Expert: Josh - 10/9/2003

Question
Hello:

If someone can consume 20 pancakes in 30 minutes, he can eat 40 pancakes in 1 hour.

Here is an example calculation:

1. 20 pancakes/30 minutes X 60 minutes/1 hour = 40 pancakes/1 hour

If I rearrange the calculation in number 1 as follows, is the calculation correct?

2. 20 pancakes X (60 minutes/1 hour)/30 minutes = 40 pancakes/1 hour

Is (60 minutes/1 hour)/30 minutes correct in the number 2 calculation?

And also, would (60 minutes/1 hour)/(30 minutes/1/2 hour) be incorrect to use in place of (60 minutes/1 hour)/30 minutes in the number 2 calculation? If so, why?

I thank you for your reply!

Answer
Hello,

* Mathematically, the left hand side expression of [1] and [2] are equivalent, since the product terms in the numerator (denominator respectively) of fractions are commutative. ie., they can be interchanged, the order makes no difference to the end result.
* It is up to you how you want to manipulate the expression. Depending on what you do (how you associate the terms) the physical entity may have a different interpretation. Here, (60 minutes/1 hour)/30 minutes has dimension [hour^(-1)], which is a frequency measure. You can read this as 2 "cycles".
* (60 minutes/1 hour)/(30 minutes/1/2 hour) is NOT the same as (60 minutes/1 hour)/30 minutes. If we let N1=(60 minutes/1 hour), D1=(30 minutes/1/2 hour), then, D1=30/0.5=30/(1/2)=30*2=60, this cancels with N1 to give 1.

Thanks.