Changing the Subject of a Formula

  • Thread starter LightbulbSun
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In summary, the formula for converting Celsius temperatures to Fahrenheit is F= (C + 40)9/5 - 40. The mistake in the attempt at a solution was getting rid of the +40 next to F instead of the -40 on the outside, resulting in the incorrect equation C- 40= (F+40 - 40)(5/9) - 40.
  • #1
LightbulbSun
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Homework Statement



Express the formula for converting Celsius temperatures to Fahrenheit.



Homework Equations



C= (F+40)(5/9) - 40



The Attempt at a Solution




C= (F+40)(5/9) - 40
C- 40= (F+40 - 40)(5/9) - 40
(C-40)9/5= F(9/5)(5/9) - 40
(C - 40)9/5 + 40= F - 40 + 40

F= (C - 40)9/5 + 40


Answer: F= (C + 40)9/5 - 40

Could someone please explain to me why the operation signs in the (C + 40) and - 40 are opposite from the solution I came up with?
 
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  • #2
LightbulbSun said:

Homework Statement



Express the formula for converting Celsius temperatures to Fahrenheit.



Homework Equations



C= (F+40)(5/9) - 40



The Attempt at a Solution




C= (F+40)(5/9) - 40
You made a mistake going from this line to the one below.
C- 40= (F+40 - 40)(5/9) - 40
You need to add 40 to both sides.. I don't know where you've got that 40 from inside the brackets. The next line should read
C+40=(F+40)(5/9)

Now, what do you think you'd do next?
 
  • #3
cristo said:
You made a mistake going from this line to the one below.
You need to add 40 to both sides.. I don't know where you've got that 40 from inside the brackets. The next line should read
C+40=(F+40)(5/9)

Now, what do you think you'd do next?

OH! I know what I did wrong. I started from within the brackets first and got rid of the +40 next to the F instead of getting rid of the -40 on the outside. Now I see where I went wrong. Thank you.
 

1. What is "changing the subject of a formula"?

Changing the subject of a formula involves rearranging the equation to isolate a different variable or term. This is often done to solve for a specific variable or to simplify the equation for further calculations.

2. Why is it important to know how to change the subject of a formula?

It is important for scientists to be able to change the subject of a formula because it allows for more efficient problem solving and analysis. By isolating specific variables, scientists can better understand the relationships between different components of a formula.

3. What are the steps involved in changing the subject of a formula?

The steps for changing the subject of a formula include identifying the variable to be isolated, using inverse operations to move all other terms to the opposite side of the equation, and simplifying the equation to solve for the desired variable.

4. Can any formula be changed to solve for a different variable?

Yes, most formulas can be changed to solve for a different variable as long as the equation follows the rules of algebra. However, some formulas may require more complex steps and techniques to change the subject.

5. Are there any precautions to take when changing the subject of a formula?

It is important to be careful when using inverse operations and to double check the new equation for any mistakes. It is also helpful to have a good understanding of the properties of algebra and how to manipulate equations before attempting to change the subject of a formula.

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