Sep 14, 2008

More mathematical tricks

11 pairs of new football boots are needed for the team. They cost £22 for each pair. How much will it cost to kit out the whole team?

Assuming that you don't carry a calculator around with you everywhere you go (it's pretty sad if you do!) at this point you dutifully get out your pen and paper (if you have one).

You then write down the following calculation:

x 22

All this is a drag, "there must be a better way of doing this" you think to yourself. Well, there is - you can do it all in your head!

Here are the steps you need to follow (note that it takes much longer to explain than it does to actually do the calculation):

1) Think of the best number to multiply by 10 to make the calculation easy- we'll call this the first number.
2) Multiply the second number by 10.
3) Multiply the difference between the first number and 10 by the second number.
4) Add the results of 2) and 3).

All you are trying to do here is to break a "complicated" calculation down into smaller bits which you can easily do in your head. What is easier than to multiply something by 10? All you need to do is add 0 to the end of the original number!

So, for this example:

1) You see that 11 is close to 10
2) You multiply 22 by 10 to give 220
3) You've now nearly got 11x22, though there's still the 1 in the 11 to cater for (you've already catered for the 10). So you now need to multiply 1 by 22 also.
4) All that remains is the simple addition 220 + 22 = 242.
Here are some mathematical tricks for you to try ....

What if you need to work out something more difficult like 35 x 44?

It is possible to do this in your head still....

Think of the best number to multiply by 10 to make the calculation easy. I would multiply 44 by 10 to give 440 as it gets the biggest number out of the way.

But, you need to multiply by 35 not 10! No fear, just multiply 440 by 3 to give 1,320 and you now have the answer to 30 x 44.

You now need to add 5 x 44 to 1,320 to get the answer to 35 x 44.

Note that 5 is half of 10 and that 10 x 44 = 440, hence 5 x 44 = 220.

Now add 1,320 and 220 together to give the final answer 1,540....phew.

"Hold on a minute" I can hear you saying "what about 440 x 3, that's not very easy is it? I didn't learn my 440 times table I'm afraid!"

Well, for starters, 440 x 3 is the same as 10 times 44 x 3 - that's still hard, so what's 2 x 44?
Aha, that's easier - it's 88. Now what's 88 + 44? Hmm...not so easy. If you think that 88 is quite close to 100, then think of 100 - 88 = 12, now all you do is subtract 12 from 44 to give 32 and add this to 100 to give 132 - multiplying by 10 gives to 1,320.

This may all seem a bit long winded, however, when you are doing calculations in your head you should always break things down into simple calculations and add all the bits together at the end. With practice you will be able to do this faster than the time it takes for a friend to get a calculator out of their pocket!

In summary, look for easy numbers to use in calculations, like 10, 100, 2, 1, break down the calculation so that you can use the easy numbers, then tidy up all the bits at the end.


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