Multiplication Meaning

[KWF]

Which one of the following (1. or 2.) best represents the following: What multiplied by 6 equals 12?


1. ? X 6 = 12


2. 6 X ? = 12

 

[ksdhart]

Strictly speaking, due to the commutative property of multiplication, the two expressions are asking/saying the same thing. That being said... if I were teaching multiplication to kids, I'd go with the first, and say something like this: ___ x 6 = 12

But, for algebra, the convention is to always put the constant first. So I'd say 6x=12. In the end it's purely a personal preference. Neither way of putting it is wrong.

 

[Bob Brown MSEE]

Which one of the following (1. or 2.) best represents the following: What multiplied by 6 equals 12?


1. ? X 6 = 12


2. 6 X ? = 12

The first one matches the words precisely. However since multiplication commutes, they both mean the same thing and either is acceptable.

 

[KWF]

The first one matches the words precisely. However since multiplication commutes, they both mean the same thing and either is acceptable.

If 2 multiplied by 6 = 12 represents 2 X 6 = 12, then is 2 X 6 = 12 also precisely represented as 2 times 6 equals 12 or 6 times 2 equals 12?

 

[Deleted member 4993]

Best way (I think) to teach kids multiplication is (as example):
3 times 4 means add 4 3 times : 4 + 4 + 4

How would you explain √2 * π ?!

 

[lookagain]

Which one of the following (1. or 2.) best represents the following: What multiplied by 6 equals 12?


1. ? X 6 = 12 \(\displaystyle \ \ \ \ \ \) This one does.


2. 6 X ? = 12

It answers the question as "best."

 

[Steven G]

I wouldn't explain that to kids.

Why not? You'd rather their 'teacher' show them?

 

[stapel]

Why not? You'd rather their 'teacher' show them?

I suspect the issue is more a matter of appropriateness of topic. Little children are not, in general, ready for this level of study. Kids who are being introduced to the concept of multiplication are probably not ready for the study of transcendentals, limits, etc. So this issue should not arise in the context of "kids".

 

[Steven G]

I suspect the issue is more a matter of appropriateness of topic. Little children are not, in general, ready for this level of study. Kids who are being introduced to the concept of multiplication are probably not ready for the study of transcendentals, limits, etc. So this issue should not arise in the context of "kids".

Of course I agree with you. I was just joking with Denis. My concern about the educational system is that (for the countries I am aware about) for the most part the people who choose to become pre college teachers are the worst people for the job.

 

[Otis]

I agree with lookagain, on this one. Particularly so, if the intent is for students to parse English statements into mathematical expressions; there's a definite order to that. :cool: