Lesson 4

MORE ELEMENTARY ADDITION

Mental calculation

We now begin the four operations of arithmetic: Addition, subtraction, multiplication, and division. We continue to emphasize problems that do not require a calculator -- problems that you should not even have to write down! Mental arithmetic is now arithmetic of the most practical kind.

The student should now have mastered the elementary addition of one-digit numbers, and should be practicing the multiplication table.

For, once you know that

These are not problems to write in a column.

The multiples of 10 are:

10,  20,  30,  40,  50, etc.

Example 1.     25 + 7  =  (25 + 5) + 2  =  30 + 2  =  32.

Similarly,

38 + 4  =  (38 + 2) + 2  =  42.

59 + 7  =  (59 + 1) + 6  =  66.

96 + 8  =  (96 + 4) + 4  =  104.

To add 96 + 8, then, an educated persondoes not have to take out a

pencil, write in a column and say,

"6 plus 8 is 14 -- write 4, carry 1.  etc., etc., etc."

Nor does an educated person count on her fingers.  Rather, an educated person knows elementary addition  and therefore that 96 + 8 is not very different from 6 + 8.  It ends in 4.

Example 2.   Since

9 + 6 = 15,

then

A 9 plus a 6 always gives a "15."  This brings us to the practical technique for adding several numbers --

7 + 8 + 3 + 9 + 4

Adding by endings.

For example, since

 8 + 4 = 12,

we would know that if we add any number ending in 8 to any number ending in 4, the sum will always end in 2.

28 + 4 = 32

38 + 4 = 42

68 + 4 = 72

And so on.  Each answer falls in the next decade.

Similarly, since

6 + 5 = 11

then

26 + 5 = 31

46 + 5 = 51

76 + 5 = 81

They all end in 1.  These are not problems to write down.

Example.   Add mentally -- or aloud -- from left to right.

Say only the partial sum as you come to it.  Do not say,
"7 plus 8 is 15" -- say only "15."  Then look at 3 and say 18.  And so on.  Use your knowledge of the ending; even exaggerate saying it.

435 + 461 = 896

First add the hundreds, then the tens, then the ones.

We now see the fundamental principle of all mental calculation:

Calculate from left to right, just as you read.
The last number you say is the answer

Example 1.  Counting by 10's.    30 + 24  =  54.

Here are other examples:

20 + 16 = 36

40 + 38 = 78

40 + 62 = 102

40 + 82 = 122

90 + 73 = 163

Example 2.     43 + 25

First add the tens then the ones.  Say

"Sixty --

43 + 25

-- eight."

Or, you could say,

"43 plus 20 is 63, plus 5 is 68."

Say, "150 plus 7 is 157."

Say only, "50 plus 14 is 64."

The art of mental calculation is to say as little as possible.  The last number you say is the answer.

"170 plus 11 is 181."

Example 6.    23 + 32 + 25 + 12

First add all the tens, then add on the ones.  As you add each place, say the partial sum.  Say

The last number you say is the entire sum.

Example 7.	34 + 25 + 32
	"50,  80,  89,  91."

Example 8.   653 + 224

First add the hundreds, then the tens, then the ones.  Again, say each partial sum:

653 + 224

Say,

"800,  870,  877."

Example 9.    Three tracks on a CD have the following times:

10:34

 6:25

 8:07

What is the total time?

(10:34 means 10 minutes 34 seconds.  60 seconds = 1 minute.  Therefore, 72 seconds = 1 minute 12 seconds.  1:12.)

Technique.   Start with the minutes and count:

"16 plus 8 is 24 minutes."

Now add on the seconds.

"24:59 plus 7 is 24: 66."

The total time is 25 minutes 6 seconds.

At this point, please "turn" the page and do some Problems.

or

Continue on to Section 2:

Adding mentally by rounding off

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