The rule 'if two ratios are equal, then their reciprocals are also equal' describes which property?

The rule 'if two ratios are equal, then their reciprocals are also equal' describes which property?

• A. Reciprocal property
• B. Transitive property
• C. Commutative property
• D. Cardinality principle

Answer: (A)

This is the reciprocal property: if two ratios are equal, their reciprocals are also equal. When a/b equals c/d with nonzero denominators, taking reciprocals gives b/a and d/c, and these are equal as well. This follows from cross-multiplying to ad = bc and then observing that dividing both sides by abcd leads to b/a = d/c. For example, 2/3 = 4/6, and the reciprocals 3/2 and 6/4 are equal. This idea is not about chaining equalities (transitive property), swapping order in addition or multiplication (commutative property), or counting elements (cardinality).

This is the reciprocal property: if two ratios are equal, their reciprocals are also equal. When a/b equals c/d with nonzero denominators, taking reciprocals gives b/a and d/c, and these are equal as well. This follows from cross-multiplying to ad = bc and then observing that dividing both sides by abcd leads to b/a = d/c. For example, 2/3 = 4/6, and the reciprocals 3/2 and 6/4 are equal. This idea is not about chaining equalities (transitive property), swapping order in addition or multiplication (commutative property), or counting elements (cardinality).