1 Dollar = 10 Dimes
1 Dime = 10 Pennies
10 Dimes / 10 Pennies = 1 <--- But this is correct. We got a whole number. 10 Dimes fits into 10 Pennies 1 time. 10 fits into 10 1 time.
1 = 10 dimes/dollar
1 = 10 pennies/dime
10 dimes / (10 pennies/dime) = 1 dimes^2/pennies
The only reason you think this calculation makes sense is because both factors are 10.
If you had a different money system that was still based on whole numbers, it wouldn't work.
1 pound = 20 shillings
1 shilling = 12 pence
20 shillings / (12 pence/shilling) = (5/3)(shillings^2/pence)
Does this mean the old english money system was invalid?
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1 Yard = 5280 Feet
1 Foot = 12 inches
5280 Feet / 12 inches = 440 <--- This is correct as well. We got a whole number. 12 inches can fit neatly into 5280 feet 440 times. 12 fits neatly into 5280 440 times.
The 1 Foot = 12 inches is implicit in the above equation.
1 nautical mile = 6076.12 feet
1 foot = 12 inches
1 nautical mile / 12 (inches/foot) = 506.34 nautical mile * feet/inches
Does this mean nautical miles don't exist?
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I just divided unlike units and got a right answer
I can do that too:
The speed limit on I-5: 70 miles/hour
Number of days in a week: 7 days / week
70 miles/hour / 7 days/week = 10 miles*week/hour*days
It's a whole number, it has to mean something.
How about
7 days in a week
24 hours in a day
60 minutes in an hour
7 days / 60 minutes/hour = 7/60 (days*hours/minutes)
7 days / 24 hours / day = 7/24 (days^2/hours)
Does this mean weeks don't exist?