why dosnt the commutitive property work with subtraction and division?
For subtraction : Because a - b and b - a are not the same. They are of opposite sign.
For division:
a/b does not equal b/a. If it did, you would have a^2 = b^2 for ANY a and b, which is impossible
To understand why the commutative property does not work with subtraction and division, let's first discuss what the commutative property actually is. The commutative property states that changing the order of the numbers in an operation does not affect the final result. In other words, if a and b are any two numbers and we perform an operation (addition or multiplication) on them, the result will remain the same regardless of the order in which we perform the operation.
However, subtraction and division are different operations compared to addition and multiplication.
For subtraction, the commutative property does not hold because changing the order of the numbers being subtracted creates a different result. For example, if we subtract 5 from 10, we get 5 (10 - 5). But if we subtract 10 from 5, we get -5 (5 - 10). The results are not the same, so the commutative property does not apply.
Similarly, for division, the commutative property does not work. Division is the inverse operation of multiplication, so it involves the ratio of one number to another. If we change the order of the numbers in division, the quotient will change. For example, if we divide 10 by 5, we get 2 (10/5). But if we divide 5 by 10, we get 0.5 (5/10). These results are not equal, so the commutative property does not apply.
In summary, subtraction and division do not satisfy the commutative property because changing the order of the numbers being subtracted or divided leads to different results.