Problem 77 - Fundamentals of Mathematics

Question

The lowest temperature on record in Concord, New Hampshire in May is \(21^{\circ} \mathrm{F}\), and in July it is \(35^{\circ} \mathrm{F}\). What is the difference in these lowest temperatures?

Step-by-Step Solution

Answer

The difference is \(14^{\circ} \mathrm{F}\).

Step 1: Identify the Temperatures

Extract the given temperatures from the problem. The lowest temperature in May is \(21^{\circ} \mathrm{F}\) and in July is \(35^{\circ} \mathrm{F}\).

Step 2: Calculate the Difference

Subtract the lower temperature in May from the higher temperature in July to find the difference: \[ 35^{\circ} \mathrm{F} - 21^{\circ} \mathrm{F} = 14^{\circ} \mathrm{F} \]

Step 3: Interpret the Result

The result \(14^{\circ} \mathrm{F}\) represents the difference in the lowest recorded temperatures between May and July.

Key Concepts

Temperature Conversion

Understanding temperature conversion is vital when dealing with different units like Fahrenheit and Celsius. Here, we are focused on Fahrenheit, but let’s quickly explore how you would convert between these and why it could be relevant.
To convert from Fahrenheit to Celsius, use the formula: \[ C = \frac{5}{9} \times (F - 32) \] This formula helps in understanding temperatures in a different scale often preferred in scientific contexts. For instance, converting our temperatures: - May's minimum: \[ C = \frac{5}{9} \times (21 - 32) = \frac{5}{9} \times (-11) \approx -6.1^{\circ}C \] - July's minimum: \[ C = \frac{5}{9} \times (35 - 32) = \frac{5}{9} \times 3 \approx 1.7^{\circ}C \] By converting, one would see these are generally warmer end of temperatures compared to some global cooler regions. Knowing how to switch between systems can help students understand different data reports they might encounter, especially in a global context.

Basic Arithmetic Operations

Being proficient with basic arithmetic operations is crucial as these operations form the foundation for solving many problems.
Consider our exercise which requires subtraction to find the difference between two temperatures:

• The operation is straightforward: start with the higher number, which in this case is 35.
• Subtract the lower number, 21, from it.
• This gives us: \[ 35 - 21 = 14 \]

It's important to always align numbers by their place value in subtraction, ensuring accuracy in our calculations. Processes like this help us understand differences that appear in various contexts, such as seeing the change in weather that happens between months.

Interpretation of Results

Interpretation of results is the final and often most important step in any calculation. In our example, the difference of \( 14^{\circ} \mathrm{F} \) between May and July informs us about temperature changes during this period.

• A 14-degree difference might indicate major climatic shifts or changes, possibly due to seasonal changes from spring to summer.
• Understanding such results can influence decisions in fields like agriculture, tourism, and even retail.

Interpreting results correctly ensures that numbers translate to meaningful knowledge. This is crucial as it dictates the practical application of numerical findings in real-world scenarios. Remember, the numbers tell a story only when understood in the right context.