And, at least when I was in school, we learned through 12 times 12. Let's say I'm taking 25 and I want to divide it by 5. But for now, you just say, well it goes in cleanly 7 times, but that only gets us to 21. So you can even work with the division problems where it's not exactly a multiple of the number that you're dividing into the larger number.
So I could draw 25 objects and then divide them into groups of 5 or divide them into 5 groups and see how many elements are in each group. Well you say, that's like saying 7 times what-- you could even, instead of a question mark, you could put a blank there --7 times what is equal to 49? But let's do some practice with even larger numbers. So let's do 4 going into-- I'm going to pick a pretty large number here --344. This is way out of bounds of what I know in my 4-multiplication tables.
Regardless of whether a particular division will have a non-zero remainder, this method will always give the right value for what you need on top.
In this way, polynomial long division is easier than numerical long division, where you had to guess-n-check to figure out what went on top.
Note that a vertical Since 3.33 x 30.027027027 does not equal 99.99, either the calculator ran out of room before the long division was completed, the quotient contains a recurring decimal, or there is a rounding issue between the calculated result and the long division result.
You will often see other versions, which are generally just a shortened version of the process below.So let's say I want to divide-- I am looking to divide 3 into 43. And, once again, this is larger than 3 times 10 or 3 times 12. If you're dividing a polynomial by something more complicated than just a simple monomial (that is, by something more complicated than a one-term polynomial), then you'll need to use a different method for the simplification.That method is called "long polynomial division", and it works just like the long (numerical) division you did back in elementary school, except that now you're dividing with variables.In order to be able to do at least some of these more basic problems relatively quickly. And you're actually saying 4 goes into this 3 how many hundred times? Now, with that out of the way, let's try to do some problems that's might not fit completely cleanly into your multiplication tables. And, if you know your 3-times tables, you realize that there's 3 times nothing is exactly 23. But the quick way to do is just to think about, well 5 times what is 25, right? And if you know your multiplication tables, especially your 5-multiplication tables, you know that 5 times 5 is equal to 25. And if you know your multiplication tables, you know that 7 times 7 is equal to 49. Once again, you need to know your multiplication tables to do this. And sometimes, even if you don't have it memorized, you could say 9 times 5 is 45. And, immediately when you see that you might say, hey Sal, I know up to 4 times 10 or 4 times 12. And what I'm going to show you right now is a way of doing this just knowing your 4-multiplication tables. So something like this, you'll immediately just be able to say, because of your knowledge of multiplication, that 5 goes into 25 five times. Not over the 2, because you still want to be careful of the place notation. It goes into it 5 ones times, or exactly five times. All the examples I've done so far is a number multiplied by itself. And 9 times 6 would be 9 more than that, so that would be 54. So just as a starting point, you need to have your multiplication tables from 1 times 1 all the way up the 10 times 10 memorized. So what you do is you say 4 goes into this 3 how many times? But 4 goes into 3 no hundred times, or 4 goes into-- I guess the best way to think of it --4 goes 3 0 times. Think back to when you were doing long division with plain old numbers.You would be given one number (called the divisor) that you had to divide into another number (called the dividend).