Alright, there is a little method that I use to multiply 3-digit numbers. Really, there are two good methods here. There is no practical trick for multipying by 411 or 213.


First, you could do what I normally do -- treat the last two digits as a single number, then treat the numbers as a two-digit number. If you know LOIF, it's basically the same thing, with three-digit numbers.

For the first two digits (ones/tens) do 13 x 11, or 143. Write 43, carry 1.
Next, add 2x11 and 4x13, just like LOIF. You get 22 and 52, so added together is 74. Remember that you carried, so your number is 75. Write that.
Next, write 2x4 = 8.
Final answer is 87543.

Sometimes this is called the rainbow method, but i call it 3-digit LOIF (which is FOIL backwards, the FOIL that you learn in Algebra 1.)

Now, the second method is what I call compound multiplication. You treat one of the numbers as a single digit, and do normal multiplication.

If you did that, I would treat 213 as a single digit. You'd get:

411 x 213:

1 x 213 = 213, write 3, carry 21.
1 x 213 = 213, add 21 = 234, write 4, carry 23.
4 x 213 = 852, add 23 = 875. Write 875.

Final answer is 87543, and you can see both methods work.

Do you understand how they work? At first, you'll be slow, but you'll get used to it and become fast after enough practice.

Nobody really visits this forum, and I just made an account on this site after visiting the forum in the past week and seeing a couple of questions. If you want more people to see your posts, go to www.texasmath.org. Make an account there, then post in the Number Sense section. There are other UIL event sections there too. You would have a much better time getting your questions answered if you went there instead.

NICE FORMULA