Joe Doe (joe_doe_zero) wrote in 0_arithmetic,
Joe Doe
joe_doe_zero
0_arithmetic

General adding - lesson 1

Adding more than two numbers



It is possible to add more than two numbers. Let's say we want to add 3, 5, and 6

3 + 5 + 6 = ?

There is a hidden beauty here. We can add the numbers in any order we desire. Let's first do (3 + 5) + 6

3 + 5 = 8
8 + 6 = 14

If that was too inconvinient for you, let's try in a different order: 3 + (5 + 6)
5 + 6 = 11
11 + 3 = 14

We arrive at the same answer!

Now, let's try a third order. (3 + 6) + 5
3 + 6 = 9
9 + 5 = 14

Another way:
5 + 3 = 8
8 + 6 = 14

There are two more ways left but we will not go into them since we have arrived at the same answer consistently.

Let's try another: 2 + 6 + 8 = ?

8 and 2 can be added to get 10 so
8 + 2 = 10
10 + 6 = 16

Another way:
2 + 6 = 8
8 + 8 = 16

This is often helpful because sometimes we can add certain numbers more easily than other numbers. The number 10 is easy to add by. Let's try:

3 + 9 + 1 + 7 = ?

3 + (9 + 1) + 7 = ?
3 + 10 + 7 = ?
3 + 7 + 10 = ?
(3 + 7) + 10 = ?
10 + 10 = ?
10 + 10 = 20

We simply paired up the 9 and 1 togather and paired 3 and 7 togather. Both add up to 10 and we added the tens to get 20.

Let's try 7 + 1 + 2 + 5

Adding by 1 is easy so 2 + 1 = 3
We're left with 7 + 3 + 5

7 and 3 make 10 leaving us with

10 + 5 = ?
10 + 5 = 15

It often helps to "pair" or "lump" numbers togather to make computation easier. Let's say we want to add: 6 + 6 + 2 + 4 + 2

Pair one 6 with a 4
Lump the other 6 with 2 and 2

6 + 4 = 10
6 + 2 + 2 = 10

10 + 10 = 20.

Thus 6 + 6 + 2 + 4 + 2 = 20

The following "number pairs might be helpful:

Pair 1 with 9
Pair 2 with 8
Pair 3 with 7
Pair 4 with 6
Pair 5 with 5 (itself)
Pair 6 with 4
Pair 7 with 3
Pair 8 with 2
Pair 9 with 1

Actually, you only need five pairs: (1 and 9), (2 and 8), (3 and 7), (4 and 6), (5 and itself).

As for the number 0, just disregard it. If you're ever faced with a problem such as

6 + 0 + 9 = ?

Think of it as simply:

6 + 9 = ?

Just like numbers can be paired, they can also be "broken". For example, 4 can be "broken" into 3 and 1 r it can be broken into 2 and 2.

4 can be broken into 3 + 1
4 can be broken into 2 + 2

Why is this helpful?

Say you want to add 7 + 8. You know how to add 7 + 3. So "break" 8 into 5 + 3. "Pair" 7 and 3 to get 10 and add the remaining 5 to get 15.

Try this one: 9 + 9 + 3

"Break" one 9 into 7 + 2 and add the 7 to 3 to get a 10. We now have

9 + 10 + 2

9 + 2 = 11
10 + 11 = 21

The beauty of these problems is that you can often do the same problem in many different ways. You can take as many steps as you'd prefer to solve a problem. Some problems can be easily solved in three steps, while others may take six steps. Choose the method that works best for you. And do not be afraid to use your creativity; have fun in the process! :)
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