Question bank: Absolute Value and Number Order

During a science expedition, a group of 7th-grade students decides to map an unknown cave, where the temperature is recorded in degrees Celsius. Upon entering the cave, they observe that the temperature outside the cave is 25°C. Walking further inside, the thermometer starts indicating negative temperatures, reaching -5°C. After some time, they return to the cave entrance, where the thermometer reads -2°C. Interested in analyzing the collected data and understanding the temperature variations, the students notice that the internal cave temperatures are always lower than the external temperature and that even when it is cold outside, the cave manages to become even colder. Based on the observation of the collected data and mathematical knowledge, what is the relationship between the absolute value of the internal cave temperatures and the recorded external temperature?

Consider the integers -5, 3, 0, -2, and 7. In a math contest, participants must order these numbers in descending order to identify the largest and smallest absolute values among them. Explain what the absolute value of an integer is and order the provided numbers, highlighting those with the highest and lowest absolute values. Remember that the absolute value of a number is its distance to zero on the number line, regardless of its sign.

Consider the real numbers a, b, and c, such that a = -5, b = 7, and c = -3. Knowing that the absolute value of a real number x is given by |x|, where |x| = x if x >= 0 and |x| = -x if x < 0, determine: 1) The absolute value of the sum of a, b, and c. 2) The ascending order of the numbers a, b, and c. 3) The absolute value of the difference between b and a, followed by the absolute value of the difference between c and a, and finally, the absolute value of the sum of these two differences.

In a study on temperatures, a group of 7th-grade students collected data on the average daily temperature in different cities around the world. To compare the information, they need to sort the temperature values recorded in ascending order, from lowest to highest. The temperatures were recorded in degrees Celsius and range from -10°C to 35°C. Additionally, the students need to calculate the absolute value of the temperatures recorded in two cities that marked the lowest and highest extremes, respectively. Based on this data, what is the absolute value of the lowest recorded temperature and what is the ascending order of the temperatures recorded by the cities?