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, or if you can't get to the Internet to watch the Math Masters Muliplication Tables video.

I was going to call this "Using the distributive property of multiplication", but who would have been tempted to read this??

Following on the heels of the brilliant and highly entertaining Math Masters Muliplication Tables video, LearnHub readers are brought back down to earth with this pedestrian yet useful lesson.

Thanks to the two Andrews, we all know what 3 x 4 is. But, do you know what 30 x 42 is? Or 63 x 15?

With a half-decent memory and knowledge of the distributive property of multiplication, it's not that hard to work out these tasks.

Take 30 x 42.

First, you know what 3 x 4 is, right? 12 of course. But it wasn't 3, it was 30 and it wasn't 4, it was 40, so add a couple of zeros to get 1200.

But it wasn't forty 30s we were asked about, it was forty-two 30s.

However, we have already accounted for forty of the forty-two 30s; all we need now is two more 30s, which is 60, and Bob's your uncle; 30 x 42 = (30 x 40 = 1200) {store that in your head} + (30 x 2 = 60) {retrieve the 1200 that you have stored}, so that 30 x 42 = 1200 + 60 = 1260.

We can do this because the distributive property of multiplication says that 30 x 42 = 30 x (40 + 2) = (30 x 40) + (30 x 2).

Note the use of the parentheses to make it clear that mulitiplication is performed before addition. The parentheses makes it more readable as well.

I like to think of it as 30 being "applied" (i.e. distributed) to as many parts of the 42 as you want - in this case 40 + 2.

Did you notice that when I accounted for the tow zeros, I was unconciously using the comutative property? Because 30 x 42 = (3 x 10) x (4.2 x 10) = {gathering like terms i.e. the 10s} = (3 x 4.2) x (10 x 10). Of course we all know what 10 x 10 is, but multiplying fractional numbers mentally can be taxing.

What about 63 x 15?

63 x 15 = (60 + 3) x 15 = (60 x 15) + (3 x 15) = (6 x 10 x 15) + (3 x 15 ) = (6 x 15 x 10) + (3 x 15) = (6 x 15) [store this in your brain} x 10 [add a zero to what you have just stored}+ (3 x15) {piece of cake, hopefully} = (90 x 10) + (3 x 15) = 900 + 45 = 945

Finally, we look at a case where we take a multiplication task, "build it up" to something we can handle, then "back off" to get the desired result.

What is 20 x 19?

If you know that 20 x 20 = (2 x 2) x (10 x 10) = 4 X 100 = 400 then you realize that you weren't asked for twenty 20s, you were asked for nineteen 20s. You have one 20 too many - so subtract, or back off, a 20 to get 400 - 20 = 380.

You could have done 20 x 19 = (2 x 19) x 10 = 38 {hopefully} x 10 = 380.

To summarize, if you have to perform a multiplication such as these, break the complicated case down into simple cases that your brain can remember, then put the cases together.