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I don't have to draw them all stacked up. These are just groups of 2. But how many groups do I have? I have 1, 2, 3. I have 3 groups.
But notice something, it's no coincidence that 6 divided by 3 is 2 and 6 divided by 2 is 3. Let me write that down. We get 6 divided by 3 is equal to 2 and 6 divided by 2 is equal to 3.
And the reason why you see this relation where you can kind of swap this 2 and this 3 is because 2 times 3 is equal to 6.
Let's say I have 2 groups of 3. Let me draw 2 groups of 3. So that's 1 group of 3 and then here's another group of 3.
So 2 groups of 3 is equal to 6. Or you could think of it the other way if I have 3 groups of 2. So that's 1 group of 2 right there.
I have another group of 2 right there. And then I have a 3 group of 2 right there. What is that equal to? That's also equal to 6.
So 2 times 3 is equal to 6. We saw this in the multiplication video that the order doesn't matter. But that's the reason why if you want to divide it, if you want to go the other way-- if you have 6 things and you want to divide it into groups of 2, you get 3.
If you have 6 and you want to divide into groups of 3, you get 2. Let's do a couple of more problems. I think it'll really make sense about what division is all about.
Let's do an interesting one. Let's do 9 divided by 4. So if we think about 9 divided by 4, let me draw 9 objects. Now when you divide by 4, for this problem, I'm thinking about dividing it into groups of 4.
So if I want to divide it into groups of 4, let me try doing that. So here is one group of 4. 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.
For example, . In general, a single value can't be assigned to a fraction where the denominator is 0 so the value remains undefined.
A compelling reason for not allowing division by zero is that, if it were allowed, many absurd results i. When working with numerical quantities it is easy to determine when an illegal attempt to divide by zero is being made.
For example, consider the following computation. The fallacy here is the assumption that dividing 0 by 0 is a legitimate operation with the same properties as dividing by any other number.
The limit. A formal calculation is one carried out using rules of arithmetic, without consideration of whether the result of the calculation is well-defined.
This infinity can be either positive, negative, or unsigned, depending on context. For example, formally:. As with any formal calculation, invalid results may be obtained.
A logically rigorous as opposed to formal computation would assert only that. Since the one-sided limits are different, the two-sided limit does not exist in the standard framework of the real numbers.
This definition leads to many interesting results. However, the resulting algebraic structure is not a field , and should not be expected to behave like one.
This set is analogous to the projectively extended real line, except that it is based on the field of complex numbers. While this makes division defined in more cases than usual, subtraction is instead left undefined in many cases, because there are no negative numbers.
Although division by zero cannot be sensibly defined with real numbers and integers, it is possible to consistently define it, or similar operations, in other mathematical structures.
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Choose the Right Synonym for division part , portion , piece , member , division , section , segment , fragment mean something less than the whole.
Examples of division in a Sentence the process of cell division a division of profits into equal shares After learning multiplication, the students were taught division.
Recent Examples on the Web Dallas and Washington are slated to pick in the top five in the NFL draft yet somehow are just a half-game back of Philadelphia in the division.
Washington," 24 Nov. Perez fight card, start time, free live stream for prelims," 21 Nov. First Known Use of division 14th century, in the meaning defined at sense 1a.
History and Etymology for division Middle English, from Anglo-French devision , from Latin division-, divisio , from dividere to divide.
Learn More about division. Most Popular Division Worksheets this Week. Division facts worksheets including division tables, division facts and worksheets with individual division facts.
Manipulatives can help students "get" the concept of division. For example, students could regroup base ten blocks into units, then divide the units into piles.
Long division worksheets for practicing various long division strategies including questions with no remainders, remainders and decimal quotients.
Need an easier way to divide large numbers? 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?
A protagonist is the main character of a story, or the lead. Division, partition suggest dividing into parts. Division usually means marking off or separating a whole into parts.
Partition often adds the idea of allotting or assigning parts following division: partition of an estate, of a country.