If 2 rational number a and b are ordered such that a is less than b then what must be true about the order for their opposites -a and -b?

If 2 rational number a and b are ordered such that a is less than b then what must be true about the order for their opposites -a and -b?
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a < b→ a - a < b - a→ 0 < b - a→ 0 - b < b - a - b→ -b < -a→ if a < b then -b < -a which can also be expressed as -a> -b
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