Painless Nine Times(I)

If you take a careful look at the multiplication table you will find many interesting patterns. Look at these two interesting patterns. Aren't they interesting? If we bring to the notice of our children such patterns, they will develop tremendous liking for these tables and will be motivated to memorize them automatically.

In this article we will experience one such pattern, with the help of the multiplication table for nine. Look at the table reproduced below.

You will immediately notice the decreasing order of numbers in the units column and the increasing order of numbers in the tens column.

Another interesting and well-known fact about nine times is that, the addition of the two digits in the product is always nine. For example, nine times 7 is 63. Adding six and three together we get nine. Similarly, nine times 5 is 45. Add 4 and 5, we get nine. So, this is true for all the multiplications of nine with numbers from 1 to 10.

You must have also noticed that in each product the number of tens is less by 1 than the number multiplied by 9. Thus, when we calculate nine times eight, we get 72. The number of tens in 72 is seven, which is one less than eight (the multiplier). This is true for all the multipliers from one to ten.

The information above gives us a clue as to how to get nine times of many numbers with the help of our very old rudimentary calculator? All of us possess this calculator free of cost! Our fingers! "Finger reckoning" is the simple method of counting we have been using since historic time. We have used it instinctively for simple additions and subtractions. But do you know that it can be used for multiplication? Let us see how interesting it is to remember nine times on fingers. Place both of your hands on a table flat, as shown in the figure here. Imagine that these fingers are numbered beginning from the smallest finger of the left hand, as numbered in the left-hand figure.

Suppose, we want to know nine times three. Just bend in the third finger of the left hand, as shown in the right-hand figure. Now, your unbent fingers provide you the answer! How? The fingers on the left of the bent finger represent the number of tens in the product, whereas, the fingers on the right of the bent fingers indicate the number of units in the product. In the present case there are two fingers on the left and seven fingers on the right of the bent finger. Hence, nine times two is twenty-seven.

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