Explain why the Multiplication Property of Equality and the Division Property of Equality can be the same property?

Answer 1

They aren't the same property, they're actually the exact opposite, or inverse of each other.

Mathematically, an operation that "undoes" the effects of another operation is called its inverse, and there are many examples.

Given some number, let's say X, by performing the following two operations successively and in either order, will return the initial value of X

- (addition)(subtraction) for all real numbers

- (multiplication)(division) for all real numbers not = 0

- (squaring)(taking the square root) for all positive real numbers

- (raising a number to the power of X)(taking the logarithm of X in that number's base) for all real numbers greater than 0

So to get to your example specifically, they aren't the same , but they are related. In fact X/Y can be expressed as (X)*(1/Y).

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True.

But what I think the question is about is the property that allows you to multiply both sides of an equation by any constant without affecting the solutions to the equation. In this context, division by any number (other than 0) is equally valid. These two properties are equivalent in the sense that dividing through by any non-zero number x is the same as multiplying through by 1/x.