Fun With 5's - 3

Now let’s move on to what to do if the numbers are further apart. For example, how would you handle 45x65? These are easy also, but I need to introduce something new to you here.
In these cases, ALL numbers more than 10 apart, to determine what the last 2 numbers will be there is a very simply process. In our example case, just subtract 6-4 (the first digits of each number). If you get an even number, the last 2 digits will be “25” and if you get an odd number they will be “75”. Easy.
To get the first part of the answer is almost as simple. First you do the normal multiplication, in this case, 4x6. When you get your answer (24) you add back in the number that is exactly in between the 4 and 6, which, of course, is 5. It will look like this: 4x6+5=29, the add on the “25” because 6-4 equals 2 (an even number). The answer for 45x65 is 2925.
If it’s 95x75 it will be 9x7+8 (71) and add the “25” (9-7=2). The final answer is 7125. Naturally, if the numbers are only apart by 20, it will always be an even number on the end. So, let’s check to see what happens when they are further apart and that “odd number” pops up.
This process also works on the 10 apart numbers, but it is easier to do with the way I showed you in part 1. For this, we will use the example 85X55. If you subtract 8-5 you get 3, an odd number. As indicated in the above paragraph, that means the last two digits to the answer will be “75”. To get the first digit(s) in the answer you add the 8 and 5 (8+5)(13) and divide that in half (6.5). You can just drop the .5 and use the 6 to add back in. That means for 85x55 we have 8x5+6 (46), then add the “75”, 4675. This one could be a little confusing so we’ll do a couple more.
Let’s go with 95x25. I like to get the add back in number first, but you do what is good for you. Here we would have 9+2=11 and 11x.5 (half) = 5.5. Drop the .5 and the add back in number will be 5. Now we have 9x2+5=23 and since 9-2=7 (an odd number) than the last 2 digits will be “75”. The final answer is 2375.
Now with 75x45? That would be 7x4+5 (plus the 75) = 3375.
Give 45x15 a try, see if you have a handle on it.
That’s it. What do you think? It’s interesting at the very least.

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