# Is 5X10 'five times ten' or 'ten times five'?

#### Englishmypassion

##### Senior Member
Hello all,
Namaste!
There are four twos: 2, 2, 2, 2. To teach multiplication to little children, should they be written 4x2 ,or 2x 4?
Does the expression 5x10 mean 'five times ten' , or 'ten times five' ? Which number is being multiplied and which number is multiplier (the number of times) and the multiplication symbol x is used, as in 5x10?
Thanks a lot.

• #### Cagey

##### post mod (English Only / Latin)
I would write this 2, 2, 2, 2 as 4X2.

In same way, I refer to this   as "3 light bulbs". I give the number of occurrences first and then name what I am counting.

Similarly, I read 5X10 as "five times ten", reading across in the order of the numbers.
I think of it as 10+10+10+10+10.

Added: If you said "ten times five" I would think of it as:
5+5+5+5+5+5+5+5+5+5 and write it as 10X5.

Last edited:

#### Englishmypassion

##### Senior Member
Thank you very much, Cagey. You have been really helpful.   #### Englishmypassion

##### Senior Member
One more question:
If the equation is written vertically, in the following way, then which number shows the number of occurrences and which number is the multiplicand or is being multiplied?
25
x10
Thanks.

#### natkretep

##### Moderato con anima (English Only)
In our primary school maths books, 4 x 2 is explained as four lots of two. This is in agreement with what Cagey has said.

I'd see

25
x 10

as another way of writing 25 x 10, hence 25 lots of 10.

#### Englishmypassion

##### Senior Member
Thank you very much.

##### Senior Member
Isn't that odd; all my life I've seen this the other way round!

Still, it makes no difference at all to the result.

#### natkretep

##### Moderato con anima (English Only)
Actually, now that I've done more searching, I'm seeing that too. Like here: #### Englishmypassion

##### Senior Member
Isn't that odd; all my life I've seen this the other way round!

Really? Unbelievable! Is that a purely BE usage?

#### Englishmypassion

##### Senior Member
Oh, I am really in a fix now.

#### natkretep

##### Moderato con anima (English Only)
I don't think it is a BrE-AmE distinction. I think people haven't been bothered to standardise things because the result is the same, as Keith said. Just use one method and stick to it.

#### DonnyB

##### Sixties Mod
If, as I did, you had to learn your "times tables" at Junior School, you would remember that:

"five tens are fifty" (from the ten times table)
"ten fives are fifty" (from the five times table)

Simples! #### Englishmypassion

##### Senior Member
If, as I did, you had to learn your "times tables" at Junior School, you would remember that:

"five tens are fifty" (from the ten times table)
"ten fives are fifty" (from the five times table)
Simples! Thanks a lot. I really need to learn multiplication/times tables as my calculation is really week. I will learn them that way. #### Glenfarclas

##### Senior Member
Isn't that odd; all my life I've seen this the other way round!
So have I, which is why I would tend to write lists with the multipliers on the right, like:

widgets × 2
eggs × 48
keychains × 19,​

etc.

Oh, I am really in a fix now.
No you're not. Multiplication is transitive, so a × b = b × a. You ask "which number is being multiplied," but the truth is that they are both being multiplied.

As to your question about how to pronounce "5 ×10", no English speaker would ever read that as "ten times five." Always from left to right.

#### Englishmypassion

##### Senior Member
Thank you, everybody.
So we write and read the multiplication table of 10 as follows:
1x10= 10 (One ten is ten.)
2x10=20 (Two tens are twenty.)
3x10=30 (Three tens are thirty.)
4x10=40 (Four tens are forty.)
5x10=50 (Five tens are fifty.)
6x10=60 (Six tens are sixty.)...
Am I right ?

#### DonnyB

##### Sixties Mod
Yep! The full set goes up to 12 and there are 12 in each table... 12 x 12 = 144.

Similar to these We'll make a mathematician out of you yet! #### Englishmypassion

##### Senior Member
Yep! The full set goes up to 12 and there are 12 in each table... 12 x 12 = 144.

Similar to these Wer'll make a mathematician out of you yet! Thank you VERY much. I have seen 12 in each table for the first time and find myself lucky to have been spared 2 in each set, though I had to learn, and Indian students still learn, tables of 1 to 20. So I got a good concession. I really start feeling dizzy the moment I open a maths book.  #### RM1(SS)

##### Senior Member
Isn't that odd; all my life I've seen this the other way round!

Still, it makes no difference at all to the result.
Ditto.

#### JamesM

##### Senior Member
Isn't that odd; all my life I've seen this the other way round!

Still, it makes no difference at all to the result.
So have I. #### Parla

##### Member Emeritus
If you want to teach little kids basic multiplication as a shorthand way of adding multiple sets, I guess that's okay (we weren't taught that way). But at some point, they must learn that mathematically, 5 x 10 is precisely equal to 10 x 5.

#### neal41

##### Senior Member
Multiplication is transitive, so a × b = b × a. You ask "which number is being multiplied," but the truth is that they are both being multiplied.

As to your question about how to pronounce "5 ×10", no English speaker would ever read that as "ten times five." Always from left to right.
The correct term is 'commutative'. Multiplication is commutative. That means that a x b = b x a for all a and b. 'a x b' is pronounced 'a times b' and 'b x a' is pronounced 'b times a'. '5.3 x 2.6' is 'five point two times two point six', which of course equals 'two point six times five point two'.

Addition is also commutative. a + b = b + a for all a and b. 5 + 2 = 2 + 5.

Addition and multiplication are also associative. That means that (a + b) + c = a + (b + c) for all a, b, and c, and that (a x b) x c = a x (b x c) for all a, b, and c.

Multiplication of integers can be viewed as repeated additions. 5 x 2 = 2 + 2 + 2 + 2 + 2 = 5 + 5. Multiplication of rational numbers and real numbers cannot be so interpreted.

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