Expert: Josh - 1/27/2004

Question
Hello:

In the following calculation, 56 miles/60 minutes represents miles per minute:

56 miles/60 minutes X 30 minutes = 28 miles

This same calculation can be expressed by the following calculation because of the commutative principle of multiplication:

30 minutes/60 minutes X 56 miles = 28 miles

Question: Part 1.

What does 30 minutes/60 minutes represent or equal since the units cancel minutes per minute as in (1/2) minutes/1 minute or 1/2?

Question: Part 2.

And also, in this calculation can 30 minutes/60 minutes be replaced by 30 minutes/(60 minutes/1 hour)?
What circumstances should the rate of 30 minutes/(60 minutes/1 hour) be used?

I thank you for your assistance and reply.  

Answer
Hello,

Answer: Part 1.
Just a fraction or percentage. Nothing more.

Answer: Part 2.
(i) The problem would not be the same, since
30 minutes/(60 minutes/1 hour)
=30 minutes*(1 hour/60 minutes)
=0.5 hour
(ii) re: circumstances
suppose you were given speed "56 miles/hour" instead of distance, "56 miles", and the question asked you to work out how much ground you will cover in 30 minutes.
This is what you would do.
Convert 30 minutes to hours, using (i).
Multiply time (hours) by speed (miles/hour) gives you distance, in terms of (miles).

Cheers.