how do people get 5/9 in the equation which converts farhenheits to celcius...?

Question

because i'm suppose to write a paper which explains how to derive an equation that converts C-->F and vise versa

Answer 1

It depends on what temperature scale you are converting from. Since
you don't say, I am going to assume that you meant to ask what 27
degrees Celsius is when converted to Farenheit. If that's not what you
meant to ask, then let me know.

Let's pretend that there is a straight-line (linear) relation between
the two temperature scales (and it turns out that in fact there is).
If that is so, then we need two "points" to find the equation for
that line.

Freezing in Celsius is 0 degrees, and in Fahrenheit it is 32.
Boiling in Celsius is 100 degrees, and in Fahrenheit it is 212.

Farenheit Celsius
--------------------
32 0
212 100

The equation for a line that converts Celsius to Farenheit is:

F = mC + b

where C is the Celsius temperature
m is the "slope" of the line
F is the Fahrenheit temperature
and b is the "intercept" of the line

So if we use our two "points" to fill in this equation we get:

Farenheit Celsius equation
-------------------- ------------
32 0 32 = 0m + b
212 100 212 = 100m + b

Now we have two equations and two unknown values (m and b) so we can
solve for these values and make an equation that converts Celsius to
Farenheit:

The two equations:

32 = 0m + b
212 = 100m + b

The first thing to do is to make both equations equal to the same
thing. The easy way to do that is to get the b terms alone on one side
of the equation:

32 = b
212 - 100m = b

Notice that we already know the value of b. And since both equations
are equal to b, they are also equal to each other:

32 = b = 212 - 100m
32 = 212 - 100m

And we can solve for m like this:

32 = 212 - 100m
32 - 212 = 212 - 100m - 212
-180 = -100m
-180 / -100 = -100m / -100
(-180/-100) = (-100/-100)m
9/5 = m

If we put the values for m and b into C = mF + b, we can come up with
an equation that converts Celsius to Fahrenheit:

F = mC + b <== m=9/5 , 32=b
F = (9/5)C + 32

Answer 2

If you had a graph of celsius against farhenheit, the 5/9 = 0.5555 would be the slope of the line, or 9/5 = 1.8 depending on whether celsius is the X or Y axis of the graph.

Try drawing yourself a graph a marking 2 points on it for the melting point of ice (0 celsius, 32 F) and the boiling point of water (100C, 212F), then drawing a straight line between them. The 5/9 or 9/5 should be the slope.

In numbers the slope is (100 - 0) / (212 - 32), the same as 100 / 180 or 10 / 18 or 5/9

Answer 3

100/180=50/90=5/9
F to c:
100-0/212-32=c-0/f-32
100/180=c/f-32
5/9=c/f-32
5(f-32)/9=c
f=9c/5+32 LQQD

Answer 4

the equation is F=9/5C plus 32. so if u have ur degrees celcius just multiply it by 1.8 and add 32 to get farenheit.

Answer 5

it's 9/5 or 1.8

the equations is:

F = 1.8 C + 32

where F is degreed Fahrenheit and C is degrees Celcius.

Going the other way would be:

C = (F - 32)/1.8