Final answer:
The average of any two real numbers is always less than or equal to at least one of those numbers because it falls between them on the number line. It is equal to both numbers when they are the same and otherwise it is less than or equal to the larger number and greater than or equal to the smaller number.
Step-by-step explanation:
The question is evaluating the properties of the average of two real numbers. It states that the average of any two real numbers is less than or equal to at least one of the two numbers. To explain: If we have two real numbers, let's call them a and b, their average is (a + b)/2. This average will always be between a and b, inclusive.
Let's consider two cases. First, if a is equal to b, the average equals both of them. Second, if a is not equal to b, one of them must be greater than the average, and the other must be less. This is because the average falls exactly midway between the two numbers on the number line. So, by definition, no number can be smaller than the smallest of the two and no number can be larger than the largest, ensuring the average lies within the range set by a and b.
By comparing this concept with similar logic, when we add fractions like 1/4 and 1/3, since 1/4 is less than 1/2, their sum must be less than 1. Using inequality symbols can be helpful to illustrate these relationships clearly.