And why do negative numbers exist?
EDIT: thank you all so much for answering. I actually understand now. I wish they explained it this simply in school 😭
In: 4
For the negative numbers part of the question:
Let’s say you have a train, and you’re on a very long, straight line of track. Somewhere on the track there is a checkered flag planted next to it that we’ll call the starting flag.
Your train only goes forwards. Say you drive it for 10 kilometers. Then your phone rings. It’s a friend of yours. They’re at the starting flag, and they want to know where you are. So you tell them, “10 km away”. And with that information alone, they will be able to find you. There’s only one place you could be.
But what if your train could also go in *reverse*? There’s track running *behind* the start flag, too. What if you chose to go in reverse for 10 km up the track?
Your friend calls, again asking you where you are. You again answer, “10 km away.” Which is true. But this time, your friend is confused. With only that info, there’s *two* places you could be. There was not enough information in that answer to tell you where you precisely are. You also need to tell them which side of the start flag you are on, either one way or the other.
This is what negative numbers are for. They are just normal numbers, like any other, but they have a little marker next to them — that minus sign — that indicates that, somewhere in the context of the problem, there is an arbitrary line where knowing which side of it you’re on is important, and that this number happens to be “behind” it instead of “in front of” it. In this example, it happened to be tracking the position of a train on a track relative to a flag. If you say you’re “-10 km away”, that can tell someone that you are 10 km away but *behind* the flag.
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