 S k i l l
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A R I T H M E T I C

Prologue 1

# ELEMENTARY ADDITION

Sums less than 10

Composing 10 itself

Sums between 10 and 20

Doubling

Zero

Practice problems

SKILL IN ARITHMETIC begins with knowing sums that are less than 10.  3 + 4 = 7,  7 + 2 = 9, and so on.

First, though, one of the elementary facts of arithmetic is that the order in which we add does not matter.  For if you know that 5 + 3 = 8: then you would also know that 3 + 5 = 8. The order in which we add does not matter.

Now practice these sums less than 10.

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Do the problem yourself first!

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

Composing 10 itself

It is useful to know all the ways of "composing" -- that is, making -- 10.

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

Sums between 10 and 20

Finally, the student must know sums such as  9 + 6 = 15 ,  8 + 5 = 13, and so on.  To become familiar with them, you can first compose 10 by regrouping.  But eventually, you must know them.

Example 1.   9 + 6.

On splitting 6 into 1 + 5,

9 + 6 = 9 + 1 + 5 = 10 + 5 = 15

Say, "9 + 1 is 10, plus 5 is 15."

Regroup 1 with 9 to compose 10.

Example 2.   5 + 7.

"5 + 5 is 10, plus 2 is 12."

Example 3.     3 + 8.

"8 + 2 is 10, plus 1 is 11."

Doubling

It will help to know the sum of a number added to itself.

5 + 5 = 10

6 + 6 = 12

7 + 7 = 14

8 + 8 = 16

9 + 9 = 18

Now, once you know that

6 + 6 = 12,

then you could know that

6 + 7 = 13,

and

6 + 5 = 11.

7 + 7 = 14

7 + 8 = 15

7 + 6 = 13

8 + 8 = 16

8 + 9 = 17

8 + 7 = 15

9 + 9 = 18

9 + 8 = 17

Zero

0 is a number. It can answer the question How much? or How many?
0 is best introduced by subtraction.

Say, for example, that you have 2 dollars.  If you spend those 2 dollars, you now have 0 dollars.

2 dollars − 2 dollars = 0 dollars.

That is,

2 − 2 = 0

for any unit:  dollars, apples, chairs, etc.

Here is a basic fact about 0:  If you add it to any number, that number does not change.

5 + 0 = 5.

0 + 6 = 6.

0 means no units.

There is a subtle difference between 0 units and nothing. Say that you have an account at the First National Bank and that your balance is \$10.  If you now withdraw \$10, your balance is 0 dollars. But say that you have no account at that bank. Then you do not have a balance of 0 dollars there -- you have nothing!

That is the difference between 0 and nothing.

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Practice the following until you remember each one.

 8 + 5 = 13 3 + 9 = 12 5 + 9 = 14 6 + 8 = 14 7 + 9 = 16 9 + 6 = 15 7 + 6 = 13 8 + 6 = 14 6 + 5 = 11 8 + 4 = 12 3 + 8 = 11 5 + 8 = 13 9 + 4 = 13 7 + 4 = 11 6 + 6 = 12 4 + 9 = 13 4 + 8 = 12 6 + 9 = 15 8 + 9 = 17 4 + 7 = 11 5 + 7 = 12 6 + 7 = 13 9 + 3 = 12 9 + 2 = 11 7 + 7 = 14 7 + 8 = 15 9 + 5 = 14 9 + 8 = 17 7 + 5 = 12 2 + 9 = 11 9 + 7 = 16 8 + 7 = 15 5 + 6 = 11 8 + 3 = 11 8 + 8 = 16 9 + 0 = 9 8 + 0 = 8 0 + 6 = 6 0 + 3 = 3 0 + 0 = 0

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