Thread: subtraction

When we use the standard subtration algorithum to subtrart
52
-19
_____

we must regroup. Which property or properties of arithmetic do we use when we regroup?
Answer this question by writing 52 in expanded form and by using parentheses carefully to show regrouping.

thank you

Well, we have:

52
-19
-----

9 cannot be subtracted from 2, so the 5 means 5 tens, we just take one away and make it 10 ones:

4 12
(5)(2)
-19
------


Now, we can completely subtract:

4 12
(5)(2)
-19
------
33

And there you go.

52 = 50+2 = 5*10 + 2 = (4*10 + 10) + 2 = 4*10 + (10+2) = 40 + 12

The important step is the bold one. That looks Associative to me.