Maths question

Drukk · 5 Mar 2017 at 23:18

Wonder if anyone could assist with the two questions below, I can work these out with trial and error but does anyone know an actual method to solve them? These are a couple of questions my 10 year old is stuck on and I'm really not sure in this instance what the method is, google also failed me!

......._12.2_
....._______
1_ /819_.00

..... _40
....____
_4/57_0

Both are partially complete division questions and need the missing digits marked by the _ symbol, ignore the lines of dots, for some reason spaces would not register so had to use dots to get the rows to line up correctly.

adolf hamster · 6 Mar 2017 at 01:00

Is this converting decimals to fractions? Kind of hard to see what theyre asking the way its written there

Cromulent · 6 Mar 2017 at 03:27

Is this some weird maths notation they are using these days? Because if it is I have no idea what it means

. I never saw any maths questions written like that and I studied Computer Science at University which is quite maths heavy.

jsmoke · 6 Mar 2017 at 04:01

That looks pretty though. Does the first say,

LeMson · 6 Mar 2017 at 04:26

This looks pretty useless lol

Hades · 6 Mar 2017 at 07:05

I think it would be easier if the OP took a photo of it and uploaded it. I can't read that question how it is written here.

GravyMonster · 6 Mar 2017 at 08:33

OP, try using [ code ] tags (minus spaces, obvs) as it's fixed width. I assume you are going for something like this:

Code:

      _12.2_
    ________
1_ / 819_.00


      _40
    _____
_4 / 57_0

h4rm0ny · 6 Mar 2017 at 10:14

Spunkey beat me to it! Yes, Drukk - please reformat this using Code tags. I like to think I can solve any maths problem intended for ten year olds, but I can't make out what the problem is. Is it how Spunkey laid it out? And we have to guess digits where the underscores are to make a correct sum? This seems rather horrible, if so.

h4rm0ny · 6 Mar 2017 at 10:20

I wouldn't call this maths as much as I would call it Applied Guessing. For example, taking the second one first, I can see that the last number of the divisor is 4 and the last numbers of the result are 40. So whatever the original number that was divided into probably ends with 60. (Because 4 * 40 = 160). So I plug in a 6 in the lower right blank to give me 5760 in the lower part. I then try a couple of sample numbers for the divisor. First I try 14, but that doesn't give me a whole number. So then I try 24 and I find 5760/24 = 240. I can fill in 2 for the top blank now. And I thus end up with the following:

Code:

      240
      ___
24 | 5760

Don't feel bad about not getting this. There isn't (so far as I know) a simple mathematical way of doing this. Just guessing and using common sense (like I did above) to rule out the number of guesses to try.

Honestly, I'm not very impressed if this is what we're asking ten year olds to do now. I suppose it checks that they know how to actually do division because they need to do it to check their guesses, but it's not really teaching them much other than if you don't know the answer, try guessing. :/

Or does anyone else have some insight which I've missed?

jsmoke · 6 Mar 2017 at 11:19

Can't see how you can solve with four variables, you would need four equations. For every n variables you need n equations to solve. So yes impossible without T & E, as far as I know.

Illgresi · 6 Mar 2017 at 11:41

That's the strangest notation I've ever seen. Bottom right, divided by top right, equals bottom left?!? Also, this appears to be a guessing game rather than actual mathematics.

I'd get your son to another school imo.

AndyCr15 · 6 Mar 2017 at 11:48

h4rm0ny said:
... *maths stuff* ...

Great, but this all assumes they're looking for it to be 1.

What if they want it to be ½? There's no = in it... it's not really a Maths question I don't think?

**EDIT** Doesn't yours give 240 over 41.6666? (24/5760)

h4rm0ny · 6 Mar 2017 at 13:12

jsmoke said:
Can't see how you can solve with four variables, you would need four equations. For every n variables you need n equations to solve. So yes impossible without T & E, as far as I know.

It would be possible, though it's been a while, to prove that there is a finite set of solutions. I'm not sure about proving there is only one solution. Remember we can assume integers because each blank is a single missing digit. So you're right except that we know each missing digit lies between 0 and 9 giving a calculable range for the answers. However, I kind of concede your point by the fact that I immediately decided to tackle the second one!

It's obviously intended for little kids to guess at numbers and see what fits. Therefore I suspect that the missing numbers are actually pretty low so that a child can work their way through them. Maybe - depends how much the author hated children, I guess.

Illgresi said:
That's the strangest notation I've ever seen. Bottom right, divided by top right, equals bottom left?!? Also, this appears to be a guessing game rather than actual mathematics.

I'd get your son to another school imo.

It is a guessing game. Spot on. The notation is common in primary school, however. Or at least used to be (no idea, these days). You write the number you want to divide into (numerator) down, draw a line to the left and over it, then put the number you dividing by (denominator) to the left of that line. So something like this:

Code:

  ___
5|78

This looks to a child a lot like doing addition and multiplication in "tens and units" style which they will already be familiar with. Only this time instead of the line being on the bottom and writing their answer underneath it, they write it on the top. Which they do because "division is the opposite of multiplication". This is how I was taught when I was (I think) seven. It's helpful to the child because they don't have to tackle the whole number at once but can work their way from left to right, or hundreds to tens to units if you prefer. And they can carry on and divide "really big" numbers this way. So in the above the child would take the 5 and look at the 7 and ask how many times 5 went into 7. The answer is 1 so they put a 1 over the 7. But they have a 2 left over (the remainder) so they put that to the right next to the 8 making it 28. Now they can ask how many times 5 goes into 28 and the answer is 5, so they put a 5 above the eight. This time they have a remainder of 3. So depending on whether or not they've done decimals yet, they'll either put that after the decimal point and carry on, or just call it "15 remainder 3". Which makes sense to a child because they thinking of numbers as real (small 'r') things and want to know how many times 5 goes into 78. Now they know it's 15 and that they'll have 3 left over. And they've done all this with only having to know their times tables up to ten even if the number is "really big" like thousands!

AndyCr15 said:
Great, but this all assumes they're looking for it to be 1.

What if they want it to be ½? There's no = in it... it's not really a Maths question I don't think?

**EDIT** Doesn't yours give 240 over 41.6666? (24/5760)

It cannot be a ½ because each blank is a single digit. Also, no. You're just unfamiliar with the notation. It means 5760 / 24 = 240. I'm surprised people are unfamiliar with this. Is it no longer used in primary schools?

Drukk · 6 Mar 2017 at 13:43

Spunkey said:
OP, try using [ code ] tags (minus spaces, obvs) as it's fixed width. I assume you are going for something like this:

Code:

_12.2_ ________ 1_ / 819_.00 _40 _____ _4 / 57_0

That is exactly it, thanks for laying it out better than I managed.

Drukk · 6 Mar 2017 at 13:50

h4rm0ny said:
I wouldn't call this maths as much as I would call it Applied Guessing. For example, taking the second one first, I can see that the last number of the divisor is 4 and the last numbers of the result are 40. So whatever the original number that was divided into probably ends with 60. (Because 4 * 40 = 160). So I plug in a 6 in the lower right blank to give me 5760 in the lower part. I then try a couple of sample numbers for the divisor. First I try 14, but that doesn't give me a whole number. So then I try 24 and I find 5760/24 = 240. I can fill in 2 for the top blank now. And I thus end up with the following:

Code:

240 ___ 24 | 5760

Don't feel bad about not getting this. There isn't (so far as I know) a simple mathematical way of doing this. Just guessing and using common sense (like I did above) to rule out the number of guesses to try.

Honestly, I'm not very impressed if this is what we're asking ten year olds to do now. I suppose it checks that they know how to actually do division because they need to do it to check their guesses, but it's not really teaching them much other than if you don't know the answer, try guessing. :/

Or does anyone else have some insight which I've missed?

Thanks for the explanation, I was thinking along the same lines in that it is all just trial and error, this seems pretty hard for 10 year old kids. My lad can do division using bus stop method or chunking but this I think is a little bit tough for them at that age. I suppose you could class it as reasoning but even so, that is not easy. I am seeing his maths teacher later this week anyway on a parents evening so will ask what it is all about then.

h4rm0ny · 6 Mar 2017 at 14:26

Drukk said:
Thanks for the explanation, I was thinking along the same lines in that it is all just trial and error, this seems pretty hard for 10 year old kids. My lad can do division using bus stop method or chunking but this I think is a little bit tough for them at that age. I suppose you could class it as reasoning but even so, that is not easy. I am seeing his maths teacher later this week anyway on a parents evening so will ask what it is all about then.

Don't be too hard on them, necessarily. It's a way of getting children to put in different numbers, try it out and see if it works and to think about what they're actually doing. If you want a young child to try and think about what they're doing and solve maths problems, you probably can't give them something by Martin Gardner. (Although I would be tempted to

).

AndyCr15 · 6 Mar 2017 at 17:31

h4rm0ny said:
It cannot be a ½ because each blank is a single digit. Also, no. You're just unfamiliar with the notation. It means 5760 / 24 = 240. I'm surprised people are unfamiliar with this. Is it no longer used in primary schools?

I don't see why it had to be one. It doesn't say =1 at any point? As I read it, it's - _40 / (_4/57_0)

Surely it's meaningless. It's not an equation, it's almost just a statement.

Pudney · 6 Mar 2017 at 18:14

AndyCr15 said:
I don't see why it had to be one. It doesn't say =1 at any point? As I read it, it's - _40 / (_4/57_0)

Surely it's meaningless. It's not an equation, it's almost just a statement.

Your equation is wrong. The notation is for long division.

AndyCr15 · 6 Mar 2017 at 18:35

Oh, I see what you mean now. I think the drawn version of it threw me.

dowie · 6 Mar 2017 at 23:00

It is long division as h4rm0ny has correctly pointed out - would be much more helpful if the OP had actually taken a picture of the question.

Presumably the kid has some notes/texbook showing a step by step way of working through long division problems, I'd just take that approach and think about it at each step.

It doesn't have to be completely trial an error - for an example lets take the second one which has already been worked through:

lets try and find the first digit on the denominator - we can see straight away that it can't be anything above 5 as that would leave a 0 in the blank space on top and 40 times any two digit number will be <4000

so the possibilities are 14, 24, 34, 44, 54

now we also know, from the 0s at the end, that the remainder of dividing 57 by one of these numbers and a _ must be divisible exactly by the denominator to give the 0 at the end AND as there is a '4' after the blank in the result then it must equal 4 times the denominator.

now we can see straight away that 54 and 14 can be eliminated, the remainder from 57 is 3 so we'd be looking for 3_ yet 54* 4 = a three digit number. Likewise for 14 the remainder from 57 is 1 yet 14 *4 is more than 1_.

so we've only got 3 possibilities now to evaluate and compare their remainder with their multiple of 4

24*4 = 96
34*4 = 136
44*4 = 176

57/24 gives 2 remainder 9 so 24 does fit - the result's blank space is 2, the denominator is 24 and the blank space in the numerator is the '6' from 24*4 = 96

57/34 gives 1 remainder 23 so doesn't fit

57/44 gives 1 remainder 13 so doesn't fit

so there is only one possible result and it is 5760/24 = 240