Video Transcript
The formula for converting degrees Fahrenheit to degrees Celsius is 𝐶 equals five multiplied by 𝐹 minus 32 over nine. Rearrange the formula to make 𝐹 the subject.
So, what we have is our formula, which is 𝐶 equals five multiplied by 𝐹 minus 32 over nine, where 𝐶 is the temperature in degrees Celsius and 𝐹 is the temperature in degrees Fahrenheit. It is worth noting though that you might sometimes hear degrees Celsius as degrees centigrade. This is an old way or an old term that’s used to describe the same thing.
So, the first step in rearranging to make 𝐹 the subject is to multiply each side of the equation by nine because that’s gonna remove the fraction on the right-hand side. So, when we do that, what we have is nine 𝐶 equals five then multiplied by 𝐹 minus 32.
So, now, what’s the next step? Well, now, what we’re going to do is expand our parentheses. And when we do that, what we’re gonna get is nine 𝐶 equals, and then we got five multiplied by 𝐹, which is five 𝐹, and five multiplied by 32, which is 160. So, we get five 𝐹 minus 160.
So then, next, what we do is add 160 to each side of the equation. And when we do that, what we get is nine 𝐶 plus 160 is equal to five 𝐹. And then, as we want to make 𝐹 the subject to the formula, we want a single 𝐹 on its own. So, to enable us to do that, what we can do is divide through by five. And we could do it term by term.
So, first of all, we’re gonna have nine 𝐶 over five. And then, we’re gonna have plus 32. And that’s because if we divide 160 by five, we get 32. And we know that because earlier on when we expanded our parentheses, we did five multiplied by 32, which gave us 160. And then, this is gonna be equal to 𝐹.
So, this is gonna give us 𝐹 is equal to nine 𝐶 over five plus 32. Okay, great! So, we’ve rearranged the formula to make 𝐹 the subject. Now, there’s a second part to the question, which we’ll take a look at now.
So, the second part of the question says, convert 30 degrees Celsius to degrees Fahrenheit.
And to enable us to do this, what we’re going to do is utilize the rearranged formula that we had from the first part of the question. So, what we’re going to do is substitute in 30 for 𝐶. And when we do that, what we’re gonna have is 𝐹 is equal to nine multiplied by 30 over five plus 32.
So, a quick way of doing this mentally would be to divide the top and bottom here by five. So, what we’re gonna be left with is nine multiplied by six over one plus 32, which is gonna give us 54 plus 32. Well, 54 plus 32 is gonna give us 86. So therefore, we can say 30 degrees Celsius is equal to 86 degrees Fahrenheit.
