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Lesson 6 THE MEANING OF SUBTRACTIONMental CalculationFirst, we will see the meaning of subtraction. Then we will see methods for achieving it easily and mentally. For, mental arithmetic is often the quickest way to do a problem. In this Lesson, we will answer the following:
IN ADDITION we are given two numbers and we have to find their sum. 28 + 7 = ? But in what is called the inverse of addition, we are given the sum and we have to find one of the two numbers. 28 + ? = 35 That has been called "subtraction ." It is the problem of finding the difference between two numbers. It is finding what number we have to add to 28 to get 35. 28 + 7 = 35. 35 − 28 = 7. The sign of subtraction is the horizontal dash (−), which we read "minus." "35 minus 28 equals 7." "The difference between 35 and 28 is 7." |
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The historical name subtraction -- literally, "taken away from below" -- referred to a specific written method, namely writing the smaller number (the subtrahend) under the larger (the minuend), and executing the method. However, that is not the only way of finding the difference of two numbers. These days, we could obviously use a calculator! In any event, we should try to come up with a new name that emphasizes the problem of the inverse of addition. We call the numbers that we are subtracting the terms. Thus when we write 35 − 28, the terms are 35 and 28. We also call '35 − 28' a difference, even if we do not name the answer If the terms are equal, of course, then their difference is 0. 5 − 5 = 0. As in addition, we can only subtract quantities of the same kind, that is, that have the same name. 35 dollars − 28 dollars = 7 dollars.
Example 1. How much is 14 Answer. 9 plus what number is 14? 9 + 5 = 14. 
14 We can say that the difference of two numbers is the distance between them. How far is it from 9 to 14? A distance of 5. Here is a simple example: 8 Knowing that, you would also know
"Subtracting" is adding to the smaller number. The complement to 10 The student should know all the ways of "completing" 10. For example, 10 3 plus what number makes 10? 7, of course. 7 is called the complement to 10 of 3. 7 "completes" 3 to make 10.
Example 2. 10 30 − 6 = 24 40 − 6 = 34 80 − 6 = 74 Similarly, 50 70 200 $8.00 Each difference ends in the complement to 10 of the smaller number. These are not problems to write in a column and do some written method. Let us now look at subtracting from a two-digit number. We often simply count backwards. 50 − 1 = 49. 60 − 2 = 58. 70 − 3 = 67. |
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Example 3. Calculate mentally 83 Solution. 83 − 5 = 83 − 3 − 2 = 80 − 2 = 78. Example 4. 72 − 6 = 72 − 2 − 4 = 70 − 4 = 66. At this point, please "turn" the page and do some Problems. or Continue on to the next Section. Introduction | Home | Table of Contents Please make a donation to keep TheMathPage online. Copyright © 2001-2009 Lawrence Spector Questions or comments? E-mail: themathpage@nyc.rr.com |
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