aka “negative fractions have never show’d up in my math classes until today but apparently I’m already supposed to know what they are”
In: 4
What is 2 thirds minus 1 third? Thats a practical example of a negative fraction.
Another would be that -1/2 = -0.5
The easiest way to think about is to put negative fractions on a number line. If 0 is in the middle, positive numbers are to the right and negative numbers are to the left. -1/2 is between 0 and -1 just like how 1/2 is between 0 and 1
A fraction is just a type of number. It may help to think of 2/3 as a *thing in and of itself* in the same way that “2” or “-17” are, not as “two thirds of something”, in this context (and in many others, because that way of thinking about fractions falls apart quickly once you start doing algebra).
In the same way that you can add two numbers, you can add two fractions, because fractions are just numbers. Similarly, in the same way you can subtract, multiply, or divide numbers, you can subtract, multiply, or divide fractions. And you can take their negatives, which has the same meaning for fractions that it does for integers: -1/2 is the number that, if you add it to 1/2, gives you zero, in the same way that -3 is the number that, if you add it to 3, gives you zero.
A negative fraction could be thought of as a fraction of a negative thing.
If you can accept that -2 is a thing, then -2/3 would be a third of that.
You know your left and right, correct? Five years old, you have heard the Hokey Pokey song.
Take one step right. Take one step left. You are back where you started, correct?
Same thing if you take one step left, then one step right. You’re back where you started.
In math, we call left “negative,” we call right “positive,” and we call where you started “zero.”
So translate “negative one-half” in your head to “one half step left.”
Fractions can be added and subtracted just like any other number.
If you and a friend are planning to order three pizzas and eat three-quarters of a pizza each, you can expect to have one-and-a-half pizzas left over afterward (because `3-2*(3/4)=1+(1/2)`). If your friend is planning to take one whole leftover pizza home, that means *you* will be left with half a pizza (because `1+(1/2)-1=(1/2)`). And if you were hoping to eat three-quarters of a pizza again the next evening, that would leave a total of negative one quarter (because `(1/2)-(3/4)=-(1/4)`). In other words, you won’t have enough pizza; better order four pizzas instead.
It’s helpful, for now and for later, to simply think if the negative sign not as an *amount*, but as a *direction*.
A simple example: -$0.50 doesn’t mean “negative fifty cents.” It means you owe someone else $0.50, and thus this fifty cents has a *direction* toward someone else.
This will be a useful idea if you ever use negative numbers in physical science courses (which you probably will). If you travel -2/3 of a mile toward something, youve just gone 2/3 of a mile in the OTHER direction, that is, away from it.
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