ratios: when to convert to same unit first?

steveopolis

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Jun 7, 2018
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I get 100% on the math of writing comparisons as ratios, but this point of confusion remains:
How do we know when we are to first convert to same unit?

For example, the exercise presents 20 questions.
Fourteen compare identical units (mm:mm).
Six compare different units (hours:minutes; hours:day; nickles:dimes).
The answer key indicates that 5 of these need to be converted to identical units (hours:hour) before creating the ratio.
The key indicates that one should be left as is (nickles:dimes).

Is there a way to know? Or is the course just not giving all the info one would normally have?
 
I get 100% on the math of writing comparisons as ratios, but this point of confusion remains:
How do we know when we are to first convert to same unit?

For example, the exercise presents 20 questions.
Fourteen compare identical units (mm:mm).
Six compare different units (hours:minutes; hours:day; nickles:dimes).
The answer key indicates that 5 of these need to be converted to identical units (hours:hour) before creating the ratio.
The key indicates that one should be left as is (nickles:dimes).

Is there a way to know? Or is the course just not giving all the info one would normally have?

I would like to see the exact wording (including the introduction to the group of exercises); the details can sometimes be subtle.

What I hope to see is that the wording of the nickels:dimes question emphasizes the individual coins, not their value, which would be the key. We convert to the same unit when the given units are, as I think of it, "measuring the same type of quantity" (e.g. mass or time), so that we can compare that actual quantity, not just the numbers. The trouble here is that you can be focusing on different quantities in relation to the coins. I can imagine asking about the ratio of the number of coins (leave as is), about their value (convert both to dollars or cents), or about their mass (convert each coin to grams)! You would have to look for some words that indicate how they are looking at it.

If all they say is, for example, "Simplify each ratio: ... 10 nickels:5 dimes", I'd call that ambiguous, especially in the context of other questions that call for conversion, and I would want to ask what is intended. But in real life, you would think about whether you care about the number of coins (there are twice as many nickels) or about something else (both piles have the same total value), based on how the ratio is to be used. Are you going to be spending them, or just counting them, for example?
 
...asking about the ratio of the number of coins (leave as is), about their value (convert both to dollars or cents), or about their mass (convert each coin to grams)! [...] based on how the ratio is to be used. Are you going to be spending them, or just counting them, for example?

Yes! This makes sense to me, and is how I would think of it.

In one area of the course, they asked us to convert to same units where possible. Because we were given that instruction, I knew to convert dimes:nickles to nickles:nickles before writing the ratio.

Here, the original instruction and question was:

Write the following as ratios: (Remember to reduce them to lowest terms.)

10 mm to 12 mm
20 cm to 1 m
16 nickles to 4 dimes
$23.00 to $1.15
 
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