This post may seem out of the ordinary with respect to the genre of posts that I usually post. However, at 10 am in the morning I looked at my colleague and I asked him about what I should write and his reply was maths. So here it goes.
So let’s consider multiplying a single digit number by 11. This is quite easy you just type that digit twice.
ex: 8 *11 = 88
Now let’s take a two digit number denoted by xy and multiply it by 11. First step is take the number present in the ones field and place it in the result one’s field. After that, take the number present in the tens field and put it in the hundreds field in the result. The third step is easy, add the two numbers x and y and place that digit in between the previously two digits or basically in the tens position in the result number.
Here’s an example to simply things:
34 * 11 =
3 (3+4) 4
26 * 11 =
Now, supposedly the addition of the two numbers x and y turned out to be larger than 9, we place the one’s number of the addition process in the field of the tens and the tens number from the addition process we add it to the hundreds position in the result. Here is an example to clarify things:
47 * 11
–> 4 (4+7) 7
–> 4 (11) 7
–> (4+1) 1 7
58 * 11
Now, let’s suppose we are multiplying any two digit number by a single digit number, now this is not a fast multiplication kinda procedure, however I just use it because it makes multiplying faster for me, I am not sure it could work for everyone.
First of all, there are two methods the first let’s call it the (multiply-add) and the second one let’s denote it by (multiply-subtract). When the two digit number has a ones digit lower that 5 we use the multiply-add, and when the number is above 5 we use the multiply-subtract.
Multiply-add, let’s say we have 23 *4.
First of all 3 is below 5, thus we neglect it and consider the number as 20.
Now 20*4=80 (this is simple). We still have that 3, we multiply it by 4 we get 12.
Final step: 80+12= 92.
Basically, we changed the number to become one that has a zero in the ones digit and then we added the number neglected multiplied by our factor.
Multiply-subtract, let’s say we have 29 *8.
The number is above 5, its a 9, so we add 1 in order to make it a 10.
Therefore: 29+1 = 30.
now 30*8 = 240(this is simple), now we multiply the number added, by 8 and subtract it from the whole.
1*8 = 8, therefore the answer is 240-8=232.
Now, I hope that I have helped somehow even though I am not pretty sure fast multiplication is quite used these days.
Have a good day.