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

Concepts in Addition

If you know how to count, then you're on your way to being an adding whiz! Even if all you can do in your head is addition, then you're still considered a calculating whiz.

For those of you who don't know counting, just memorize these numbers in this particular order: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12...

Those are known as the counting numbers. (If you're a mathematics major, you might better know them as the natural numbers.)

Now, let's add by 1.

1 + 1 = 2
2 + 1 = 3
3 + 1 = 4
4 + 1 = 5
5 + 1 = 6
6 + 1 = 7
7 + 1 = 8
8 + 1 = 9
9 + 1 = 10

Simple? See if you can memorize it. Better yet, see if you can find an alternative to memorization. You should know that if 1 is added to a number then the result is the next counting number.

A general pattern: (counting number) + 1 = (next counting number)

So if 13 is the next counting number after 12, then 12 + 1 = 13

Let's take the number 6.

6 + 1 = 7

We can reverse the order the numbers are added and still get the same result.

6 + 1 = 7
1 + 6 = 7

6 + 1 is the same thing as 1 + 6.

Let's do a quick review of the counting numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 and so on...

1 and 6 are known as addends and the number 7 is known as the sum.

A general pattern: addend + addend = sum

If you're starting to think of mathematics as a bunch of general patterns, then you're already thinking like a mathematician.

But the general pattern can be put into a more general pattern.

Sum = addend + addend

Let's say with the numbers 6, 1, and 7, we can formulate four equations.

6 + 1 = 7
1 + 6 = 7
7 = 1 + 6
7 = 6 + 1

Let's take another case, say 3, 1, and 4.

3 + 1 = 4
1 + 3 = 4
4 = 1 + 3
4 = 3 + 1

Got it? Good. Now make equations out of these numbers.

Problem 1: 1, 2, and 3
Problem 2: 6, 1, and 7 (already done)
Problem 3: 8, 1, and 9
Problem 4: 9, 1, and 10
Problem 5: 10, 1, and 9 (see problem 4 but re-do it)
Problem 6: 11, 12, and 1
Problem 7: 10, 1, and 11
Problem 8: 88, 89, and 1
Problem 9: 1, 100, and 99
Problem 10: 566, 1, and 567
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