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# Multiplication - Which way round?

Posts1
Joined04/07/14

hello there. My colleagues and I have been having a discussion about which way round a multiplication number sentence should go. Can you please help?

Should 4+4+4 be written as 4x3 or 3x4. Obviously I understand it will give the same answer. I just want to find the correct way.

Many thanks

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Rebecca_Hanson 18 November 2016 18:09
Posts1125
Joined28/01/08

It's arbitrary.  People do it either way and think their way is the way everyone does it.

The most important thing as a teacher is to be aware that your children may be seing it either way.  This is demonstrated clearly with an array layout of objects.  If you just turn your head you can see they're the same thing.

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saran 02 December 2016 10:31
Posts2
Joined08/11/13

I would say that when you are introducing multication as a step on from repeated addtion 4 + 4 + 4  is '3 groups of 4' so it should be written as 3 x 4.

4 x 3 is '4 groups of 3' so would be written as 3 + 3 + 3 + 3

It is important to be able to 'read' a number sentence to visualise what it represents. Once children are secure with that then they will know that 3x4=4x3.

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Balderdash 16 April 2018 10:31
Posts1
Joined21/10/15

The numbers being multiplied in a 'number sentence' have different names.

e.g. a X b

a is a the multiplicand

b is the multiplier.

a is the value of the set (group)

b is the number of times it is being 'produced' hence 'product'

so 4 X 4 X 4 is actually 4 X 3.  (three lots of 4) (4 produced 3 times)

This goes against what is commonly seen on posters and on the web - e.g. times tables often start 1 X 4, 2X 4, 3 X 4 etc

Personally I'm not a stickler for this - though we had a visiting consultant once, who was.

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RuthBull 19 April 2018 21:57
Posts48
Joined24/11/08

Yes I agree with the above.

4+4+4 is 4 multiplied 3 times     4 x 3

The trouble with English is we tend to say 4 lots of 3 reading from right to left but definitions show it is

multiplicand x multiplier = product

Arrays are nice - they show the relationship without worrying about the order.

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Elizabeth_Lambert 18 May 2018 18:37
Assistant Director (Primary)
Posts185
Joined18/02/15

I think lots of teachers will have multiplicand and multiplier in a particular order in their head. The multiplicand doesn’t have to come first, and the product is the same if it comes first or second.

3 x 4 = 3 lots of four = 3 + 3 + 3 + 3 = 4 x 3 = 4 three times = 4 + 4 + 4 = 12

¾ of £20 The ‘of’ gets replaced by the ‘x’ symbol, so the multiplicand comes second.

If you think of multiplication as

factor x factor = product

the order of the factors will not matter. If we want children to reason and be fluent when calculating, we really don’t want them to get hung up on the order. When we abstract and write a calculation, we want them to use an order that makes sense to them and know what each factor means in the context of the question.

Hope this helps!

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amanda_simpson 19 May 2018 07:03
Posts223
Joined01/02/10

Both ways are correct. Neither is more correct than the other. Best to consider it as factor x factor= product.

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jocayley 06 January 2019 17:52
Posts15
Joined18/02/10

Hello

What is the actual NCETM advice on this as there are both points of view shown above?

I have been told by consultants that it should be multiplicand first, i.e. 4+4+4 = 4 x 3

But most websites and textbooks show the other way round.

Obviously we show through commativity that the product is the same, but it does seem confusing, would be nice to see one 'mathematically correct' way.

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RachO 15 January 2019 20:03
Posts17
Joined30/04/12

Many other written calculations start with an amount eg addition, adding onto an amount if its augmentation, in subtraction taking away from an amount (not relating to difference), the whole if its division, so perhaps it should be the 'amount' first which is then mulitplied a certain number of times- I think, this is the official way.  However, if you use language like lots of its often refers to the second number as the amount, which is more common place ( partly due to all the posters/ workbooks that use this model).  The important element to me, is to ensure that children understand that in the written calculation only one of the numbers relates to an amount and the other is how many times we have it, whichever  way round; often this understanding can be demonstrated if you ask a child to show you 4 X 3, if they get 4 blocks out and 3 blocks out, you can be sure they haven't developed this understanding.

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conceptmaths 02 April 2019 09:12
Posts19
Joined21/07/13

I'm leaning towards 4 x 3 since the latter part of the calculation normally shows the operation (as with addition, subtration and division). I have 4... I'm multiplying it by 3. Having said that, in algebra we put the multiplier first e.g. 3(x+2). Another contributor  has mentioned fractions and % calcluations where we replace the 'of' with 'x', so in these instances the multiplier comes first (as we would say it). But again, it can be written the other way too: Half of 16 can be written as 16 x operation (16 x 1/2).

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