Question

If you know that a < b, and both a and b are positive numbers, then what must be true about the relationship between the opposites of these numbers? Explain.

Answer 1

Answer:

Sample response:

The number further left on a number line is the smaller number. For positive numbers, the number closest to zero is smaller. For negative numbers, the number closest to zero is larger. If a is less than b, and they are both positive, then a is closer to 0 than b. The opposite of a is also closer to zero than the opposite of b, so the opposite of a must be larger than the opposite of b.

Answer 2

If a and b are changed to their opposite numbers -a and -b, the lesser than symbol changes to a greater than sign, and the relationship becomes:

-a > -b

• Given: a and b are both positive numbers and a is less than b, which means a is a number closer to 0.

• In the negative form, the numbers closer to 0 are considered to be greater. For example, -5 > -10.

• Therefore, -a > -b if a and b are negative numbers.