I don't know how to regroup addition numbers and it has to be 3 numbers and what should I do

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steveschoen's profile pic

steveschoen | College Teacher | (Level 1) Associate Educator

Posted on

Regrouping addition numbers would refer to the associative property of addition, where:

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

Which means, as long as you have only and all addition, you can regroup the numbers any way you want.

This is a very handy property.  For instance, you may be given something like:

(31+58) + 42

I wouldn't like to do this problem.  But, given that we have only and all addition, the associative property allows us to say:

(31+58) + 42 = 31 + (58+42)

It is a lot easier to do the right side, since:

58+42 = 100

Then, we would have:

31+100 = 131

So, (31+58) + 42 = 131.

In keeping the same order, you would put the parenthesis around any other 2 or more numbers next to each other in the problem.  It doesn't make a difference which numbers.  So, how to regroup the numbers can be a matter of perspective.  For instance, if we have the following, we could regroup is as:

(41+42) + 43 + 44 + 45 =

41 + (42+43) + 44 + 45 =

41 + 42 + (43+44) + 45 =

41 + 42 + 43 + (44+45)

It doesn't make a difference which one the numbers get regrouped in.  Depending upon the numbers, you would look to regroup to make easier numbers to add, like what I did with the 58 and 42.  So, "where" to regroup can all be a matter of one's own individual perspective.  But, "how" to regroup, you would simply put parenthesis around another pair of numbers next to each other that you are adding, like I showed above.

mchandrea's profile pic

mchandrea | Student, College Junior | (Level 1) Salutatorian

Posted on

By regrouping addition numbers, you are referring to the associative property of addition. This means that no matter which numbers you add first you will still get the same answer. In equation form it should look like this

A + ( B + C ) = ( A + B ) + C

For example you are to add and regroup 3, 5 and 7.

      A                                     B                              C

3 + (5 + 7)                     (3 + 5) + 7                 (3 + 7) + 5

3  + (12)                          (8) + 7                       (10) + 5

= 15                                   = 15                           = 15

This means that, as long as you're adding the same numbers, the answer will be the same regardless of which couple of numbers you add first.

If you are still confused you can check this out. It is a very simple explanation of the associative property of addition.

Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on

Regrouping refers to the associative property of addition. It works because numbers can be added in any order and still have the same total. You should regroup numbers to make the addition easier. 

for instance: 

28 + 56 + 32 + 24 = 

can be regrouped into: 

(28 + 32 ) + ( 56 + 24 ) = 60 + 80 = 140

Placing parentheses around the groupings helps make it clear when showing work. 

rimmery's profile pic

rimmery | Student, Undergraduate | (Level 1) Honors

Posted on

To regroup addition numbers, the easiest thing to do is to ignore the brackets given to you in the original question. Then, try to find another pair of numbers that are easier to add up. Usually that's what regrouping is used for anyways.

For example, if you have something like (27+5)+20, try to see that 5+20 is easier to do than 27+5. So ignoring the original brackets, 27+5+20, then doing the last addition first, so you get 27+(5+20) = 27+25 = 52

For 3 or more numbers of additions, you can put brackets around any two of them and that would be a regroup. Remember to regroup to make it EASIER ON YOURSELF, because it will make solving the problem a lot faster and simpler. 

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