To convert to Fahrenheit, you multiply the Celsius temperature by \frac{9}{5} and add 32. Which equation can you use to convert Celsius temperatures to Fahrenheit temperatures? F = Fahrenheit temperature C = Celsius temperature F = \frac{9}{5} + 32C F = C(\frac{9}{5} + 32) F = \frac{9}{5}(C + 32) F = \frac{9}{5}C + 32
Adam is in Mexico, where the temperature is given in degrees Celsius. To convert to Fahrenheit, you multiply the Celsius temperature by \frac{9}{5} and add 32. Which equation can you use to convert Celsius temperatures to Fahrenheit temperatures? F = Fahrenheit temperature C = Celsius temperature F = \frac{9}{5} + 32C F = C(\frac{9}{5} + 32) F = \frac{9}{5}(C + 32) F = \frac{9}{5}C + 32
The Correct Answer and Explanation is:
F = (9/5)C + 32
Explanation :
To convert a temperature from degrees Celsius (°C) to degrees Fahrenheit (°F), you use a formula based on the relationship between the two temperature scales. This relationship is linear, meaning that the temperatures change at a consistent rate.
The formula is: F=95C+32F = \frac{9}{5}C + 32F=59C+32
Here’s how and why this works:
- The Ratio (9/5):
The Celsius and Fahrenheit scales are both linear but start at different points and have different unit sizes. The freezing point of water is 0°C and 32°F. The boiling point is 100°C and 212°F. This means 100°C spans the same range as 180°F (212 – 32). The ratio of change between Fahrenheit and Celsius is: 180100=95\frac{180}{100} = \frac{9}{5}100180=59 So, each degree Celsius is equal to 1.8 degrees Fahrenheit, or 9/5 in fraction form. - The Constant (+32):
The 32 in the formula adjusts for the different starting points of the two scales. Since 0°C equals 32°F (the freezing point of water), we must add 32 to align the scales after multiplying by 9/5.
Now let’s analyze the incorrect choices:
- F = (9/5) + 32C: Incorrect order of operations; it adds 32 times Celsius instead of adding 32 after scaling.
- F = C(9/5 + 32): This incorrectly adds 32 to the 9/5 ratio before multiplying by Celsius.
- F = (9/5)(C + 32): This incorrectly adds 32 to the Celsius value before scaling.
Only F = (9/5)C + 32 correctly follows the two-step process: scale the Celsius temperature, then shift it up by 32.
Thus, the correct and scientifically accurate formula is: F=95C+32\boxed{F = \frac{9}{5}C + 32}F=59C+32
