# 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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