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Lesson 4 MORE ELEMENTARY ADDITIONMental calculationWe now begin the four operations of arithmetic: Addition, subtraction, multiplication, and division. The emphasis will continue to be on problems that do not require a calculator  problems that you should not even have to write down! Mental calculation is now arithmetic of the most practical kind. In this Lesson, we will answer the following:
The student should now have mastered the elementary addition of onedigit numbers, and should be practicing the multiplication table. For, once you know that
These are not problems to write in a column. 



Example 1. 27 + 5 = (27 + 3) + 2 = 30 + 2 = 32 Similarly, 38 + 4 = (38 + 2) + 2 = 42 59 + 7 = (59 + 1) + 6 = 66 96 + 8 = (96 + 4) + 4 = 104 An educated person then does 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 must be 104. These numbers that we compose  10, 20, 30, 40, 50, etc.  are called the multiples of 10. 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,
The following is a basic technique for mental addition: 



435 + 461 = 896 First add the hundrededs, then the tens, then the ones. Example 1. Counting by 10's. 30 + 24 = 54 Here are other examples of mental calculations. In each case, add the numbers as you read them, from left to right. Add the 10's: 20 + 16 = 36 40 + 38 = 78 40 + 62 = 102 40 + 82 = 122 90 + 73 = 163 Example 2. 43 + 25 First add the tens, then add the ones. Say "Sixty  43 + 25  eight." Or, we could say, "43 plus 20 is 63, plus 5 is 68." Say, "150 plus 7 is 157." Say only, "50 + 14 equals 64." The art of mental calculation is to say as little as possible. The last number you say is the answer. "170 + 11 = 181" Example 6. 23 + 32 + 25 + 12 Add up all the tens, then add on the ones. Say each partial sum. Say The last number you say is the entire sum. Example 7. 34 + 25 + 32 Example 8. 653 + 224 First add the hundreds, then the tens, then the ones. Again, say each partial sum: "800" 653 + 224 "870" 653 + 224 "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 Introduction  Home  Table of Contents Please make a donation to keep TheMathPage online. Copyright © 20012007 Lawrence Spector Questions or comments? Email: themathpage@nyc.rr.com 