Commutative Property ????

Question

can you give me an example of Commutative Property of Addition
i dont understand it

Answer 1

(4+2)+3=(3+2)+4

the numbers moved around and that's why it's called commutative property.

Answer 2

Actually, blackrose's example is needlessly complicated: it invokes the commutative property _twice_ as well as the associative property. Look

(4+2)+3=(3+2)+4
requires:
(4+2)+3=4+(2+3) (associative property)
4+(2+3)=(2+3)+4 (commutative property)
(2+3)+4=(3+2)+4 (commutative property again)

What the commutative property states is simply:

a+b=b+a

That's it. a and b can be anything, it could 7+13=13+7, -9+2=2+(-9), π+φ = φ+π, and so on. All it means is that given a sum of any two numbers, you can swap them around without changing the sum. Combined with the associative property, it means that given the sum:

a+b+c+d

You could write this in any of 24 different ways, including (but not limited to):

a+b+d+c
d+a+b+c
d+c+b+a

and so on, and know without checking that you will always get the same result.

The main thing that you will need to watch out for at your level is confusion with the associative property. As you will probably recall, this states:

(a+b)+c = a+(b+c)

In fact, it is because of the associative property that I can justify writing things like a+b+c+d without using parentheses, because it really doesn't matter which sums you do first. You could compute it as (a+b)+(c+d) or a+(b+(c+d)) or even (a+(b+c))+d and still get the same result. Probably the best way to remember the distinction is that the associative property allows you to rewrite (or omit entirely) the parentheses, whereas the commutative property allows you to exchange _adjacent_ pairs of addends. You can, in fact, interchange pairs of addends which are not adjacent, but this invokes (usually implicitly) both the commutative AND associative properties. For instance, consider the following transformation:

(a+b)+(c+d) = (a+b)+(d+c)

This involves a single use of the commutative property, to interchange d and c. On the other hand:

(a+b)+(c+d) = (d+b)+(c+a)

To do this, I must use both properties. Here I list each step in order to make it explicit which property I am using:

(a+b)+(c+d)
a+(b+(c+d)) (associative property)
a+((b+c)+d) (associative property)
a+(d+(b+c)) (commutative property)
(a+d)+(b+c) (associative property)
(d+a)+(b+c) (commutative property)
d+(a+(b+c)) (associative property)
d+((b+c)+a) (commutative property)
d+(b+(c+a)) (associative property)
(d+b)+(c+a) (associative property)

Of course, in most cases this is considered as a single step, which can make it difficult to see which properties are being used. Hopefully this example will help clarify the distinction between the two.

Answer 3

The commutative property of addition says that if you add two numbers, it doesn't matter which order you add them in; you'll get the same answer either way.

For example, 1 + 2 = 3, and 2 + 1 = 3 also.

A very compact way of stating the commutative property of addition is: "For every `a' and `b', a + b = b + a."

Answer 4

Basically, it means that the order doesn't matter when you add two numbers, so 8+5 = 5+8 = 13.

Another example, if the Prologue of a two day biking tour is 5.6 km and Stage 1 is 180.5 km, the biker can add the distances in either order to get the total for the two days.

5.6 + 180.5 = 180.5 + 5.6 =186.1

Answer 5

you eat baby rabbits..? o.O you're not cool.