The cool thing about math is watching how seemingly impossible combinations seem to walk out perfectly in the end. By doing certain operations, you can turn wildly complex equations into simple, step-by-step solutions.
Using the Vertical and Crosswise Pattern, we can easily multiply large two-digit numbers like the one pictured below.
Instead of doing the standing method of multiplication, we are going to separate and conquer.
12 x 34
First, we multiply vertically up the right side. 2 x 4 = 8. So, 8 will be the last digit in our answer.
Next, we cross-multiply. 3 x 2 = 6 and 4 x 1 = 4. Now add 6 + 4 to get 10. Carry over the 1 like you normally would, and you are left with 0, which will go in front of the 8 we already have.
So, as of now you should have 08 in you answer line.
Lastly, we vertically multiply up the left side. 3 x 1 = 3 and add the carried 1. Place that in the front of our answer line and we get 408.
All you need to do is add the digits of the number you are multiplying by 11 and place that in the middle of the original number. If the sum of the digits is 10 or larger, simply carry it over. Better to see it than me write it.
See how easy that was? Basically, if you know how to add, you know how to multiple by 11.
Now, let’s look at another example.
11 x 11
Just separate the number being multiplied by 11 (in this case, also 11) so that there’s room for your number in-between. Now, just add the two digits in that number together (1 + 1 = 2) and throw the sum in that space you left open. That gives you 121.
58 x 11
Just add 5 + 8, which gives you 13. The slide it in-between the 5 and 8 and you get 5138. But, that’s not right, since you need to carry that one over. Go ahead and carry it over and you’ll end up with 638.
Needless to say, I feel like a complete badass now that I know this.