The relationship between the temperature in degrees Fahrenheit, F, and in degrees Celsius, C, is given by the formula C equals five-ninths times F minus 32. What temperature, in degrees Fahrenheit, is equivalent to 60 degrees Celsius?
Some temperature in Celsius is equal to five-ninths times the temperature in Fahrenheit minus 32 degrees. We want to know what Fahrenheit temperature is equivalent to 60 degrees Celsius. We plug in 60 for the C value and then solve for F. Because 32 is being subtracted from F and then multiplied by five-ninths, we need to do the opposite. We need to get rid of this five-ninths first. To do that, I can multiply the right side of the equation by nine-fifths. And if we multiply one side of our equation by nine-fifths, we need to multiply the other side of the equation by nine-fifths.
On the right side, we have five over five, which equals one. And nine over nine, which equals one, leaving us with F minus 32. On the left-hand side, we can say that five and 60 are both divisible by five. Five divided by five is one. 60 divided by five is 12. Then we need to multiply nine times 12, which is 108. Finally, to get F by itself, we need to add 32 to both sides of the equation. 108 plus 32 equals 140. Minus 32 plus 32 cancels out. 140 equals F. When it is 140 degrees Fahrenheit, the equivalent temperature in Celsius is 60 degrees.
Using this method, we plugged in 60 degrees for Celsius and then solved for F. But we could have solved for F before we plugged in our 60 degrees. If we were going to solve for F in terms of C, we would still multiply both sides of the equation by nine-fifths. Nine-fifths times C would just be nine times C over five. On the right-hand side, the five-ninths and the nine-fifths do cancel out, again leaving us with F minus 32. From there, add 32 to both sides. And you’ll have nine C over five plus 32 equals F. Once you solve for F in terms of C, you could plug in 60. You would have nine times 60 divided by five plus 32. Again, 60 over five reduces to 12. And nine times 12 is 108. 108 plus 32 equals 140.
And so we’ve shown that 140 degrees Fahrenheit is equivalent to 60 degrees Celsius in two different ways.