In continuation of Part I, we now plunge more deeply into the Quick-Add Method and show how this makes doing addition quite easy. This procedure hinges on two key ideas: 1) the method of complements; and 2) the Quick-Add Conversion. To refresh your memory (also see "Teach Your Kids Arithmetic - The Quick-Add - Part I), complements of a number are those numbers, which when added to the given number, yield a sum of 10, or some multiple of 10. For example, the 10-complement of 8 is 2, since 8 + 2 = 10. The 10-complement of 4 is 6, since 4 + 6 = 10. The Quick-Add conversion is simply the way in which we convert our given addition problem into a "quick-add;" for once done, the problem becomes--well, what the method says: a quick-add. That is, the addition can be done quickly and easily. As mentioned previously, the Quick-Add works as follows: in analyzing 10 + 7, we rewrite this example as 10 + 07. We insert a 0 in front of the 7 as a placeholder for the empty "tens column," and to bring the numbers into parallel structure. The brain performs 1 + 0 in the "tens column" and 0 + 7 in the "ones column," thus capitalizing on the "Additive Identity Property" of 0.
Whenever we are confronted by an addition problem, we are going to convert it to a "quick-add." For example, take the addition of 7 + 5. This is 12, but some children might not get this straight away. Ask them what 10 + 2 is, however, and the answer is for the most part immediate. Nobody struggles with the latter addition problem because it is in "quick-add format." Now to get the problem into this format, we simply do the "Quick-Add Conversion," and this is when the idea of complements comes in to play. We always work with the bigger number, which in this example is 7. We take the 10-complement of 7, which is 3. We reduce the smaller number, 5, by 3 to become 2. Now we have the converted example: 7 goes to 10, and using its complement 3 to reduce 5, 5 goes to 2. We now have the "quick-add" 10 + 2 = 12. Let's look at another example: 8 + 9. In this case, the 10-complement of 9 is 1; thus 8 is reduced by 1 to 7, and we have the "quick-add" 10 + 7 = 17. A snap! If both numbers are the same, no problem. Look at 6 + 6. The 10-complement of 6 is 4, thus the other 6 gets reduced by 4 to 2. We now have the "quick-add" 10 + 2, which is 12.
This method can be extended to larger and larger numbers, using the idea of 100-complements, 1000-complements, and so on. For now, I will examine just another two examples, using additions with numbers bigger than 10. Take 18 + 8. We break down 18 into 10 + 8, and observe that the 10-complement of 8 is 2; 18 then becomes rounded to 20, the next 10 up from 18, and 8 becomes reduced by the 2 to 6. Thus we have 20 + 6 = 26. For the example of 19 + 17, we have 19 is 10 + 9 and 17 is 10 + 7. The 10-complement of 9 is 1, so 19 goes to 20, and 17 is reduced 1 to 16. So the converted example is 20 + 16, which can be further broken down to 20 + (10 + 6) = 20 + 10 + 6 = 30 + 6 = 36. In the last example, I was using some forgotten rules of arithmetic, such as the Associative Property of Addition, and breaking down the example quite extensively; however, I think the point is made and the procedure is now established.
Try looking at addition problems from this perspective by using the idea of complements and "Quick-Add" conversions. I don't think you or your kids will be having trouble with addition anymore. Stay tuned for more arithmetic magic in my future series of articles on this most important topic.
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