Applying multiplication rules (Part I)

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Jan 4, 2002

The rules we considered in the last article are like the many tools lying in our house. They lie somewhere forgotten. If available when needed, on demand, they would save us time and efforts. Let us see how we can develop a habit to use these rules and simplify our multiplication operation.

Let us do this simple multiplication: 8 x 49. Unless we try to do this by using all the methods known so far to us, we will not be able to find out which one is the quickest, as well as the one with which we are most comfortable.

I have shown it here:

In these solutions I have not included the "compensation in multiplication," simply because in this particular case the compensation does not provide any advantage.

Suppose, anyway, we try to use compensation, as we can certainly do it.

Let us do it! The multiplication 8 x 49 can be performed by transforming the same into 56 x 7. We have reduced 49 to 7 by taking 1/7 th of 49. Since, 49 is reduced by 1/7th we have to increase 8 by 7 times, in order to compensate the whole multiplication. However, the transformed form is in no way simpler or less complicated than the original multiplication.

Let us now try the other example, 18 x 36, By using the methods known to us.

In this example the use of compensation in multiplication transforms the multiplication into the easier form. The simpler multiplication then can be carried out by using the table of nine or by using the distributive property of multiplication, as shown above. There are, of course, other ways to simplify this, and we will learn about those a little later.

In the first example, the multiplicand was less than 10 and the multiplier was more than 10, whereas in the second example the multiplicand and the multiplier, were both greater than 10.

In the next example, let us use a multiplicand that is less than ten and a multiplier greater than hundred. For example, 256 x 8. As before, in this case let us also use all the methods.

As in the case of the first example above, in this multiplication also there is no advantage in using compensation in multiplication. Hence, it is not used. You may try to do it yourself!

Now try these problems yourself.

45 x 120
48 x 45
128 x 12
62 x 35
64 x 25

In the next article we will see some more examples and weigh suitability of various methods in different multiplication situations.

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The copyright of the article Applying multiplication rules (Part I) in Math for Kids is owned by Vidya Narayan Wadadekar . Permission to republish Applying multiplication rules (Part I) in print or online must be granted by the author in writing.