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

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

• A. The product is 0
• B. The product is -1
• C. The sum is 1
• D. The sum is -1

Answer: (B)

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.

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.