Minus forty is:

• the temperature (in degrees) at which Celsius and Fahrenheit scales read the same; often referred to as 40 below.

This can be shown easily. To convert from Fahrenheit to Celsius, one subtracts 32, then multiples by 5/9. This is expressed mathematically as C = (5/9)(F − 32), where F = Fahrenheit and C = Celsius. Alternatively F = C(9/5) + 32 .

Therefore, to find this special temperature, choose a formula and set the variables equal, denoting a temperature that is the same in both scales:

      F = F(9/5) + 32
(−4/5)F = 32
      F = −40

or

     C = (5/9)(C − 32)
(9/5)C = C − 32
(4/5)C = −32
     C = −40

These are mathematically equivalent demonstrations.