Confusion on simple division arithmetic

[chromechris]

I'm a bit confused as to what the answer to the following problem is: 4/x (1/4)

Is the answer 1/x OR 1

 

[Dr.Peterson]

Do you mean, [MATH]\frac{4}{x}\left(\frac{1}{4}\right)[/MATH]?

If you simplify it (this is algebra, not just arithmetic, because it contains a variable), you get [MATH]\frac{4\cdot 1}{x\cdot 4} = \frac{1}{x}[/MATH].

We should probably discuss why you are unsure, to make sure you understand.

 

[chromechris]

I guess in mind I kind of see the 4 on the top and bottom cancelling out and dissapearing, so then I get kind of confused as to why there is a 1 in the numerator. But I guess I can see why if try [MATH]4/4x=1/(1)x=1/x[/MATH] Is that right?

 

[Deleted member 4993]

I guess in mind I kind of see the 4 on the top and bottom cancelling out and dissapearing, so then I get kind of confused as to why there is a 1 in the numerator. But I guess I can see why if try [MATH]4/4x=1/(1)x=1/x[/MATH] Is that right?

Yes - but it would be preferable to write:

4/(4x) = 1/((1)x) = 1/x

Those parentheses () are important for accuracy of work-description.

 

[chromechris]

I see, thank you very much.

 

[Steven G]

I'm a bit confused as to what the answer to the following problem is: 4/x (1/4)

Is the answer 1/x OR 1

Lets see if 1 makes sense as an answer. You are multiplying two fractions. One fraction is 1/4--a known value. The other fraction 4/x is an unknown value. Now how can you multiply an unknown number by a known number and get a known answer (like 1 or any other number)? The answer is that you can't!