# Math: Properties of Addition; Commutative vs. Associative

The math lesson today is on the Properties
of Addition- the differences between the Commutative and Associative Properties of Addition. You will notice that there is a reason I have
wheels on the Commutative Property and a little face sitting there waiting at the Associative
– a friendly face you might even imagine… Now you’ll notice that I colored the 3 and
4 in this case, and the 4 and the 3. When the 3 “leaves home it drives” to a new
location, but it is still a value of 3, even if it’s not in the first position anymore. Same for the 4; it also drives to a new position
in its little car… and drives over to this new position. Now it’s first! But, that doesn’t change the answer; 3 +4
=7, and 4 + 3=7. The difference, this is Commutative. You’ll notice, it’s because the values commute,
just like you might do in the morning, from home to school. Now, on the bottom, we have no changing colors,
no changing numbers, because it’s not the numbers that move or change! What changes is “with whom the friends choose
to hang out”. In this first value, we’ll say that 1 + 2,
1 and 2 are friends, and so they associate with each other, like friends do. In the second case, we’ll say that 2 + 3 happen
to be buddies, so that 2 will hang out with 3 first when they go to play. And, so they are associating with each other. In this first case, we see that 1 + 2=3,
plus the 3 we already had. 3 + 3=6. In the second case, we see that 2 + 3=5,
bringing down the 1 we have not yet accompanied, we have 1 + 5; again 6. So we have proven that no matter with which
value the 2 associates first, the [sum] value will be coming to 6 either way. This [is] the Associative Property, because
of with whom the 2 associates. This is the Commutative Property because the
values commute. Thank you very much for today’s lesson on
Properties of Addition – Commutative versus Associative. Now I imagine the decorations make a little
bit more sense! Thank you.

## 38 thoughts on “Math: Properties of Addition; Commutative vs. Associative”

1. Thank you SOOOO much! I was looking to understand and you kept it very simple and did it in a way that people can relate to. Thank you again :0)

2. Thanks for this! I have yet to pass my math proficiency test, and need my high school diploma to do so. It's the only thing I'm missing. Anyway, this always confused me, the difference between the properties. So thanks again!

4. . I was confused but once you explained it, I got it.. Thank you for taking the time to make the video

5. the problem I am having is that in my head I can't get past that 1+2+3 = 1+3+2
so I keep making the mistake of saying (1+2)+3 = 1+(2+3) is commutative because really you can switch any of those numbers and get the same freaking answer.

WHY even differentiate in addition when in the end it's always going to be the same?

I can understand if it's multiplication but there really is no need for this sort of thing with addition. or am I wrong?

6. Excellent!! Thank you so much for this!

7. Coo

8. Thanks

9. I love the way you explained it! That's awesome.

10. Thank you for your help!

11. Very informative. sticks to the mind.

12. Thanks for doing this because I was doing my homework and I was stuck on that problem. Thanks agin now I can watch my videos on YouTube. By the way my big brother has a YouTube channel his channel name is TheGamingKojo99. Thanks agin you also explained it in a good way.

13. Me 9 thanks

14. huge fast help

15. thanks

16. thanks.

17. I wish I could dislike this more than once.

18. OMG IM DOING MY HOME WORK RIGHT NOW AND IM SOO confused 2D

19. This is gonna help me so much in my math test.thank you so much

20. Its so easy that its confusing lol, I don't understand why these people who make up these math terms have to make things a bit more confusing. Just say that they both switch around numbers in different ways.

21. This was great! Very easy to understand. Thanks for sharing.

22. this didn't help

23. thanks for clearing this up…. that was a nice example 🙂

24. so like in associative property it must includes parenthesis? if It does not includes parenthesis it will be commutative property? in other words the difference between these two are the parenthesis?

25. nice video – helped me a lot with homework

26. This is possibly the easiest way to provide an analogy of why these are different (yet the same). I couldn't get it through my head until you explained the Moving around vs being buddy buddy. Makes 100% more sense, even though this whole thing is kinda pointless, hahahah.

27. Помогло, круто

28. Thank you, I was having trouble with this ♡♡🐰

29. you lost me at smiley face

30. Thank you

31. Music too loud, sudden

32. Too childish

33. I got them mixed up and this helps

34. than you

35. thank*

36. Thank you

37. Ya thanks for helping I appreciate it

38. can we all just take a minute to appreciate the fact that when she started explaining things she put on some 80's elevator music