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I was listening a lecture on computer performance measurement and the professor was giving an analogy of aircrafts performance measurement. He showed a table which contained different parameters of different aircrafts such as:

Aircrafts:     Passenger Capcity         Speed
Concord              132                1350 mph
DC9                  146                544  mph

then he asked the questions from the students that "How much faster is the Concord compared to DC9?". Then he explained that its more than 2 times. My question is, why did he use Division to compare two values and not Subtraction? I know its a very fundamental question but please excuse my incompetence for that.

Black_Zero
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    One argument is that a quotient is independent of the physical units (if they are properly defined, not like e.g. Celsius degrees for temperature). – gammatester Mar 04 '16 at 11:00
  • In numerical analysis you use different type of comparisons depending on the contest. For example it is not reasonable to use quotients for quantities of norm almost 0. – crbah Mar 04 '16 at 11:03
  • Sometimes you have to use a ratio to describe a phenomena, for example, probability of winning a game. Sometimes, it is optional, as in your case. You may find this interesting:https://en.wikipedia.org/wiki/Relative_change_and_difference – NoChance Mar 06 '16 at 17:40

3 Answers3

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Consider a situation - I ate $1000$ apples. My friend ate $1050$ apples.

Two statements- My friend ate $50$ apples more than me from difference, My friend ate $1.05$ times number of apples as me from ratio.

Consider another situation where I ate $100$ apples and my friend $105$

The two statements would be My friend ate $5$ apples more than me and
My friend ate $1.05$ times the number of apples as me

A third situation- I ate $1$ apple, my friend ate $51$

The two statements - My friend ate $50$ apples more than me and
My friend ate $51$ times the number of apples as me

Conclusion - We need both difference and ratio to clearly know the situation. However, we use different things at different scenarios which I hope is clear from the above exmple.

Win Vineeth
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I posted the same question on Dr.Maths and got the following response which in my opinion is more precise and elaborated.

Ask yourself which would be more meaningful to you:

The Concord is 806 mph faster than the DC9.
  The Concord is 2.5 times as fast as the DC9.


If you have no idea how fast the DC9 is, the first statement would be
nearly meaningless -- you can't tell whether it's just a small
improvement (from, say 100,000 mph to 100,806 mph!) or a huge
improvement (from 10 mph to 816 mph). I'm exaggerating to make a
point: interpreting the significance of the number depends on having
at least some knowledge of related numbers.


The ratio, on the other hand, requires no such knowledge.


Also, and perhaps even more important, the ratio will be the same
regardless of the units used. We don't need to know whether the speeds
were measured in mph or kph or inches per second. In effect, the ratio
amounts to using the DC9 itself as a unit of measurement -- the
Concord flies at 2.5 DC9's.


The same is probably true in comparing computer speeds. Who knows,
these days, what is a good speed? But anyone can tell that twice as
fast is a lot better. This is something we can visualize a lot better
than nanoseconds or gigabytes!
Glorfindel
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Black_Zero
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Let me try to help you with this. The professor asked "How much faster is the Concorde compared to the DC-9?" The right way to solve the question mathematically is to find the keywords. He mentioned "Faster" which is measured in terms of speed so you were not wrong to immediately to use subtraction in order to find the "difference" between the speeds and the reason is because he mentioned the keywords "faster" and "compared" which is a direct comparison in regards of speeds so the answer has to be the difference in speed between the two aircraft.In math you have to be very specific when you pose a problem so theoretically your thinking process was correct all along and it is incorrect that your professor used division as a question.

But if division as for what it is has confused you let's make sense of what division really is first. Division is comparing one number to another in regards of their difference in size, quantity between the two amounts, showing the number of times one value is contained within the other. So the quotient (result) you get from a division equation is basically a ratio. To prove it i will give you an example. 9 ÷ 3 = 3 As you can see the quotient (answer) is 3. Now slap a 1 on top and make it a ratio. 1:3 so three is to nine as one is to three. 3:9 is the same as 1:3 analogy wise. So when you divide something the answer you get is a ratio and always compared to 1. It works with all numbers. 60 ÷ 3 = 20 so slap a 1 on top of the 20. There is your ratio (comparison) which simply 20 is like 1/20 of 60.

Thomas Alexander
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