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## Topic D: Systems of linear equations and their solutions

Current time:0:00Total duration:2:58

# Converting Fahrenheit toÂ Celsius

## Video transcript

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-- they're giving us the
Fahrenheit temperature-- what is the corresponding
Celsius temperature? And then they give
us the two formulas, that if we know the
Celsius temperature, how do we figure out the
Fahrenheit temperature, or if we know the
Fahrenheit temperature, how do we figure out
the Celsius temperature. And these are actually
derived from each other, and you'll learn more about
that when you do algebra. And we also-- maybe
in another video-- will explain how
to derive these. It's actually kind
of interesting, involves a little
bit of algebra. But they gave us the formula. So they really just want us to
apply it, and maybe make sure we understand which
one we should apply. Well, they're giving us
the Fahrenheit temperature right here, so F is
going to be equal to 56. And they're asking us for
the Celsius temperature, so we need to figure out what
the Celsius temperature is. Well, in this one over here,
if you know the Fahrenheit temperature, then you can solve
for the Celsius temperature. So let's use this
right over here. So our Celsius
temperature is going to be 5/9 times the Fahrenheit
temperature-- the Fahrenheit temperature is 56 degrees
Fahrenheit-- minus 32. Well, 56 minus 32 is 24. So this is going to be
equal to 5/9 times 24. And this is the same thing
as 5 times 24, over 9. And before I even
multiply out 5 times 24, we can divide the numerator
and the denominator by 3. So let's do that. If we divide the numerator
by 3 and the denominator, we're not changing the value. 24 divided by 3 is 8. 9 divided by 3 is 3. So it becomes 5 times 8,
which is 40, over 3 degrees. And if we want to write
this as a number that makes a little bit more sense
in terms of temperature, let's divide 3 into 40 to get
the number of degrees we have. 3 goes into 4 one time. 1 times 3 is 3. Subtract. 4 minus 3 is 1. Bring down the 0. 3 goes into 10 three times. 3 times 3 is 9. Subtract. Get a 1. And then you could
bring down another 0. We now have a decimal
point over here. You're going to get a 0 here. 3 goes into, once
again, 10 three times. And this 3 is going
to repeat forever. So you could view this--
this is equal to 13.333-- it'll just keep repeating. This little line on top means
repeating-- degrees Celsius. Or you could say that, look,
3 goes into 40 13 times with a remainder of 1. So you could say that this is
also equal to 13, remainder 1. So 13 and 1/3 degrees Celsius. Either way, it works. But that's our
Celsius temperature when our Fahrenheit
temperature is 56 degrees.