property of multiplication.
The associative laws are particularly useful when dealing with expressions involving multiple operations, as they allow us to rearrange or group terms in any way we desire without changing the value of the expression.
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