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# Manipulating formulas: temperature

Video transcript

We're told that the formula
for converting a Celsius temperature into Fahrenheit is
the Celsius temperature, or C, is equal to 5/9 times
the Fahrenheit temperature minus 32. Rewrite the formula so it
solves for Fahrenheit. So just like I mentioned, the
C is Celsius, is the Celsius temperature. And the F is the Fahrenheit
temperature. So right now, it's expressed in
terms of, we've solved for C in terms of F. Now we want to solve for
F in terms of C. So let's see how we're
going to do that. So I'll just rewrite it. C is equal to 5/9 times
F minus 32. And we want to solve for F. So the first useful thing to do
might be to get rid of this 5/9 from both sides, or at least
from the right side of the equation, so we just
have an F minus 32. And the easiest way to do
that is to multiply by the inverse of 5/9. So if we multiply both sides of
this equation by 9/5-- and I could put it here, but it'll
squeeze a little tight, let me try it-- 9/5 in there. If I do it to the right-hand
side of the equation, I also have to do it to the left-hand
side of the equation. And what do I get? The left-hand side becomes 9/5
Celsius, or the Celsius temperature, 9/5 times the
Celsius temperature, is equal to-- the whole reason we wanted
to multiply the right side by 9/5 is these 9's cancel
out, this 5 cancels out, and this just
becomes a 1. So 9/5 times the Celsius
temperature is going to be equal to this expression:
the Fahrenheit temperature minus 32. We don't need the parentheses
anymore, because this is the only expression on the
right-hand side. Now, we want to solve for the
Fahrenheit temperature. So let's see if we can get
rid of this 32 from the right-hand side. The easiest way I know how
to do that is to add 32. Add 32 to both sides
of this equation. Add 32 to both sides. The left-hand side now becomes
9/5 times the Celsius temperature, plus 32. And that's going to be equal
to-- this negative 32 and positive 32 cancel out, that
was the whole point behind adding 32, so it's just going
to be equal to F. And we're done. We have rewritten this formula,
up here, so it solves for Fahrenheit. This is the Fahrenheit
right here. We've solved for Fahrenheit
in terms of the Celsius temperature.