Thursday, August 11, 2011

Some Tricky 11’s – in each place

Remember that A and I have been talking about patterns in multiplication? Well, the easiest of the multiplication tables (besides 10s) are 11s – just double the number, right? Well, what happens when you get to 11 * 11? It isn’t as hard as you might think – you just have to figure out the right pattern.

Think about 11 * 9:
 image       We don’t even really have to think about it as “90 + 9” because we can just think of it as “write 9 twice”. But now when we move on to 11 * 10, looking at it this way will help when we do 11 * 11 and 11 * 12:

imageWe can think of the number 11 as “one in the tens place, and one in the ones place” – which when extended to multiplication (for example, 11 * 5) becomes “5 in the tens place and 5 in the ones place” (where you replace “5” with whatever number you are multiplying by.

For 9, that is easy, for 10, it isn’t quite as straightforward – because what does “10 in the tens place” mean? Well, in the illustration above, it means “100” – because a 10 in the tens place means we need to put another zero on the end, and a 10 in the ones place is really just 10. So that’s how we get 11 * 10 = 110.

Now we can move on to 11 * 11. We think the same thing; “11 in the tens place, and 11 in the ones place.” Let’s write it out like we did with 9 and 10:


So you can see that when we write “11 in the tens place” what we get is 110, and when we put “11 in the ones place” we get 11. So the answer is 11 * 11 = 121.

image We can do the exact same thing for 11 * 12, and we get 120 + 12 = 132.

Now you can probably figure out 11 * 13, 11 * 14, and 11 * 15! And after a while, you can probably see a new pattern as you go.

So when thinking about the 11’s times tables, you can just think “the number in the tens place, and the number in the ones place.” This rule works for all the times tables – from 1 to infinity!

If you have questions, you can ask them in the comments, email me, ask on Facebook, or on Twitter. I am on Facebook and Twitter live from 3:00-3:30 pm Mon-Thurs MDT.

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