Is there a convention as to whether the first factor or the second factor represents the number of groups in a multiplication problem? This came up as we were doing arrays to demonstrate the commutative property. So, in doing 5 x 7 and 7 x 5, which one represents 5 groups of 7 and which one represents 7 groups of 5? Hope this makes sense.

I’d say that 5 x 7 is five groups of seven, and 7 x 5 is seven groups of five. But I don’t think there’s any kind of formal convention.

Yes, I also think that 5 x 7 leans toward 5 groups of 7. I meant to add before though that the textbook shows the array for 5 x 7 as 7 groups of 5. I agree that it doesn’t matter much…

If there is such a convention, I’ve never heard of it.

What there is a convention for is that, when you have a constant times a variable, the constant is written first (like 5*n*, not *n*5). So if you had 5 groups of *n*, you’d write 5*n*; if you had *n* groups of 5, you’d still write 5*n*.

http://mathworld.wolfram.com/Multiplier.html says that in the expression a x b, a is the multiplier and b is the multiplicand. I interpret that as a groups of b, which agrees with everyone else.