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# Manipulating formulas: temperature

CCSS.Math:

## 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 - 32 rewrite the formula so it solves for Fahrenheit so just like I mentioned the C is a Celsius is the Celsius temperature and the F is the Fahrenheit temperature 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 gonna do that so I'll just rewrite it C is equal to 5/9 times F - 32 and we want to solve for F so the first useful thing to do might be to get rid of this five nights from both sides or at least from the right side of the equation so we just have an F - 32 and the easiest way to do that is to multiply by the inverse of five ninths so if we multiply both sides of this equation by 9/5 and I could put it here but it'll squeeze a little tighter let me try nine fifths in there if I do 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 nine fifths Celsius or the Celsius temperature nine fifths times the Celsius temperature is equal to the whole reason we wanted to multiply the right side by nine fifths is these 9s cancel out this five cancel out and this just becomes a one so nine fifths times the Celsius temperature is going to be equal to this expression the Fahrenheit temperature - 32 we don't need the parentheses anymore because this is the only expression on the right-hand side now we want to 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 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 fifths times the Celsius temperature plus 32 nine fifths 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