Chapter 10.3, Problem 4GP

To determine

The formula $F=\frac{9}{5}C+32$ for C .

Answer to Problem 4GP

  $C=\frac{5}{9}\left(F-32\right)$

Explanation of Solution

Given information:

The conversion formula between degrees fahrenheit and degrees celsius for temperature is given as : $F=\frac{9}{5}\left(C+32\right)$ .

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to solve the formula for C , first subtract 32 from both sides and then multiply both sides by 5/9 , to simplify further as shown below:

  $\begin{array}{l}F=\frac{9}{5}C+32\\ F-32=\frac{9}{5}C+32-32\\ F-32=\frac{9}{5}C\\ \frac{5}{9}\left(F-32\right)=\frac{5}{9}\times \frac{9}{5}C\\ C=\frac{5}{9}\left(F-32\right)\end{array}$

Thus, the formula is $C=\frac{5}{9}\left(F-32\right)$ .