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.
About the author:
Joe is a prolific writer of self-help and educational material.
Under the penname, JC Page, Joe authored the classic of
mathematical ABC's Arithmetic Magic. Joe is also author of the
charmingly pithy and popular ebook, Make a Good Impression Every
Time: The Secret to Instant Popularity; the seminal collection
of verse, Poems for the Mathematically Insecure. For more
information, visit his website at
www.mathbyjoe.com.
