About this video
To compare scales that use different units, convert both parts to the same unit and write the scale without units. The video rewrites 2 m to 10 km as 2 to 10,000, which is the same as 1 to 5,000 or 4 to 20,000, and uses this to pick the equivalent scales.
You'll be able to
- convert both parts of a scale to the same unit.
- write a scale without units and simplify it.
- decide whether two scales with different units are equivalent.
Key words
- scale
- A comparison like 2 m to 10 km between a drawing length and a real length.
- equivalent scales
- Scales that describe the same size relationship, like 1 to 5,000 and 4 to 20,000.
- scale without units
- A scale written as just numbers, like 1 to 5,000, after both parts are in the same unit.
Transcript
- [Instructor] Which two scales are equivalent to two meters to 10 kilometers? We can pick two answers. So pause this video and give it a try. All right, so as we can see, everything has all these different units. So my simple mind just tries to say, let's put it on to one standardized representation.
And the way I could do it is essentially make it not dependent on the units. So in this first one, if I were to convert everything to one unit, and I think it would be easier to convert to meters, this can be rewritten as two meters for every, or to, 10 kilometers in meters is the same thing as 10,000 meters.
So this ratio, or this scale, is the same thing as two to 10,000. I can write that because these are the same units now. Now, I can also write that as one to 5,000, if I just divide both of these by two. And let's see, I see some 20,000s in here. So let's see, another way to think about it, I can double both of these, and I could say this is also the same thing as four to 20,000.
Now let's see which of these are equivalent. And we have to be very careful. If you just look at these numbers here, you might say, okay, B looks a lot like that top one, but we have to make sure that the units make sense. So this first one right over here, one meter to five kilometers, this is the same thing as one meter to 5,000 meters, if we rewrite kilometers as thousands of meters.
And so this is one to 5,000, which is this one right here. So this one is equivalent, four meters to 20,000 meters. Yeah, that actually, these are the same units. So this is the same as four to 20,000. So this one looks good as well. So this last one should not be the answer, but let's just check.
Here the units are the same. So this is the same thing as a scale of one to 500, which is of course not the same thing as our equivalent, or as our original scale. So yes, I like choices A and B.
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