Problem 144 - Prealgebra and Introductory Algebra

Question

Find the temperature after a rise of \(9^{\circ} \mathrm{C}\) from \(-6^{\circ} \mathrm{C}\)

Step-by-Step Solution

Answer

The temperature after the rise is \(3^{\circ}\mathrm{C}\).

Step 1: Identify the temperatures to be added

Here, the initial temperature is \(-6^{\circ}\mathrm{C}\) and the temperature rise is \(9^{\circ}\mathrm{C}\). So, the task is to find \(-6^{\circ}\mathrm{C} + 9^{\circ}\mathrm{C}\).

Step 2: Add up the temperatures

Perform the addition operation: \(-6 + 9 = 3\). The unit of the answer is in \(\mathrm{C}\), as we are dealing with temperatures recorded in degree Celsius.

Key Concepts

Degree Celsius

The degree Celsius (), symbolized as is a unit of temperature named after the Swedish astronomer Anders Celsius. It's one of the most commonly used temperature scales in the world and is used to gauge the temperature of various substances including the weather, in cooking, and for many scientific purposes.

It's important to understand that the Celsius scale is a relative scale set between the freezing and boiling points of water at standard atmospheric pressure, with 0 representing the freezing point and 100 the boiling point. When temperatures are noted in degrees Celsius, sub-zero values represent temperatures below the freezing point of water. For example, a temperature like 6 suggest colder conditions than would be felt at 0.

Basic Addition

Basic addition is one of the fundamental operations in arithmetic. It is the process of combining two or more numbers to get a new total value. When adding integers, there are a couple of simple rules to follow, especially with positive and negative values. If numbers have the same sign (both positive or both negative), you add their absolute values, and keep the sign. If they have different signs, you subtract the smaller absolute value from the larger one, and take the sign of the number with the larger absolute value.

For instance, when you have 6 and 9, imagine you owe six apples (6) and then you get nine apples (9), the result is having three apples overall (3). Addition is commutative, meaning that the order of numbers doesn't change the result; so, 9 + (6) will also be 3.

Temperature Change

Temperature change refers to the difference in temperature between two states. Recognizing temperature change is crucial when considering the effects on the environment, substances, or reactions. A rise in temperature is indicated by a positive number (), whereas a fall in temperature is shown by a negative number ().

When calculating temperature change, it's as simple as performing basic addition with the value of the initial temperature and the amount of change. If a substance at 6, experiences a temperature increase of 9, the calculation performed would be 6 + 9, resulting in a temperature of 3. This arithmetic operation is akin to how we might adjust a thermostat or gauge the warming or cooling of a room.