Does anyone know any shortcuts for multiplication?

Question

Does anyone know any shortcuts for multiplication? I'm also looking for ones that involve the ones we all memorize 8x7, etc. because I am a tutor and this would help my students. So any tricks for memorizing the basic multiplication tables are good too.

Here are the ones I know already.

I'm writing like this: AB x 11 means (10a + b) x 11

AB x 11 = 100a + 10(a + b) + b
Ex. 24 x 11 = 264

I know the algorithm for multiplying single digit numbers times 9. If you don't know it, its a x 9... first digit is (a-1). Then digits need to add up to 9. So 7 x 9, 7-1 = 6. Then second digit must be 3.

I don't need to go over the obvious trick when multiplying single digits times 5.

Then we have the (a-k)(a+k) = a^2 - k^2 trick.
Ex. 23 x 27 = 25^2 - 2^2 = 625 - 4 = 621.....(assuming of course that you know 25^2 = 625)
This is useful for lots of things 27 x 33, 35 x 45, etc.

Also if the numbers are low, ab x cd = 100(ac)+10(ad+bc)+bd is useful.

Answer 1

Well, I developped lots of tricks to the time tables. Im not only a teacher, I am a mother too...

For 7x8 I have the best one:

5 6 7 8
56 = 7x8

Simple, isnt it?

In fact, you can do this

1 2 3 4
12 = 3x4
5 6 7 8
56 = 7x8

I use to teach my daughter and my students this as a little "poem"

I developped too this one to the 6 time table

6x2 ends in 2
6x4 ends in 4
6x6 ends in 6
6x8 ends in 8
6x10 ends in 0

Now watch this:

6x2 = 1.. 2
6x4 = 2..4
6x6 = 3.. 6
6x8 = 4..8
6x10 = 6..0

I used the .. so that the trick is clear to you, but you can use colors while tutoring children

This only functions with even numbers, of course. They always ask if this functions with odd numbers too, and you can take advantage of this question to explain them that 6 is even and the product of a even by an odd is even, so it can be possible that ir 6x3 ends in 3

*But* you can tell them that they already know 6x1, 6x5 and 6x9 from other time tables. They probably know too 6x3. The only "difficult" is 6x7. But tell them that the result is 42 and that 4+2 is 6 too!!!

I developped these ones too

3,2,1
7x43 = 21

4,3,2
8x4 = 32

And, if you change this a little bit, you have too

3 2 4
8x3 =24

I hope that these little tricks help you, they help me a lot!

Ana

Answer 2

Well..... You seem to know most of the ones I know. But here's a trick for squaring numbers less than 100. If the number is x form the product of (x-k)(x+k) and choose the k so that one of the factors is an exact multiple of 10 (so that it's an 'easy' multiplication). Then add k² to the sum to get x². For example:
43²=(43-3)(43+3) + 3² = (40)(46) + 3² = 1840 + 9 = 1849

It works (obviously) because (x-k)(x+k) = x²-k².

With a bit of practice, you can square numbers in your head almost as fast as someone can ask you the question. I know it always impressed the hell out of my students when I was teaching ☺


Doug