Mathematics units

Hi guys, if I have 120 gallons , and for every gallons I have 4 quarts so how many quarts in 120 gallons?
the teacher in the video said immediately 120*4 .. but why? and how does he know that immediately!!?! is there a technique that I can do it to answer those questions immediately?! thanks alot
 
I'm with you, but I'm not understanding it .. !!! so how could I practice something that I'm not understanding? that's why I'm asking the question to understand why the answer is like that
 
Ryan, my point is that you've already posted similar questions. You don't seem to be doing math; you seem to be passively watching math.

If you were to practice doing a lot of unit-conversion exercises (writing out each step on paper), then eventually you would start to recognize patterns, and then your brain will encode them, and things become easier.

\(\displaystyle \frac{120 \; \cancel{\text{gal}}}{1} × \frac{4 \; \text{qt}}{1 \cancel{\text{gal}}} = \frac{120×4 \; \text{qt}}{1}\)

With sufficient practice, you can remember how to do basic unit conversions like this right away. Don't worry now when the video teacher says 120×4 "immediately". ? They have done a lot more practice than you have.

\(\;\)
 
but lets assume I have 150 gallons, and one gallon is 40 quarts, so how many quarts in 150 gallons?
here I'm stuck and the teacher in the video said 150*40 immediately without thinking about it .. so I guess there's a quick way to assign for knowing the answer!
 
Ryan$ said:
but lets assume I have 150 gallons, and one gallon is 40 quarts, so how many quarts in 150 gallons?
here I'm stuck and the teacher in the video said 150*40 immediately without thinking about it .. so I guess there's a quick way to assign for knowing the answer!
Click to expand...
150 gallons = 150 times 1 gallon. But 1 gallon is 40 quarts (make believe). So in 150*1 gallon you just replace 40 quarts where you see 1 gallon or gallon.
So 150 gallons = 150*gallon = 150*40 quarts = 6000 quarts (of course this is not true as 40 quarts does not equal 1 gallons, but if it did, then t would be true)
 
I know that there are 60 minutes in 1 hour.
So in 7 hrs there are 7*60 minutes.
All I did was replace hrs with 60 minutes. That is 7 hrs =7 * 1hr = 7*60 min = 420 minutes. At some point you should be able to skip writing the blue part.
 
Ryan$ said:
… I guess there's a quick way … for knowing the answer!
Click to expand...
Yes there is, and you will never know what it is, until you start acting like a math student.

You're not in school. You're not studying math to learn. Why are you posting here?

:confused:
 
Hi guys!
we already done that representation in math doesn't matter ... so how 5cm != 5m they are equal in value , but not equal in what?! I want to know how math's logic going .. if the value are equal , doesn't say they are the same?! what makes two things equal aside its values

what I know that if two values are equal then they are the same... isn't the correct?!
 
Ryan$ said:
Hi guys!
we already done that representation in math doesn't matter ... so how 5cm != 5m they are equal in value , but not equal in what?! I want to know how math's logic going .. if the value are equal , doesn't say they are the same?! what makes two things equal aside its values

what I know that if two values are equal then they are the same... isn't the correct?!
Click to expand...
The magnitude of the two "items" are equal.

However, the UNITS are NOT equal.

Hence the two items are not equal....
 
Hi guys, it's really weird to know there's what's called in algebra "unitless" numbers .. but yeah I learned something new and I'm satisfied with.
but what's confusing me so if it's unitless so we can't say anything on that number it's abstract ! here I'm fine with!

but why for example if I want A in terms of B then I say A/B which it's number "unitless" and it's representing how much I've from B that's equal to A, so in other words the number (A/B) is not unitless .... it's representing how much we have from A in aspect of B. so how we say that the number (A/B) is unit less? it's representing something ..
 
In pure math, we deal with quantities in the abstract. When we apply mathematics, we must deal with issues outside mathematicss.

[MATH]\dfrac{7}{3}[/MATH] simply represents a rational quantity as do 7 and 3.

We are talking about the Platonic ideals of quantity. Nothing has units.

In much of scientific teaching, we deal with things as absolute truths without regard to exceptions or uncertainty about the measurements on which we rely. So we are dealing with a different kind of Platonic ideal: our theories are certainly true and our measurements are exact.

In actual life, we are never absolutely certain of anything. And we recognize that many of our numbers are approximations or estimates.

You need to understand which level of abstraction you are dealing with.

In the realm of pure math, 7 and 3 represent abstract quantities pure and simple. There are no units. 7/3 is another abstract quantity. There is no external ruler to measure against. The quotient has no units because 7 and 3 have no units.

If you are dealing at a lower level of abstraction, where 7 and 3 both represent some quantity of units, 7/3 may or may not have a unit associated with it.
 
Ryan$ said:
Hi guys, it's really weird to know there's what's called in algebra "unitless" numbers .. but yeah I learned something new and I'm satisfied with. but what's confusing me so if it's unitless so we can't say anything on that number it's abstract ! here I'm fine with! but why for example if I want A in terms of B then I say A/B which it's number "unitless" and it's representing how much I've from B that's equal to A, so in other words the number (A/B) is not unitless .... it's representing how much we have from A in aspect of B. so how we say that the number (A/B) is unit less? it's representing something .
Click to expand...
I have been is serious study of the philosophy of mathematics sense 1962. I have been an NIH fellow in the study. I have never see the term(s) "unitless numbers" used. Look at the quote in my so called signature from Albert Einstein. You seem to enjoy posting that sort of question. You should read that entire essay found in Redings in THE PHILOSOPHY OF SCIENCE. Feigl & Brodbeck editors. Any research university library should have that collection. In fact given the questions you have posted, you would benefit greatly from reading the entire collection.
 
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Hi guys ! I don't know if it's a problem or not but yeah I'm still on doubt with that.
if I've an equation (called it equation $ ) which it's just implicitly understand in unit "Meters" , so if a question given with data type of cm, for example 100cm, and in that question I forced to assign and use the equation $ , so do I need to convert 100cm to meters in order to use the equation?
if so, then why? I really need to understand how logic words, and if there's more analogy senseable to illustrate why I need to be adjusted logically to what's given in my problem, would be really appreciated.

once again I know two things : I've to assign 100cm to the equation, I know that my equation just dealing with meters and not cm .
here's my struggle , why I need to convert 100cm to meters?! if I convert 100cm to meters, what's ringing in my head we changed the value of 100cm which means we changed the given data and that's not allowed !

I'm not claiming that I'm right ! I just want to learn the right and why it's right to improve my learning !

thanks for your help!
 
As long as you are consistent with your units nothing changes the answer.

For example, say you have the equation [math]x = vt[/math]. If you use m for x then you need to use m/s for v. If you use cm for x then you need to use cm/s for v. If you use s for t then you need to use m/s for v (or cm/s, depending on what unit you are using for x.) Similarly if you use min for t you need to use m/min for v. The numbers do change but if you are using a consistent set of units the meaning of the answer is the same.

-Dan
 
topsquark said:
As long as you are consistent with your units nothing changes the answer.

For example, say you have the equation [math]x = vt[/math]. If you use m for x then you need to use m/s for v. If you use cm for x then you need to use cm/s for v. If you use s for t then you need to use m/s for v (or cm/s, depending on what unit you are using for x.) Similarly if you use min for t you need to use m/min for v. The numbers do change but if you are using a consistent set of units the meaning of the answer is the same.

-Dan
Click to expand...

I mean from my post, why I need to be consistent in my logic!!
 
Ryan$ said:
I mean from my post, why I need to be consistent in my logic!!
Click to expand...
You cannot logically add different units. 3 meters plus 2 chickens does not create 5 of some one thing.

You do not need to be consistent. You can be illogical.
 
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