What does it mean for two numbers to be negative reciprocals?

Two numbers are considered negative reciprocals of one another if their product is equal to -1. This relationship occurs when one number is the negative inverse of the other. For instance, if you take a number, say ( a ), its reciprocal is expressed as ( \frac{1}{a} ), and its negative reciprocal is thus ( -\frac{1}{a} ).

To confirm that they are negative reciprocals, if you multiply ( a ) and ( -\frac{1}{a} ), the calculation would be: [ a \times -\frac{1}{a} = -1 ] This indicates that the two numbers are indeed negative reciprocals. Therefore, the correct understanding of negative reciprocals centers around the product being equal to -1, signifying their distinct yet intertwined relationships in mathematics.