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 5n, not n5). So if you had 5 groups of n, you’d write 5n; if you had n groups of 5, you’d still write 5n.
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.