How would you approach this maths question?

[yoyo123]

if he did it straight away it is the easiest for him!

Well done Master Scarlett!

[mystery]

something x39 = 624

If you knew from the question that something was a whole number (but I don't think the question made it clear that something was a whole number, or did it?) something would end in 6 wouldn't it as 6x9 = 54.

As a child I would just have done a straighforward long division and got the answer. I wouldn't have thought it was an 11+ question at all, just a pretty routine plodder question. Is this 11+ material?

[menagerie]

I'm sorry Mystery, I still don't understand that at all. I just don't get how 6x9 equalling 54 is automatically relevant to the figure 624, to the extent that you can 'know' without working out that the answer ends in a 6.

Not saying I couldn't work out the question. It's not hard by long division. But we were never taught any patterning in maths at school and discovering all these patterns now we've started 11+ prep is like learning there's a whole host of new colours in the world. It's exciting but also very hard to get to grips with.

But y'know, my English isn't bad. I'm not a total write off...

[xyzzy]

I'm sorry Mystery, I still don't understand that at all. I just don't get how 6x9 equalling 54 is automatically relevant to the figure 624, to the extent that you can 'know' without working out that the answer ends in a 6.

If you multiply two numbers together, the only place that the units of the answer is coming from is the units of the numbers you're multiplying.

So 73 x 47 has to end in 1, because 3 x 7 = 21. If something x 73 = 3431, something has to end with 7, for the same reason. Why? This is where the grid method used for multiplication these days makes things so clear:

73 x 47:

Code: Select all

x     40    7
70  2800  490
 3    120   21

2800 + 490 + 120 + 21 = 3431

Note that every number you're adding ends in zero, because one or the other or both of the numbers being multiplied is a multiple of ten, except for 3 x 7, ie the units. So the last digit of the answer has to be 1.

You can't easily multiply 3276541267 x 43276781234 and see what the last digit is --- a simple calculator can't do it, and a scientific calculator can only tell you the first 8 or 10 digits. But the last digit is 8. Can you see why?

[mystery]

Ah thank you, I've never known what the grid method of multiplication was until you did that.

I just can see that if I have

ab
x cd
--

that the units in the answer will be made up from b x d
Sorry I am not being clear tonight Menagerie.

[menagerie]

Thank you xyzzy! Lightbulb moment. I have got through 47 years not knowing that. Now it's explained, it seems clear and logical, but I'd have spent another 47 years trying to work it out and not getting there. Thank goodness DC have DH's mathematical ability not mine.

Mystery - don't apologise. I have zero intuitive aptitude for maths. It must all be explained. I can't work a single thing out for myself.

[dadofkent]

I taught my DS's that fractions and division are the same. Therefore try and simplify.
Both sides clearly divide by 3.

Left with

13/208

Far easier to then divide.

[matreshka]

It's from one of the bond books.

How many times can I take 39 from 624.

Normally, I would suggest these be done as straightforward division-but this is quite hard! I did it quickly by chunking
39 x 10=390 (624-390= 234)
39 x 5= 195 (234-195=39)
39 x 1= 39
so 16 x 39 = 390

Would you tend towards getting them to do more traditional division in these questions?

Hi. I explained to my child how to divide with remainders and we have never had this problem. We are in Grammar School now!!!!!!!!!!!!

[xyzzy]

Would you tend towards getting them to do more traditional division in these questions?

Hi. I explained to my child how to divide with remainders and we have never had this problem. We are in Grammar School now!!!!!!!!!!!!

I've never understood why you wouldn't use chunking whenever long division is traditionally used. It's simply a better way to work, both on paper and in your head. Chunking pays the price of having to add at the end, rather than producing the results a digit at a time, but it avoids endless trial and error divisions for the dubious benefit of not having to add up the chunks.

[mystery]

If you get really good at chunking you're able to long divide without trial and error. I did long division straight off at school and I don't remember lots of trial error - a little bit sometimes maybe, but not much at all. But we did lots of number facts drilled into us.