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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. 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 finding the difference between two numbers. It is finding what number we have to add. 28 + 7 = 35. 35 − 28 = 7. 



If the two numbers are equal, of course, then their difference is 0. 5 − 5 = 0. The traditional terms subtrahend and minuend are leftovers from written calculation. The subtrahend was the number written under and taken away. The minuend was the number made less. Both refer to a written method, not to the meaning of subtraction as the inverse of addition, which is finding the number to add. "Subtraction" itself is a historical term, meaning "taken away from below." We should try to coin a new term that emphasizes the inverse of addition. Example 1. How much is 149? Answer. 9 plus what number is 14? 9 + 5 = 14 149 = 5 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: 86 = 2 because 6 plus 2 = 8. Knowing this, we 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, 103 = ? 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. 106 = 4. In fact, whenever we take a 6 from any multiple of 10  20, 30, 40, 50, 60  we always get a 4. 30 − 6 = 24 40 − 6 = 34 80 − 6 = 74 Similarly, 508 = 42 709 = 61 2003 = 197 $8.004¢ = $7.96 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 twodigit number. We often simply count backwards. 50 − 1 = 49. 60 − 2 = 58. 70 − 3 = 67. 



Example 3. Calculate mentally 835. 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 © 20012007 Lawrence Spector Questions or comments? Email: themathpage@nyc.rr.com 