Did anyone learn ratio and proportions, a is to b as c is to d, written in the form "a:b::c:d" ?
Asked by
LuckyGuy (
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October 3rd, 2020
If I recall we would have been taught this in elementary school. We used to say: “a is to b as c is to d.
A sample problem would be “The shadow of a 3 ft yardstick is 2 ft. The shadow of a flagpole is 20 ft. How tall is the flagpole?” We’d say 2 is to 3 as 20 is to x. We’d write: 2:3::20:x
Then we’d multiply the 2 inner numbers, 3×20, to get 60 and divide by the first number, 2, to get the answer 30ft.
I do not recall ever seeing the colons or double colons anywhere else. Did you learn it that way?
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12 Answers
I was taught to use the colons in that manner when learning parallel analogies and being tested.
Mustard : Hot dog
::
Ketchup: ?
Yes, I did. I think it was probably junior high rather than elementary school. That’s when (seventh grade) we started to get into more abstract stuff, at least in my time and place.
2 : 8 :: 16 : 64
The same format was used for analogies:
shoe : foot :: glove : hand
London : England :: Paris : France
calf : cow :: kitten : cat
They appeared this way in standardized tests, and in particular the Miller Analogies; for example, taken from their sample page,
MASON : (____) :: CARPENTER : WOOD
I don’t think your example works, though, @zenvelo. Ketchup does not imply any one particular answer that’s in the same relation as mustard to hot dogs. Ketchup can go on lots of things, including hot dogs. It’s not a direct parallel and could imply numerous possibilities.
I have seen someone eat a ketchup-and-mayonnaise sandwich. She also put mustard on scrambled eggs.
Thanks! I now remember the analogy questions in that format. In 5th grade our teacher grabbed a yardstick and told us we were going to measure the height of the flagpole. We all thought someone was going to climb the pole. Instead he used the ratio and proportion method.
@Jeruba While there might be other possible answers to @zenvelo‘s analogy problem, “hamburger” is the only answer that is not an affront to those with discerning palates. Recall the criticism a certain loud mouthed radio and TV personality subjected our previous President to because he chose the wrong condiment for his hamburger. It is clear they had to work hard to find something to criticize.
Yeah (IIRC), but I had forgotten about it.
Yes. I loved school so much.
@LuckyGuy, if it were multiple choice, and the possibilities were dust mop, television, virus, and hamburger, certainly hamburger would be the right choice.
But I would argue that the response hamburger requires a cultural context. The parallel is not implicit in the meaning of the word ketchup or its relation to hot dog and mustard, not in the way that a true analogy is. Something doesn’t turn into a hamburger just because you put ketchup on it; fries, for example.
@Jeruba Multiple choices are usually provided. I just did the first test of Miller Analogies from your link above. That was very enjoyable. 14/15. Thank you.
Yes, I learned it that way
@Jeruba.
A hot dog is cooked meat placed in a bread roll. (I am not getting into the hot dog/sandwich debate). Mustard is a sauce one puts on a hot dog.
Ketchup is a sauce. What cooked meat in a bread roll do you put ketchup on? And don’t say hot dog, ketchup on a hot dog is unAmerican and considered a crime in many parts of the country.
I put ketchup on my hot dog. Also, a hot dog is one of only 2 things I’ll put mustard on.
@Dutchess_III We already knew you were unAmerican. You probably don’t like baseball.
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