How many times have you heard someone say
'I can't do mental arithmetic'or 'I can't do mental maths'?
 

Keywords: mental arithmetic, mental exercises, mental workout [421 words]
 

How many times have you heard someone say 'I can't do mental arithmetic'?

Perhaps it is something that you have said yourself many times . . . I know I have!

The problem, I have found, is not 'I can't do mental arithmetic' but 'I don't know how to do mental arithmetic'.

This certainly was the case for me.

Let me show you what i mean.

If I were to ask you to multiply 43 x 11. Would you be able to do it? How long would it take you to do it?

If you asked me that 1 year ago, I would have said 'I can do it but it will take me a while'. You see, like many people, I believed that I couldn't do mental arithmetic.

Now, let me show you how to do 43 x 11 in your head in less than 1 second (it will take you less than 1 second once you know how to do it).

1. separate the 4 and the 3 thus: 4 __ 3 (because we are going to put a number in between the 4 and the 3),

2. add 4 + 3 to get: 4 + 3 = 7,

3. place the 7 between the 4 and the 3 to get: 4 7 3,

That is your answer: 43 x 11 = 473

How easy is that?  

Practice on the following and see how quickly you can do them in your mind:

- 23 x 11 =                 (23 x 11 = 253)  

- 18 x 11 =                 (18 x 11 = 198)

- 71 x 11 =                 (71 x 11 = 781)

If I were to ask you now, what is 27 x 11? You would be able to work it out in your head in less than 1 second and tell me: 297.

Congratulations! You have gone from 'I can't do mental arithmetic' to 'Gee, that was easy!'.

The thing about mental arithmetic is: the problem is not 'I can't do mental arithmetic' but 'I don't know how to do mental arithmetic'.

There are many such tricks to doing mental arithmetic and once you know them, you will be amazed at the type of mental arithmetic calculations you will be able to do in you head in less than 1 second:

- divide by 5 eg. 42 / 5 = ?

- multiply by 5 eg. 68 x 5 = ?

- square a number that ends in 5 eg. 45 x 45 = ?

- and so on . . .

So, take heart! You are not as 'dumb' as you think. You can't do mental arithmetic simply because you were never shown how to do it . . . and not because you can't!

Serge M Botans

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Serge M Botans is the CEO of the web site
http://www.mental-workout.com and has
taught Maths/Science for 14 years in a High School.
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Mental Arithmetic Magic Tricks
 

Keywords: mental arithmetic, arithmetic, arithmetic tricks, magic tricks [647 words]
 

While working on a divisibility section for my web site, I across some interesting facts about numbers that, to someone who does not know about these things, would seem like mental arithmetic magic.

In case you don't know, the divisibility of a number refers to whether a number can be evenly divided by another. For example, 24 is divisible by 2 but 13 is not as it leaves a remainder.

Here are some mental arithmetic magic tricks I have found that you can use to impress your friends, your colleagues, your teachers, . . .

1. if a number is divisible by 3 then so are the numbers based on mixing up the digits of the original number. For example, consider 123 which is divisible by 3. Then 132, 213, 231, 312 and 321 (which are obtained by mixing up the digits 1, 2 and 3 that make up 123) are all divisible by 3. This is called a permutation of the digits of a number. Check it for yourself!

2. to make up a number that is divisible by 4, make up a numberr and tag on the end any 2 digit number divisible by 4. For example, I make up the number 111111111, and now I tag 16 (which is divisible by 4) on the end to get 11111111116. This number is divisible by 4. Check it for yourself!

An interesting trick follows on from this one. The following numbers are all divisible by 4: 116, 1116, 11116, 111116, and so on . . . Not what you would expect!

3. if a number is divisible by 6, then any permutations of its digits will give you a new number divisible by 6 as long as the last digit is even. For example, 1272 is divisible by 6. Permutations of its digits while keeping the last digit even gives me 2172, 2712, 1722, 7122, 7212 which are all divisible by 6. Check it for yourself!

4. to make up a number that is divisible by 8, the process is similar to point 2. above. Make up a number and tag on the end any 3 digit number divisible by 8. For example, I make up the number 777777, and now I tag 016 (which is divisible by 8) on the end to get 777777016. This number is divisible by 8. Check it for yourself!

Another interesting trick follows on from this one. The following numbers are all divisible by 8: 7016, 77016, 777016, and so on . . . Again, not what you would expect!

5. if a number is divisible by 9 then so are the numbers based on mixing up the digits of the original number. For example, consider 189 which is divisible by 9. Then so are 198, 819, 891, 918 and 981. Check it for yourself!

6. if a number is divisible by 11, then permutations of its odd digits and/or its even digits will give you a new number also divisible by 11. For example, consider 154 which is divisible by 11. Then so is 451 (obtained by swapping its first and third digits). Another example, consider 1122 which is divisible by 11. Then so is 1221 (obtained by swapping its second and fourth digits). Check it for yourself!

7. if a number is divisible by 12, then any permutations of its digits (except for the last 2) will give you new numbers also divisible by 12. For example, 14652 is divisible by 12. Then so are 16452, 41652, 46152, 61452 and 64152. Check it for yourself!

You have to agree that such tricks do look like arithmetic magic which you can do in your head. Hence the title of this article being 'mental arithmetic magic'. In case you are wondering 'why is it so?' The answer lies in the test that determines whether a number is divisible by another.

Serge M Botans

=======================================
Serge M Botans
S M Botans is the CEO of
www.mental-workout.com and
has 13 years experience teaching
Maths, Science and Physics.
======================================

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