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Try this method using powers of ten. To successfully use this method, students need to be able to multiply by powers of ten and to subtract. Students subtract the dividend multiplied by decreasing powers of ten until they have zero or a remainder.
Note that was subtracted twice, so the number of times that 54 "goes into" so far is 20 times. Since 54 was subtracted seven times, the quotient increases by seven for a total of In other words, 54 "goes into" , 27 times.
We might also mention that this method can be even more sophisticated by using multiples of powers of ten. Have you ever thought that you could help a student understand things better and get a more precise answer while still using remainders?
It's quite easy really. Remainders are usually given out of context, including on the answer keys below. A remainder is really a numerator in a fractional quotient.
Using fractional quotients means your students will always find the exact answer to all long division questions, and in many cases the answer will actually be more precise e.
We thought it might be helpful to include some long division worksheets with the steps shown. The answer keys for these division worksheets use the standard algorithm that you might learn if you went to an English speaking school.
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We are thankful for obscure words. I just picked any of them right like that. That's one group of 4. Then here's another group of 4 right there.
And then I have this left over thing. Maybe we could call it a remainder, where I can't put this one into a group of 4. When I'm dividing by 4 I can only cut up the 9 into groups of 4.
So the answer here, and this is a new concept for you maybe, 9 divided by 4 is going to be 2 groups. I have one group here and another group here, and then I have a remainder of 1.
I have 1 left over that I wasn't able to do with. Remainder-- that says remainder 1. If I asked you what 12 divided by 4 is, so let me do So let me write that down.
So I want to divide these 12 objects-- maybe they're apples or plums. And divide them into groups of 4. So let me see if I can do that.
So this is one group of 4 just like that. This is another group of 4 just like that. And this is pretty straightforward. And then I have a third group of 4 just like that.
And there's nothing left over like I had before. I can exactly divide 12 objects into 3 groups of 4. So 12 divided by 4 is equal to 3.
And we can do the exercise that we saw on the previous video. What is 12 divided by 3? Let me do a new color. Now based on what we've learn so far we say, that should just be 4 because 3 times 4 is But let's prove it to ourselves.
So 1, 2, 3, 4, 5, 6, 7, 8, 9, 20, 11, Let's divide it into groups of 3. And I'm going to make them a little strange looking just so you see that you don't always have to do it into nice, clean columns.
So that's a group of 3 right there. Let's see, here is another group of 3 just like that. And then, maybe I'll take this group of 3 like that.
And I'll take this group of 3. There was obviously a much easier way of dividing it up then doing these weird l-shaped things, but I want to show you it doesn't matter.
You're just dividing it into groups of 3. And how many groups do we have? We have one group. Then we have our second group right here. In some programming languages, an attempt to divide by zero results in undefined behavior.
The graphical programming language Scratch 2. Some modern calculators allow division by zero in special cases, where it will be useful to students and, presumably, understood in context by mathematicians.
From Wikipedia, the free encyclopedia. This article is about the concept in mathematics and exception in computing.
For other uses, see Division by zero disambiguation. The result yielded by a real number when divided by zero. This article includes a list of general references , but it remains largely unverified because it lacks sufficient corresponding inline citations.
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