Rectangular Array Division

thunc14

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I haven't done rectangular array division ever in my life, and after watching some videos I'm still at a complete loss as to how to do this problem. My hunch was answer C, because it seems to make the least amount of sense. Can someone help guide me through this problem? Again, I am completely unfamiliar with rectangular array division.

If we are to divide 3961 by 17 using a rectangular array, which of the following is NOT a good model?
 

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Dr.Peterson

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They can't all be correct, since one gives a different quotient than the others. Can you see where the quotient is?

Then we can talk about what this model means, if you're still unsure.
 

thunc14

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I see that A and B give 233, the quotient of 3961÷17
C gives 333 which is why I chose it. I used the answer choices to come up to the answer I thought was best for this one, but I still do not understand the rectangular model with a division problem of this size.
 

Jomo

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Understand that division is repeated subtraction. You can start at 3961 and subtract 17 and then another 17 and another 17 ... until you get to 0 (or less than 17). Then you count the number of times you took away 17. Or you can subtract many 17's at once. Maybe you subtract 1700 at once which is the same as subtracting 17 100 times. Just keep subtracting multiplies of 17 until you get to 0. Then count the number of 17s you subtract. That is what is being done in this problem. Do you see where the numbers are coming from?
 

thunc14

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Understand that division is repeated subtraction. You can start at 3961 and subtract 17 and then another 17 and another 17 ... until you get to 0 (or less than 17). Then you count the number of times you took away 17. Or you can subtract many 17's at once. Maybe you subtract 1700 at once which is the same as subtracting 17 100 times. Just keep subtracting multiplies of 17 until you get to 0. Then count the number of 17s you subtract. That is what is being done in this problem. Do you see where the numbers are coming from?
I understand that. Like in A, you are subtracting 17 from 3400 200 times, 20 times from 340, 10 from 170, and 3 times from 51, which all lead to 0. C still just seems wrong because of the way the top line adds up as well as the boxes. In my naive eyes, it looks like C is talking about a completely different number other than 3961
 

Jomo

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In my naive eyes, it looks like C is talking about a completely different number other than 3961
Yes, that is why C is NOT the correct answer.
 

Dr.Peterson

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You can either check each division (by multiplication), as we have done to see that C is wrong; or you can follow along with the work and look for an error. For C, they start with 3961 and subtract 100*17 = 1700, leaving 3961 - 1700 = 2261; then they subtract another 1700, leaving 2261 - 1700= 561; but then they can't subtract the third 1700, so they made a mistake. If I were a teacher grading this, I would guess that they lost count and put down three 1700's instead of two.
 
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