Question

Describe the relative locations of the rational numbers -(- a/b ) and a/b on a number line.

a. The rational number - ( - a/b ) is the opposite of the opposite of a/b, so the numbers are the same location on the number line.
b. The rational number - ( - a/b ) is the opposite of the opposite of a/b, so the numbers are on a different location on the number line.

Answer 1

The rational numbers -(- a/b ) and a/b are located at the same point on the number line because the two negative signs cancel each other out, resulting in the same value.

Step-by-step explanation:

The relative locations of the rational numbers -(- a/b ) and a/b on a number line are the same because -(- a/b ) signifies the negation of a negation. Mathematically, when two negative signs are present, they cancel each other out following the multiplication rule that states when two negative numbers multiply, the answer has a positive sign. Therefore, -(- a/b ) equals a/b. Both expressions represent the same point on the number line.

For example, if a/b is 2/3, then -(- a/b ) becomes -(- 2/3 ), which simplifies to 2/3 after the negative signs cancel each other. Both -(- 2/3 ) and 2/3 correspond to the same location on the number line, which is a positive position at two thirds along from zero.