# What's smaller than the smallest

**Peter:**If I owe 5 euros, then I owe more than if I only borrowed 3 euros. So -5 must be greater than -3.**Susanne:** But we learned beforehand that debts are not given in negative numbers! Look, if I have -5 euros in my account, I have a lower balance than if I only have -2 euros in my account. Therefore -5 must be less than -2.

**Peter:** Okay, in that case you might be right. But what if it is -10 C? Then it is more cold than at -2 C. Then I'm right again.

**Susanne:** But here, too, it has to be the case that -10 C is a lower temperature than -2 C, right? So -10 should be less than -2 again.

But which of the two is right now? Take a look at the following picture and consider which side is the representation of Peter's opinion and which side is the representation of Susanne's opinion.

**Marianne**into the discussion. She says:

*"You surely won't deny that 4 is less than 5, will you?"*Marianne writes the inequality on the blackboard.

**4 <>**

Then she says: *"If we subtract 3 on both sides, the inequality is still true."*

So she writes on the board:

**1 <>**

*"If we subtract 3 again, this is what comes out."*

**-2 <>**

*"So -2 is definitely less than -1."*

Marianne is right. The order of the negative numbers is exactly the same as that of the positive (and **NOT MIRRORED!**), so **a number (a) that is further to the left on the number line than another number (b) is smaller **(i.e. a <>

** Task:** Download the following file and print out the document. Do the tasks and stick the exercise sheet in your school exercise book.

**So, now you've done quite a bit. You now know the extended number line and the extended coordinate system, you can draw points in it and order negative numbers according to their size. You have already done a large part! :-)**

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