Question

Tell which temperature is warmer. \(-35^{\circ} \mathrm{F}\) or \(-25^{\circ} \mathrm{F}\)

Short answer

-25^{\circ} \mathrm{F} is warmer.

Step-by-step solution

- Understand the Number Line

When comparing negative temperatures, it's useful to think of a number line. The further to the right a number is on the number line, the larger (or warmer, in this case) it is.

- Place the Temperatures on the Number Line

Place \(-35^{\circ} \mathrm{F}\) and \(-25^{\circ} \mathrm{F}\) on the number line. \(-35^{\circ} \mathrm{F}\) is to the left of \(-25^{\circ} \mathrm{F}\).

- Compare the Positions

Since \(-25^{\circ} \mathrm{F}\) is to the right of \(-35^{\circ} \mathrm{F}\) on the number line, \(-25^{\circ} \mathrm{F}\) is the warmer temperature.

Key concepts

Number Line

A number line is a simple yet powerful tool to understand numbers and their relationships. Imagine a straight line where numbers are placed at equal intervals.
On a number line moving to the right means increasing value, while moving to the left means decreasing value.
For negative numbers, the closer they are to zero, the larger they are.
Understanding this concept is essential when dealing with negative temperatures. Think of placing the numbers on this line.
This makes it easier to visually grasp which number is greater or smaller. By identifying position, you can easily compare any set of numbers, including temperatures.

Temperature Comparison

When comparing temperatures, especially negative ones, the number line becomes even more crucial.
Temperatures are essentially numbers on this line.
For instance, let’s place \(-35^\circ \mathrm{F}\) and \(-25^\circ \mathrm{F}\) on a number line. Since \(-35^\circ \mathrm{F}\) is further left than \(-25^\circ \mathrm{F}\), it indicates a colder temperature.
In comparison, \(-25^\circ \mathrm{F}\) is to the right on the number line, making it warmer.
Visualizing positions can clarify which temperature is warmer or colder.
Always remember, among negative values, the one closer to zero represents a warmer temperature.

Mathematical Reasoning

Mathematical reasoning involves clear, logical thinking.
For comparing temperatures like \(-35^\circ \mathrm{F}\) and \(-25^\circ \mathrm{F}\), we use the number line and basic principles of numbers.
By reasoning that numbers farther right are greater, we conclude \(-25^\circ \mathrm{F}\) is warmer.
Applying reasoning helps validate our comparison.
Always break down steps: place numbers, visualize, compare positions, and deduce the result.
This approach is effective for any mathematical problem, offering a structured, understandable solution path.