Consecutive Digit Products (CDP’s)

Part I

Carefully find the products of these multiplication exercises.

(A)   41  × 3

(B)   576 × 6

(C)   11728 × 2

Did you notice something interesting about your answers?

If you did your work correctly, you should have noticed that the digits in each product were “in order”. That is rather interesting, don’t you think?

When the digits appear “in order” like that, we say they are consecutive digits.

Here are some more problems. Each one has a “consecutive digit product (CDP)”.

(1)     81 × 7            (6)     18 × 13
(2)     263 × 3          (7)     335 × 7
(3)     57 × 8            (8)     64 × 54
(4)     23 × 15          (9)     219 × 31
(5)     27 × 21         (10)     167 × 34

tt(8/4/82)

Teacher’s Note: This and the following three activity pages were written before calculators were commonly accepted for use in the classroom. Hence, you should take this into consideration when using this material.

The fundamental purpose behind this seeming “drill & kill” sort of activity is actually the opposite. Namely, once you have multiplied the numbers, you should have, if done correctly, a surprise awaiting you: a product with some interesting aspect, in this case consecutive digits of one form or another. In this way, a reward of sorts is provided while at the same time practicing the old fashioned (or, if you prefer, time honored) skill of multiplying whole numbers. And not to be overlooked is the encouragement of the habit of examining one’s answer to see if it is reasonable; in this activity the focussing on the answer is merely to see if it meets the criteria of the lesson. But in general the habit of “looking back” is one that is not well established in the minds of many and needs to be promoted more.

tt(6/5/98)

Part II

Here are some more problems that have “consecutive digit products”. But this time there is a difference. What is it?

(A)   48  × 9

(B)   727 × 9

(C)  18107  × 3

Of course, you see that the digits are still in order, but this time their order is reversed!

Try the following exercises to see yet another type of answer.

(D)   27 × 5

(E)  617 × 4

(F)   3251 × 3

In those problems the digits are either odd or even, while at the same time they are still consecutive.

Now, all the problems below use these ideas. But, which is which?

(1)     107 × 3             (6)     443 × 17
(2)     181 × 3             (7)     149 × 58
(3)     51 × 15             (8)     89 × 86
(4)     679 × 8             (9)     149 × 29
(5)     1193 × 3          (10)     59 × 23

tt(8/4/82)

Part III

Here are twenty more problems. Most of them have products of consecutive digits; but some of them do not! Can you find those that do not have CDP’s?

(1)     617 × 2           (11)     73 × 12
(2)     47 × 21           (12)     197 × 45
(3)     36 × 12           (13)     823 × 12
(4)     128 × 27         (14)     2932 × 8
(5)     65 × 19           (15)     2659 × 13
(6)     93 × 73           (16)     953 × 57
(7)     76 × 31           (17)     178 × 43
(8)     97 × 56           (18)     733 × 32
(9)     298 × 29         (19)     557 × 8
(10)     24 × 19         (20)     138 × 331

tt(8/4/82)

Part IV

This lesson presents several new ideas. Two of them are: number palindromes and number tautonyms.

Perform the multiplications to see these interesting types of products–and others–come out.

In all of them, however, the idea of consecutive digits is still there.

(1)     3261 × 14             (11)     945 × 143
(2)     333 × 37               (12)     3717 × 143
(3)     353 × 91               (13)     2354 × 273
(4)     8182 × 8               (14)     902 × 273
(5)     407 × 333             (15)     3435 × 33
(6)     6105 × 87             (16)     2277 × 243
(7)     3737 × 66             (17)     537 × 418
(8)     9731 × 66             (18)     20134 × 33
(9)     443 × 223             (19)     20219 × 6
(10)     2442 × 263         (20)     50471 × 3

tt(8/7/82)

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