Which statement represents the Laws of Equality?

The statement that "Equals operated on by equals remain equal" encapsulates the Laws of Equality, which are fundamental principles in mathematics. This law asserts that if two values are equal, performing the same operation on both values will maintain that equality.

For example, if you have an equation where ( a = b ), and you add the same number ( c ) to both ( a ) and ( b ), the relationship remains true: ( a + c = b + c ). This principle underlies many mathematical operations and is essential for solving equations and manipulating expressions accurately.

In contrast, the other statements do not accurately reflect the Laws of Equality. The first statement pertains more to the concept of counting or unique elements, while the third implies a restriction on numbers that is not relevant to equality. The fourth statement suggests a lack of relationship between operations across fractions, which does not connect to the principles of equality at all. Thus, the correct answer effectively illustrates one of the core axioms governing equality in mathematics.