Lesson 7 Section 2 THE MEANING OF SUBTRACTIONMental calculationSubtract by the ending Knowing the endings in addition (Lesson 4) becomes skill in subtraction. For example, to find the number we must add to 8 to get 32  32 − 8  let us ask: 8 + ? ends in 2 ? 8 + 4 ends in 2  because 8 + 4 is 12. Therefore, 32 − 8 will also end in 4. It must be 24. The answer falls in the previous decade. In fact, whenever we take an 8 from a 2, the answer always ends in 4. 42 − 8 = 34 62 − 8 = 54 92 − 8 = 84 The answers fall in the previous decade. These are problems you should not have to write down. Example 1. 41 − 9 Solution. 9 + ? ends in 1. Solution. 9 + 2 ends in 1, because 9 + 2 is 11. Therefore, 41 − 9 = 32 Example 2. You could know 84 − 8 = 76, because 8 + 6 ends in 4. To summarize: 



* Next, how can we find the difference between twodigit numbers? First: 



Example 3. 52 − 46 Say only, "4 + 2 is 6." That is, 46 plus 4 is 50, plus 2 is 52. Example 4. 57 + ? = 65 "3 + 5 is 8." Example 5. 23 − 18 "2 + 3 is 5." These are problems that you should not have to write, and certainly should not require a calculator. Next, let's look at twodigit numbers that are farther apart. 42 + ? = 96
How to do it? First add enough tens to get to the 90's. "42 + 50 is 92, plus 4 is 96." 42 + 54 = 96.
That is, 25 + 62 = 87. Finally, here is the case where the ones digit of the smaller number is greater. 27 + ? = 80 First consider this case where we're going to a multiple of 10. In this case, add to get to the previous decade  the 70's. "27 plus 50 is 77, plus 3 is 80." 27 + 53 = 80. In practice, say only, "50 + 3 is 53."
(38 plus + 20 is 58, plus 2 is 60.) Now say that the larger number is not a multiple of 10. 38 + ? = 64 Again, add to 38 to get to the previous decade. But in this case we know that the difference will end in 6  the ones digit will be a 6. (8 + 6 ends in 4.) 38 + 26 = 64. 38 plus 20 is 58, plus 6 is 64. To summarize: 



Example 9. 23 + ? = 61 Solution. The difference will end in 8. (3 + 8 ends in 1.) Therefore, 23 + 38 = 61. (23 plus 30 is 53, plus 8 is 61.)
The difference ends in 7. 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 © 2014 Lawrence Spector Questions or comments? Email: themathpage@nyc.rr.com 