Speed Mathematics Simplified (21 page)

If you fully mastered the last chapter, you answered, almost without a second thought, “zero.”

What is the right-hand (units) digit?

If the digit 8 sprang into your mind with little or no effort, you are already well on the way to accelerating your multiplication with the no-carry method. If you had to stop and think, however—as most of us do at this point—then that is exactly what this chapter is for.

Your first exercise is to go through the following digit pairs with the object of “seeing” only the left-hand (tens) digit—the one we have been describing as “is in the 20's, 70's,” etc. See and think, as well as you can, 4 x 4 as “1.”

The first time you go through these, it might be wise not to try for speed. The first job is to begin training the habit of recognizing the left-hand digit automatically. Just as important, you should build the habit of thinking “zero” when there is no real left-hand digit (that is, when the full product is less than ten) because this is so important to accuracy in multiplying longer numbers.

Remember to see 4 x 9 as “3
”—not
“the left-hand digit of 4 x 9 is 3, because 4 x 9 is 36 and 36 is in the 30's”—just as you see
u
and
p
as “up.”

Go slowly and carefully this first time, training your mind to see only the answer. Left-hand (tens) digits only:

That is enough for the first dose. You will go through every possible digit combination before you are through, but doing them all at once might become tedious.

Compare, if you will, the study of speed mathematics to learning any new skill. There is a specific objective in mind, of course—in this case, to solve problems more rapidly and easily. But there is also a helpful secondary objective: becoming fascinated with the process of
doing
and excited about your mastery of the technique. Just as a craftsman enjoys the actual process of making a perfect joint in a woodworking project because it is satisfying to do something skillfully, so can you become fascinated with the dispatch and accuracy of your working of a sample problem in a new way.

When we use them in business, numbers always stand for something. When we practice with them, however, they become an impersonal sort of puzzle. Look on them as a crossword puzzle, or a chess problem, or a brain-teaser. Just as satisfying as these and far more rewarding—because your growing skill at this type of puzzle will pay you solid dividends for the rest of your life.

Now, carefully rather than hastily this first time, continue working at the habit of seeing only the left-hand (tens) digits of these combinations:

By now you should find the habit beginning to take hold. Once the proper response starts becoming a habit, you can go back over the examples with the objective of speeding up your reaction time.

Make very sure at this point, though, that you work at giving your response in the right fashion, rather than giving a fast but improper one. Going reasonably slowly now will contribute to greater speed in the future.

Now finish your practice on left-hand (tens) digits with the rest of the basic digit combinations:

Stop and take stock of your technique now. Do you find that you are looking only for the left-hand digit as you glance at each pair? Have you schooled yourself to give only the answer? Are you
always
thinking “zero” when the product of the two digits is less than ten?

If not, make a point of going back over the combinations from time to time, working specifically to develop this habit. If you feel that you are making the proper responses a routine, then your next step should be to develop speed. Time yourself in completing the tables, and make a note of how long it took. Next time, see if you can shave a few seconds off the last record.

So far, you have worked at accuracy and speed in seeing

Right-Hand Digits

only the left-hand, or tens, digit of each product. This is only half the story. The other half is to do precisely the same thing for what the product “ends in.”

Glance at this example:

What is the left-hand digit?

What is the right-hand digit?

There would be little point to repeating all the tables again just for the right-hand digit practice. Instead, use the same tables on the last few pages.

Keep in mind the important practice points mentioned in connection with left-hand digits. Go slowly the first time, consciously making an effort to “see” only the right-hand digit, rather than the problem. You may find it helpful to say the answer to yourself; if you do, be very careful not to say the problem.

After you have gone over the tables just a few times, you should begin to find yourself simply reading the answers—just as you read these words or phrases rather than the letters.

If you need proof of this, stop right now and try to recall whether there were any f s in the paragraph above. In all likelihood, you haven't the vaguest idea. You undoubtedly read the first word “after” without even noticing the
f
in it. In the same way, you can approach this “end-result-only” ability with digit combinations.

Go back to the tables and do your first right-hand digit practice now.

Work at the tables conscientiously, but I would suggest that you alternate practicing the digit combinations with some of the other practice to come. Avoid the stale, “overtrained” reaction of too much consecutive time spent at only one part of the whole.

Two-Digit Practice

The whole reason you practice the basic multiplication table with left-hand and right-hand digits is so you can multiply from left to right without carrying. Picking up the right-hand digit from one product and adding it to the left-hand digit of the product to the right is the secret that eliminates carrying altogether.

You do have to keep one digit in your mind for a moment, but this is considerably simpler than juggling three (and sometimes four) digits in traditional right-to-left multiplication.

Refresh your memory with this example:

See if you can anticipate each step of this review:

Step one: 7 x 4 is in the 20's:

Step two: 7 x 4 ends in 8. 8 x 4 is in the 30's. 3 minus 2 (complement of 8) is 1, and record the ten: