Associative
The term “associative” in math refers to the property that some mathematical operations possess
The term “associative” in math refers to the property that some mathematical operations possess. Specifically, an operation is said to be associative if the grouping of the numbers or expressions being operated upon does not change the result.
To understand this concept better, let’s consider addition and multiplication as examples of associative operations.
Addition Example:
For any three numbers a, b, and c, the associative property of addition states that:
(a + b) + c = a + (b + c).
In other words, it doesn’t matter if we first add the numbers a and b and then add the result to c, or if we first add b and c and then add the result to a. The final sum will be the same in either case.
For instance, let’s take the numbers 2, 3, and 4. We can perform the addition in two ways:
(2 + 3) + 4 = 5 + 4 = 9
2 + (3 + 4) = 2 + 7 = 9
As you can see, regardless of how we grouped the numbers for addition, the sum remains the same.
Multiplication Example:
Similarly, for any three numbers a, b, and c, the associative property of multiplication states that:
(a * b) * c = a * (b * c).
Just like with addition, it doesn’t matter if we first multiply the numbers a and b and then multiply the result by c, or if we first multiply b and c and then multiply the result by a. The final product will be the same in either case.
Let’s consider the numbers 2, 3, and 4 for multiplication:
(2 * 3) * 4 = 6 * 4 = 24
2 * (3 * 4) = 2 * 12 = 24
In both cases, the result is 24, showing that the multiplication is associative.
It’s worth noting that not all operations are associative. For example, subtraction and division are not associative operations.
More Answers:
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