Speed Mathematics Simplified (31 page)

Learning to “see” what we might call the breaking point of each answer digit cannot help but ease and speed up your automatic division. Once you have learned to “see” 3
as 4 rather than “almost 5,” you should have no trouble reading 3
as 4 also. If you recognize 8
as 8 rather than “almost 9,” then whenever you need an answer digit for 8
8
and all the intermediate possibilities down to 8
, you should answer without a second thought “8.”

Go through the rest of these “breaking point” combinations now:

That finishes all the possibilities. This practice section is vastly different from any other in the book, in that it calls for you to give what you know to be a very
approximate
answer—an answer you know full well will need adding to later. Yet this is the way we must divide, and what at first may seem very odd must become second nature.

Having done the single-digit tables, expand your practice a bit now by doing precisely the same thing with these examples. In each case, be sure to divide by only the first digit of the divider, raised in value by one. See only the first answer digit for each of these problems:

Those are the basic vocabulary elements in speed division. When you put them together with simultaneous left-to-right multiplication and subtraction, short hand division really becomes short-cut division.

See how well you remember the entire system now by working this problem out in detail on your pad:

Cover the demonstration below with your pad while you work it out. This problem comes out even, so you know without looking ahead whether or not you solved it properly.

When you are finished, compare your working with this model:

One way to speed up your working of any problem such as this is simply to jot down your working figures on whatever piece of paper you have handy. You do not always have to copy the entire problem, although this is often helpful during early stages of practice, when each move still seems rather strange.

If you have been doing your practice, you should be able to solve the following problem by the shorthand method without copying it. I do not suggest that you solve it in your head (some people can, but most of us have to lean on our pencils even with simplified techniques), but you should be able to glance from printed problem to jotted working figures and produce the answer without turning yourself into a stenographer:

See if you can do this problem without copying it. Use your pad only for jotting down the answer and working figures. If you have never done it this way before the technique may seem difficult, but it can save you a great deal of time in your number work.

When you have finished, compare your jotted figures with these: