Question

If two rational numbers, aa and bb, are ordered such that aa is less than bb, then what must be true about the order for their opposites: −a and −b?

Answer 1

Explanation:

a is less than b which means

a<b

When we change the numbers to negative what happens is the -b is farther than -a to zero. Now, -b is less than -a. Whether, a number is smaller or larger is determined by the number's distance to zero. If the number is negative the farther the number the smaller it is. If the number is positive the farther the number the larger the number is.

Let us take an example

3<4

Now their opposites are

-4 and -3.

4 3 2 1 0 -1 -2 -3 -4

Now, it can be seen that -4 is farther hence -4 is smaller than -3.