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More Than Two Addends

Up to this point, we've been talking about addition problems with only two addends. Sure, some of that regrouping had you bringing a "1" over so that you were adding three numbers. Let's look at concepts that are used with multiple addends.

12 + 34 + 43 = ?

Or...

12 34 + 43 ?

When you add two and three-digit numbers, you start with the ones column. The same rule applies if you are adding three values. Start with the ones. From the above example, you would add "2 + 4 + 3." This is a nice clean problem with no carrying. Your answer for the ones column is nine (9). Then you move to the tens column. "1 + 3 + 4" gives you a tens value of eight (8). Put it all together and you get the sum "89".

Examples:
12 + 34 + 43 = 89
51 + 21 + 13 = 85
13 + 11 + 15 = 39

Grouping Numbers

Your homework problems might not be that easy. You might be given a list of ten numbers. We find it easier to break down the number of addends. Instead of trying to add eight numbers together at one time, you might want to add two numbers, then three numbers, and then the remaining three numbers. In the last step, you add those three temporary sums together.

Example:
15 + 26 + 34 + 45 + 19 + 22 + 44 = ?

Think of it this way...
(15+26) + (34+45) + 19 + (22+44) = ?

(1) Add smaller groups together.
15 + 26 = 41
34 + 45 = 79
22 + 44 = 66
and there is a 19 sitting there.
You now have 41 + 79 + 66 + 19 = ?

(2) Add those temporary sums together.
41 + 19 = 60
79 + 66 = 145

(3) Finish it off by adding those values.
60 + 145 = 205

Can you see how it's not as big of a problem when you break it down into smaller pieces? You can tackle one hundred addends in a problem if you try that grouping strategy. When you get a problem that is complicated, just take a moment to look for patterns or ways to break it down into simpler ideas.

Did you see how we used parentheses in the first step to set up grouping? In addition you can group any numbers you want with parentheses. We use the Associative Law of Addition to group and regroup all sorts of numbers. We are allowed to reorder the addends because of the Commutative Law of Addition. We describe these laws in a later section.

Use Your Tools

All you need to remember is that if you are only adding terms, you can reorder and group any time you want to make the problem easier to solve.

Example:
45 + 68 + 22 + 157 + 8 + 12 + 35 = ?

• Reorder: 45 + 35 + 68 + 12 + 8 + 22 + 157 = ?
• Group: (45+35) + (68+12) + (8+22) + 157 = ?
• Solve the groups: 80 + 80 + 30 + 157 = ?
• Group: (80+80+30) + 157 = ?
• Solve the groups: 190 + 157 = 347

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