Final answer:
If a = 4.75 and 4.75 = b, then a = b due to the transitive property of equality. This illustrates a basic concept in algebra that is analogous to the commutative property of addition. It demonstrates the consistency of equality when the same operations are applied to both sides of an equation.
Step-by-step explanation:
The student's question concerns an elementary property of equality and real numbers which states that if two quantities are equal to the same number, they are also equal to each other. This can be represented as if a = 4.75 and 4.75 = b, then by the transitive property of equality, it follows that a = b. This is fundamental in algebra, where we often manipulate equations to solve for unknown variables. Conceptually, it's similar to the commutative property where the order of addition does not affect the sum, e.g., A+B = B+A.
Further, in mathematics, maintaining an equality by performing the same operation on both sides of an equation is crucial. For example, multiplying both sides by the same factor (rule of algebraic manipulation), will yield an equivalent equation. Additionally, any fraction with the same numerator and denominator is equal to 1, showing the consistency of operations performed on both sides of an equation.