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Just seeking a little help with one of my daughter's Yr6 math questions, as the answer I get on a calculator is different from what she (and I) get by doing it the long division way.

The question is 2912 ÷ 52

Now by calculator it's 56, but by the long division way (admittedly I'm a little rusty on the method nowadays) I come up with 57 r48, which is completely wrong but I can't figure out why, yet when I simply work out 52 x 56 I get 2912.

I'm assuming I'm missing something, but not having needed to work out long division in my head since I left school, I'm (embarrassingly) not proving to be much use so any help would be grateful.

Thanks in advance.

Mark N Walker
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    Could you show us your work? It's pretty hard to find a mistake without it. – Jed Nov 28 '16 at 21:54
  • Take a look at https://www.mathsisfun.com/long_division.html – John Douma Nov 28 '16 at 22:13
  • It won't let me upload a picture of the written working out as I don't have enough reputation to post images yet, so in a nut shell and as best I can describe, here goes: I've got 52/2912, 52 goes into 291 5 times (250) with 41 remaining, then drop the 2 down off the end of 2912 to make 412 of which 52 goes into 7 times (364) with 48 remaining, so there you have the 57 r48. Yet I know the answer to be a simple 56, but I've gotten it wrong by doing it this way. – Mark N Walker Nov 29 '16 at 23:28
  • $5\cdot 52=260$ (think: two suits total 26 cards in a deck of 52) – Jyrki Lahtonen Nov 30 '16 at 16:20

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I will explain a possible explanation to the problem, so you can check your work by using many possible methods of division. Here's how I'd solve it: 100 × 4 = 400. So, since 25 × 4 = 100, we can assume that $25\times 4\times 4 = 400$, where $4\times 4 = 16$, from your basic times tables. So, we can say that 25\times 16 = 400. Now that we've gotten 400 into groups of 25, now we can add the extra $400 + 25 = 425$, and $25 × 1 = 25$, so $25 × (16 + 1) = 25 × 17$. So, now, we have the fact family $25 × 17 = 425$, and, since division is backwards multiplication, we can switch around the fact family to then get $425 ÷ 25 = 17$, and this is our final answer.

And now, allow me to answer your question about the problem $2,912 ÷ 57$. Yet again, we only have to find the fact family. You already solved the crucial multiplication part, which is $52\times 56=2912$. Then, we take that, and we reverse it to make $2,912 ÷ 52=56$, the answer you wanted to know in the first place.

Hopefully this was helpful in answering your question, and I hope you can now get a right answer, regardless of disagreement from your calculations and the calculator's calculations.

Questioner
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