91Ó°ÊÓ

When solving equations, one common goal is isolating the variable you need to solve for. This means getting the variable by itself on one side of the equation. Starting with the equation \( F = \frac{9}{5} C + 32 \) our task is to isolate \( C \). This involves a few clear steps: First, we identify the term containing \( C \) which is \( \frac{9}{5} C \). To isolate it, we need to remove any other constants from that side. Here, 32 is on the same side as \( C \), so we subtract 32 from both sides to get: \( F - 32 = \frac{9}{5}C \). At this point, \( C \) is almost isolated, but not quite. We still need to deal with the fraction \( \frac{9}{5} \). We will handle this in the next step.

Dealing with fractions is easier if you understand the concept of reciprocals. A reciprocal of a number is simply one divided by that number. For example, the reciprocal of \( 2 \) is \( \frac{1}{2} \), and the reciprocal of \( \frac{9}{5} \) is \( \frac{5}{9} \). To get rid of the fraction \( \frac{9}{5} \) in our equation \( F - 32 = \frac{9}{5}C \), we multiply both sides by the reciprocal of \( \frac{9}{5} \), which is \( \frac{5}{9} \). This gives: \( C = (F - 32) \times \frac{5}{9} \). Remember, multiplying by the reciprocal transforms the equation into a simpler form, where the variable \( C \) is now isolated.

Now that we have derived \( C = ( F - 32 ) \times \frac{5}{9} \), let's connect it to the concept of temperature conversion. This equation is used to convert temperatures from Fahrenheit ( \( F \) ) to Celsius ( \( C \) ). Why is this conversion important? Here are some reasons:

• Scientific measurements are often done in Celsius.
• Understanding local weather forecasts when traveling can depend on knowing both scales.

To interpret this equation in words: First, subtract 32 from the Fahrenheit temperature. Then, multiply the result by \( \frac{5}{9} \). This allows you to compute the equivalent temperature in Celsius easily. Let's break this down step by step:

• If \( F = 86 \), after subtracting 32, you get 54.
• Then, multiplying 54 by \( \frac{5}{9} \) results in 30.

So, 86°F is equal to 30°C.