Calling all Maths teachers, need tour help with homework question

[forago]

my child is doing some summer holiday maths set by his maths teacher. The question is:

32.45 x ? = 253.11

What is ?

obviously the answer is 7.8 and I think the question wants him to show that to work it out you do 253.11/32.45 which is the same as 25311/3245 so I am telling him to do 25311 divided by 3245 as a pretty convoluted long division to get 7.8, which is confusing him.

Am I over-complicating it? is there an easier way? what is the teacher after do you think?

are you sure he is not allowed a calculator?

yes he's y5 going into y6 no calculators yet, this is 11+ practice

25311 and 3245 are both divisible by 11 - maybe that's the place to start

ooo that's an alternative - not sure he'd spot that though but we'll try it thanks. I'm not great at maths myself so have to follow a rigid method :)

Bloody hell, what a waste of time all round. (Secondary maths teacher).

My mistake I copied one if the numbers down wrong.

why is it a waste of time? yes I'd use a calculator too but presumably its supposed to demonstrate some technique or mentl maths? what's a better way to learn? I do wonder if there's lots of secondary school teachers our there pulling their hair out when they get then in y7?

Forago - I made a mistake and will look again

It might be that he is just expected to write 25311/3245. If it in 11+ practice the question need to be done in one minute or less and this is a tall ask for a 10 year old (even a bright one)

I did make a mistake but not the one I thought I'd made.

If we write out the numerator and denominator as a product of their prime factors they look like this:

25311=31113*59
3245=51159

Therefore 25311/3245=(3*13)/5=39/5=7.8

It's a waste of time because it's just a slog, the sort of question calculators were invented for. No nice factors to cancel the fractions, you end up doing prime factorisation which is ridiculous.

There is nothing like this at GCSE or A-level.

For future reference:

A number is divisible by 3 if the sum of it's digits is divisible by 3 (similar for 9)

A number is divisible by 11 if alternate digits add up to either the same sum or the difference is a multiple of 11 e.g. 25311 is divisible by 11 because 2+3+1=5+1

It tests ones knowledge of how numbers and arithmetic work. I did it without a calculator inside 2 minutes.

Yes, but you are not a primary school child.

thanks all of you that's very helpful. noble I see what you're saying and kind of agree with you. sadly we don't seem to have any options than to play the 11+ game.

Can you contact the teacher and ask whether your child is supposed to use prime factorisation to simplify the calculation, or whether there is an error in the worksheet?

I thought the point of the 11 plus was that a bright child could pass without tutoring, but if that sort of thing is on there, then that is beyond what is expected of even the secondary curriculum. I have no experience of the 11 plus though.

Maybe not but I'd mastered prime factorisation by age 12. I do have a natural aptitude though.

thanks noble sorry just to clarify this is a paper given to him by his school teacher to do over the summer. It's not specifically for the grammar school 11+, where the questions are much snappier I think as somebody else mentioned. Not that he has any chance there really as we are in a non grammar school area where there are only a couple so they cherry pick the exceptional maths kids and the pass marks are in the 90%s, he is good at maths but not exceptional. There will also be kids trying for local independent secondaries too so possibly longer questions are more appropriate there, I don't know as I haven't looked at the papers yet. he also has to do an entrance exam to get into one of our local state comps as well as we are slightly out of catchment. Hence the summer practice. whichever way I would be surprised if they were expected to to prime factorisation at this stage though!! so I will email the teacher and ask him. I can make it work doing the long division way so I'll go through that with him later after weve done something else this afternoon.

I do wonder about maths teaching at primary these days - I couldn't do most of the paper at 10 and I'm a professional educated to masters level. what the hell do they teach them at GCSE now?

Agree with noblegiraffe
Also when you get practice papers for 11+ look on the answers yourself. I was hugely suprised about a sample paper for one independent with its own exam, that as a rough guide say a good level 5 to pass, that appeared to require gcse algebra to solve one question, but actually they only wanted the equations deriving from the problem not the answers.

We teach prime factorisation in Y7, but only use it to find highest common factors and lowest common multiples, not for simplifying fractions.

What paper was it you were given? I would love to know what institution is asking 11 year olds questions like that! I suspect it is meant to be done with a calculator, tbh. It looks like it's testing inverse operations, rather than inverse operations, division by a decimal, long division and possibly prime factorisation!

Glad it's not just me that though this was hard for a 10y old. It must be a typo surely as it's only worth 1 mark! Paper is an in-house school one but questions come from various independent secondary 11+ entrance exams, I suspect. It is by far the hardest question buried amongst some easier ones which you can see for comparison. Have also uploaded my attempt at doing it by long division but god knows if it's allright, I am making it up as I go along - I think by the time I got to doing maths like this at school I was allowed to use a calculator.

btw he also gave us the answer sheets where it says the answer is 7.8 so if its a typo its on there as well. Jesus maybe this is what they have to do to get into grammars and indies - I hardly dare look at the papers now!

If it's only 1 mark, then it's got to be a calculator question. If they expected students to do it longhand, then they'd have to give some credit for working out if the final answer was wrong.

I know weird isnt it - as far as I know he has never used a calculator and they cant use them in any of the tests - weird.

Is my long division method correct out of interest? and is that how you handle dividing non integers - lose the decimal point in both?

It's not simply losing the decimal point in both, although that works in this situation because they both have the same number of decimal places. It's to do with equivalent fractions. Dividing by a decimal is a pain so we find an equivalent fraction where the denominator is a whole number.
253.11/32.45 = (253.11 x 100) / (32.45 x 100) = 25311/3245
So we can do 25311/3245 and it will give us the same answer as 253.11/32.45

but if it had been 253.11/324.5 we'd have

253.11/324.5 = (253.11 x 10) / (324.5 x 10) = 2531.1/3245

So we'd do 2531.1/3245 and it would give us the same answer.

It doesn't matter that there's still a decimal place in the numerator because this is easy to deal with when doing bus stop division.