Solving temperature conversion formulas
Solving the temperature conversion formula C = (5/9)(F - 32) for F demonstrates multi-step equation solving with fractions in enVision Algebra 1 Chapter 1 for Grade 11. Starting from C = (5/9)(F - 32), multiply both sides by 9/5 to get (9C)/5 = F - 32, then add 32 to both sides: F = (9C)/5 + 32. At 25°C: F = (9×25)/5 + 32 = 45 + 32 = 77°F. At 0°C (freezing): F = 0 + 32 = 32°F. At 100°C (boiling): F = 180 + 32 = 212°F. This real-world example reinforces solving literal equations for a specified variable.
Key Concepts
The temperature conversion formula $C = \frac{5}{9}(F 32)$ can be solved for $F$ to get: $$F = \frac{9C}{5} + 32$$.
Common Questions
How do you solve C = (5/9)(F - 32) for F?
Multiply both sides by 9/5: (9C)/5 = F - 32. Then add 32 to both sides: F = (9C)/5 + 32.
What is 25°C converted to Fahrenheit?
F = (9 × 25)/5 + 32 = 225/5 + 32 = 45 + 32 = 77°F.
What is 0°C in Fahrenheit and what does this represent?
F = (9 × 0)/5 + 32 = 0 + 32 = 32°F. This is the freezing point of water.
What is 100°C in Fahrenheit?
F = (9 × 100)/5 + 32 = 900/5 + 32 = 180 + 32 = 212°F. This is the boiling point of water.
What algebraic technique is most important for solving this formula?
The inverse operation for the fraction: multiplying both sides by the reciprocal (9/5) to clear (5/9). This is the same technique used for any literal equation with fractional coefficients.