Final answer:
The associative property applies to addition and multiplication, but not to subtraction or division. An example of this property for addition is (1 + 2) + 3 equals 1 + (2 + 3), which both result in 6. However, this property doesn't hold for subtraction, as shown by the different results of (10 - 5) - 2 and 10 - (5 - 2).
Step-by-step explanation:
The associative property in mathematics states that the way in which numbers are grouped in an operation does not change their result, but this property only works with addition and multiplication, not with subtraction or division. For addition, an example of the associative property would be: (1 + 2) + 3 = 1 + (2 + 3). Both expressions will result in 6, no matter how the numbers are grouped. However, subtraction is not associative, meaning that changing the grouping of numbers can change the result. To demonstrate this, consider the expression (10 - 5) - 2 which is not equal to 10 - (5 - 2). The first calculation gives you 3, while the second gives you 7, showing subtraction's non-associative nature.
When you subtract numbers, you can think of it as adding the additive inverse (the opposite) of the number being subtracted. This is seen when subtracting scalars, such as saying 5 minus 2 is the same as 5 plus negative 2, and the same concept can be applied to vector subtraction. Here, the order in which you perform the subtraction doesn't matter because you're effectively adding the opposite vector.