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## Algebra 1

### Course: Algebra 1>Unit 3

Lesson 1: Rate conversion

# Same rate with different units

Sal shows how we can describe the rate 50 km per hour in a variety of different units, using dimensional analysis. Created by Sal Khan.

## Want to join the conversation?

• What units would be a good choice for the rate in a "per minute" basis? •   I think we need to discuss what a unit is. A unit is a descriptive term that tells you what you have a certain number of. For example, I have 4 cookies.
You can then say: I eat 3cookies per glass of milk. This gives me a relationship for my 2 units (cookies and milk).

A good corresponding unit for per minute, might be: inches, feet, food, blinks....
Usually when you think of this "per" unit, you think of a car: miles per hour (MPH).
• how is dimensional analysis unit conversions? I thought dimensional analysis would actually have some dimensions and not just easy conversions from 1 unit to the next. • Hello :)
I would like to say that this is a great video and I really like it :) everything makes perfect sense to me so far expect at .. why did Sal put the 1000meters in the numerator and the 1km in the denominator ??
Why didn't he do the same with hours and seconds from when he was converting before ?? at
Thanks ^_^ • I am not quite sure what you are asking. I think you are asking about why he put hours on top, and meters on the bottom.

It has to do with canceling units. Units of measurement (likes hours or seconds), can be cancelled with Algebra. Let's say you have 12x. If you want to get rid of the "x", you will need to divide the "x" away. If you have 12/x, you can get rid of the "x" by multiplying by "x".

When you have KM/Hour, if you want to get rid of the "Hour" in the denominator, you need to multiply by "Hours" to get rid of it... so "Hours" goes on top in the numerator. When Sal wanted to get rid of the "KM" in KM/Hour, he would need to divide by "KM" since "KM" was originally in the numerator.
• How does Sal have such a good handwriting on a computer using a mouse? • I got confused in the Rate Conversion practice, and when I decided to get a hint because the videos were of no help, they said that if I wanted to convert cm^3 to m^3, I had to cube the number of centimeters and that was the number of centimeters cubed in just a plain old meter, and then I had to convert plain old meters to cubed meters by cubing again, and everything just got really confusing and muddled. Does anyone know if there is an easier way? All the work just got messed up on my paper and I couldn't figure out what, if anything, to do next - there was too much. • Can it be explained more straight forward? as soon as I looked at the problem i knew the answer, but the way it was explained in the video just made me even more confused then ever. • @melovecats13 What Sal sir is trying to do is create an equivalent of 50 km per hour in minutes and seconds by multiplying their values by an order like 3600 for seconds to a minute. If you are still confused here is a somewhat detailed explanation of the same

Q: You wish to convert 50 km per hour into seconds ie how many seconds does he cover 50 km?
Here is a way to solve it:
You know that 1hour has 60 mins and for every min there is 60 seconds and so 1 hour has 3600 seconds
Now in km/hour you don't need to change the km value, now hours in denominator from the question. We do the necessary conversion like this 50 km/hour * 1hour/3600 seconds. (Logically for every one hour there is 3600 seconds)
``Write down what is given in the bold along with the words hour km seconds and you will find that you can cancel the words hour on the numerator and denominator just like how you would cancel multiples value ie 5 and 10 you get 2``

P.S: This concept is more dealt in Physics than in Maths and knowledge of powerful formulae like F = m * a (Force = Mass * acceleration) will help
P.S.S: Do let me know if it still confuses you..
• at why do we have to multiply 50 by 1 hour? I thought all we needed to do was divide 3600 by 50 . Also i did not get whether it was 72 km per second or 1 km per 72 seconds. Although i had some questions this was a fantastic video that triggered a much needed Eureka! moment!! Would i need to multiply 50 by 2 hr if a question said 20/km per 2 hrs or is that not mathematically correct to use 2 hours as a unit • Hello zahra ismail:
At we multiply 50 by 1 hour (multiplying first before division, as in the order of operations; sometimes referred to as "PEMDAS" -there are videos of it in Khan Academy, just in case...). We do this even though essentially it won't change the answer...since 50 multiplied by 1 is 50 and THEN we divide by 3600 seconds. I think Sal did this so the viewers would see step by step, but sometimes it becomes confusing, especially if you do this on your head beforehand.

Also, at it is 1/72 of a km per second or you could also view it as 1 km per every 72 seconds.
Hope this helps :)
• I don't understand anything and tried the exercise thrice HELP • Unit of Conversion Rule:

(SU, LU, DU = Starting, Linking, and Desired Units)

Ratio: 50 km/h, but we want the km per second

SU: Hours
DU: Seconds
LU: The link between the SU and the DU. In this case it’s 3600 seconds/1 hour because there are 3600 seconds in an hour.

Rule:

SU * LU/SU * DU/LU = DU

The first part of the equation is designed to cancel out the SU, so you can replace them with the DU

1 hour (SU) * 3600 seconds/1 Hour (LU/SU) = 3600 seconds/1 * 3600 seconds/1 (DU/LU) = 3600 seconds (DU)

Replace hours with seconds in the ratio:

50 km/3600 seconds= 50 * 1km/3600 seconds = 50km/3600 seconds. Reduce: 1km/72 seconds.

Hope that helps  