Final answer:
The two division expressions 156 ÷ 24 and 102 ÷ 15, despite having the same quotient and remainder, are not equivalent due to their different dividends and divisors.
Step-by-step explanation:
Even though the division expressions 156 ÷ 24 and 102 ÷ 15 both result in a quotient of 6 with a remainder of 12, they are not equivalent to each other. This is because the dividends (156 and 102) and the divisors (24 and 15) in the two expressions are different. In mathematics, division expressions are considered equivalent if they can be simplified or manipulated algebraically to become the exact same expression.
However, when you look at these two cases, there isn't any algebraic manipulation that can transform one expression into the other exactly. They simply share the coincidence of having the same quotient and remainder when divided.
The truth in mathematics is that while different expressions may sometimes yield similar results, they are not necessarily equivalent unless they can be morphed into one another through legitimate algebraic transformations. Here, the differences in the original numbers mean that despite similar outcomes, the expressions are distinct.