Fast Multiplication

When students learn the multiplication tables in 3rd grade (I think that is when they do it), they memorize numbers up to a 10x10 matrix and sometimes a little higher. There was a time that it was a need for people to be able to do basic arithmetic in their heads.  Unfortunately people now rely on calculators which means that people do not gain the ability to have a feel for numbers. When a number is higher than this 10x10 matrix, many people cannot multiply it in their heads.   

To do the following calculations, I assume that a person has a knowledge of all the multiples in a 10 by 10 matrix.

Lets start with all the squares. 11x11=
Here is how to do it in your head:

1x11=11 and 10 x 11 =110
so 11+110=121

Not too bad but some may not see this at first so lets discuss it. We have a 2 digit number 11 and it is composed of a 10's digit and units digit. If we break 11 into 10 and 1 it is easy to multiply and fairly easy to add in our heads. The part that is hard when multiplying numbers in our heads is remembering all the numbers and placing the numbers in their corresponding slots (ie thousands, hundreds, tens, and units).  The more digits we have the harder it becomes to keep track of these numbers in our head.  We need something to help us. 

I will expaln this as we multiply 12 x 12. How hard is it to multiply 12 by 10? It is not hard at all. How hard is it to remember? Not hard at all. 12 x 12 is equal to 24 + 120=144. What you are doing is multiplying 2 by 12 and getting 24 and knowing that you will add this to 120.

So lets do some more:

13x13=39+130=169
14x14=56+140=196
15x15=75+150=225
16x16=96+160=256
17x17=119+170=289 (This is a little harder)
18x18=144+180=324
19x19=171+190=361

Now when we multiply the units digit by a 2 digit number  and the resultant number has three digits it bcomes  a little harder.  This is because we typically don't learn these numbers in our math classes. However, don't let this stop you. You have 3 numbers to memorize right. Not a 100 like you did when you memorized your times tables.

Now lets say that we have 12 x 18, we do this in the same fashion but it is not a square. This looks like:

96 + 120=216 or how about 36 +180=216. Smaller number that result from the units digit result will be easier to utilize.

If it is hard for you to mulitply a one digit by a 2 digit number with a three digit resultant here are some numbers for you to memorize:

6x17=102, 6x18=108, 6 x 19=114
7x15=105, 7x16=112, 7x17=119, 7x18=126, 7x19=133
8X13=104, 8x14=112, 8x15=120,8x16=128,8x17=136,8x18=144, 8x19=152
9x12=108, 9x13=117, 9x14=126, 9x15=135, 9x16=144, 9x17=153, 9x18=162, 9x19=171

That is not a lot to memorize but I can hear the groans as well as the boos and hisses. So lets just learn a methodology so we don't need to remember. Okay?

The easy part will always be the tens digit. Remember this and forget about the 10's digit for now. Say that you want to multiply 17x19.

Lets look at 7x9=63 and 7 times 10 =70. 70 +63 is 133. Like clockwork we have 133 in our heads and we can easily add this to 190. Our answer would then be 323.

The key is to not juggle too many number in our heads. Before calculators people had to use numbers and more people where able to do basic multiplication in their heads. A person who practices this 30 minutes a day for week should have it mastered.