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. |
