A thermometer in a science lab displays the temperature in
both Celsius and Fahrenheit.
If the mercury in the thermometer rises to 56
degrees Fahrenheit, what is the corresponding Celsius
temperature?
So right from the get go, there's a formula that if you
get have the Celsius temperature, it'll give you
the Fahrenheit, if you have the Fahrenheit, it'll give you
the Celsius.
Now I have a bad memory, so I always have to
pseudo-derive it.
And maybe in future videos, we'll totally derive it.
Once we get a little bit more algebra, if you just know the
boiling and freezing points in both scales, you should be
able to figure out the relationship between the two.
Now the way I always remember it is that there's a
relationship of 5/9 or 9/5 between the two.
And then you have to add or subtract 32.
And the way I think about it is, the Fahrenheit number is
always going to be larger.
So if you start with-- or at least while we are in our
normal, everyday living scales when water is in its liquid
form and all that.
So if you start with a Celsius, I say, oh I have to
make it bigger.
So I have to say, OK, I'm going to multiply that by 9/5.
That will make it bigger.
And then I'm going to add 32 to it.
And the reason why I know to add 32 is because when Celsius
is 0, 0 times 9/5 is still 0.
And we know when Celsius is 0, Fahrenheit is going to be 32.
So I know I have to add 32 to it.
So, at least my gut is telling me, that the formula is 9/5
times the Celsius degrees, plus 32.
And you can verify that this works for the boiling point.
This definitely works for the freezing point.
When Celsius is 0, this is going to be 0, you add 32,
that's going to be Fahrenheit.
When Celsius is 100, 9/5 times 100 is 180, plus 32 is 212.
So this works.
They've given us the Fahrenheit temperature, and we
need to get the Celsius temperature.
Now I could just put the 56 in here, and solve for C, and
that will completely work.
Or I could solve for C using this, so I have the equation
for Celsius in terms of Fahrenheit.
Either way.
So let's do it the second way, so we
have the second equation.
So if we subtract 32 from both sides of this equation, we get
Fahrenheit minus 32 is equal to 9/5 times Celsius.
Now to solve for Celsius, we can multiply both sides of
this equation times 5/9.
And so we will get 9 cancels with 9, 5 cancels with 5.
That was the whole point behind multiplying by the
reciprocal.
Remember, this 5/9 is going to be times this whole left side.
We're left with Celsius.
Celsius is equal to 5/9 times Fahrenheit, minus 32.
So we just rearranged this equation up here to get this
equation down here.
I didn't derive the equation in this video, I just kind of
pseudo-remembered it, and made sure I got the equation right.
But you can derive it if you just remember, it's
essentially, if you know how to find the
equation of a line.
You say, well, when Celsius-- if you use the x-coordinate as
Celsius-- when Celsius is 0, Fahrenheit is 32.
And when Celsius is 100, Fahrenheit is 212, and find
the equation of the line between these two points.
Don't worry about it if you don't know that.
All you need to know for this problem is this right here.
But if you know how to solve the equation for the line, you
would come up with this answer right here, and you wouldn't
have to memorize it.
Now that we've actually gotten this far, let's just put in 56
degrees for the Fahrenheit temperature, and figure out
what the Celsius temperature is.
So if we put 56 in there, we're going to have 5/9 times
56 minus 32 is equal to the Celsius temperature.
So 56 minus 32-- let me continue it up here.
56 minus 30 is 26, minus 2 is 24.
So this is going to be 24.
So it's going to be 5/9 times 24.
This right here is 24.
5/9 times 24 is going to be equal to C.
And let's see if we can simplify this at all.
So this is the same thing as 5 times 24 over 9.
24 is divisible by 3.
You divide it by 3, you get 8.
9 divided by 3 is 3.
So 5 times 8 is equal to 40/3 Celsius, degrees Celsius.
Now if we wanted to write this as a mixed number, 3 goes into
40 thirteen times.
And you have a remainder of 1.
So it's 13 and 1/3.
Now we could even check that.
3 times 13 is 39, plus 1 is 40.
And if this wasn't obvious to you, you could actually just
take 3 into 40.
3 goes into 4 one time.
1 times 3 is 3.
Subtract.
You get 1.
Bring down that 0.
3 goes into 10 three times.
3 times 3 is 9.
You subtract.
You get a remainder of 1.
So it's 3 and 1/3.
So this is 13 and 1/3 degrees Celsius.
So if it's 56 degrees outside in Fahrenheit, it's 13 and 1/3
degrees in Celsius.